Year: 2021


  • 5 NBA Thoughts [#2]

    5 NBA Thoughts [#2]

    (? The Ringer)

    Inspired by the likes of Sports IllustratedSB Nation, and Thinking Basketball among countless others, I’m continuing here a “5 Thoughts” series. Watching and studying the NBA means there’s a constant jumble of basketball thoughts in my head. However, I rarely touch on them in detailed articles or videos, so that’s where this series comes in: a rough, sporadic overview of five thoughts on the NBA!

    1. Bradley Beal and the OPOY

    During a live chat discussion on Halftime Hoops, a surging topic was whether the league should implement an Offensive Player of the Year (OPOY) Award to counterbalance the defense-only counterpart. A contribution to the topic was that the OPOY Award would too closely resemble the scoring title leaderboard, stating players like Bradley Beal and Stephen Curry will inevitably win because of their scoring, so why bother creating a new award to recognize a pool we’re already aware of?

    The voter tendencies could support this claim; in other words, the patterns of the voters suggest scoring is the largest factor in offensive evaluation, so in a practical sense, the opinion makes sense. To me, the more pressing question here is what that says about voter criteria and how it influences the public eye in general. There’s always been a misstep in how offense is treated: teams win games by scoring more points, so the highest-volume scorers are often the best offensive players. The poor connection is here the exclusion of other skills; namely, shot creation, passing, screening, cutting, floor-spacing, and all the crucial qualities that go into building a high-level offensive team.

    Bradley Beal isn’t in the conversation as a top-5 offensive player in the league to me, and while that’s mainly in part to a lack of eliteness in multiple areas that would bolster his overall value on offense, his scoring doesn’t pop out as much to me as it does other. Efficiency is generally treated as a luxury piece, and that volume scorers with “good enough” efficiency (within a reasonable range of league-average) shouldn’t be penalized. However, an argument could be made to flip the script entirely: efficiency may be equally, if not more, important than volume.

    Beal is currently fourth in the league in scoring rate, clocking in at 30.3 points per 75 possessions. (That also brings up the issue with the scoring title being assigned to the points-per-game leader: it erroneously assigns credit to high-minute players on fast-paced teams.) Thus, there are too many hindrances in placing a heavy amount of stock in how many points a player scores each game. System design, quality of teammates, the plethora of other skills that amplify a team’s offense: all evidence points toward an OPOY Award being an entirely separate entity from the scoring title.

    2. Making teammates better is a myth

    Raise your hand If you’ve ever seen someone argue on behalf of one player over another because “he makes his teammates better.” (If you aren’t raising your hand right now, I’d be very surprised.) High-quality facilitators are often treated in this fashion, and the cause for belief isn’t way off track: When elite shot creators and passers are setting up teammates for open field goals that would’ve otherwise been contested, the teammate’s shooting percentages will increase. Thus, the illusion that a player can make his teammates better was inspired.

    The problem with this idea is that it treats a player’s “goodness” as dependent on who’s on the floor with him. If an elite spot-up shooter is paired with an all-time black hole like Stephen Curry, the openness frequency of his shots will likely increase. Conversely, if he were playing alongside someone antithetical to this style like Elfrid Payton, his shooting efficiency would probably go down. The big question here is whether the increase in scoring efficacy should be attributed to the shooter or the playmaker. To me, the answer is fairly simple given how complex most of these problems can be.

    The teammate’s shooting in a vacuum is unaffected by his teammates. Namely, regardless of lineup combinations and synergies, the true skill of his shooting remains constant. A three-point specialist doesn’t go from a 40% to a 45% shooter overnight because he’s going to start playing with better teammates. Therefore, a “better” interpretation of these shooting improvements is that the playmaker is bettering the team’s shot selection (per-possession efficiency), but he’s not bettering the teammate’s shooting skill. This case applies to every other skill that creates a similar illusion.

    3. Rim protection vs. perimeter defense

    After spending a good amount of time in the aforementioned Halftime live chat rooms, it’s become increasingly clear that a large chunk of NBA fanatics may solely focus on man defense when evaluating this side of the ball. This directly parallels the strong focus on isolation scoring when the general public evaluates offensive skill. Just as we discussed in the first thought, these types of approaches can be extremely limiting and leave out a lot of information and skills that go toward building strong team defenses. This creates an ongoing conflict between weighing the value of rim protection and general “perimeter” defense, so which one is better?

    A recurring theme that has followed with basketball analysis’s anti-education culture is the tendency to try and solve complex problems with the simplest solutions possible. (This led to the original reliance on the box-and-record MVP approach.) So when defensive skills outside of isolation defense and shot-blocking are brought up, they might be met with some reluctance. The opposing style will be used here: the most important piece of the premise here is that rim protection isn’t just limited to shot-blocking ability, as perimeter defense would be to “locking up” an opponent’s best perimeter player. The cause-and-effect relationships these skills have on the totality of defensive possessions can be much stronger than meets the eye.

    Strong rim protectors in the paint can drastically alter game-planning against the opposition, meaning an increased focus on a perimeter attack can deter a large number of field-goal attempts at the rim, thus taking away the sport’s (generally) most efficient shots. Similarly, perimeter defense doesn’t just refer to a player’s one-on-one defense. How do they guard the pick-and-roll? How do they maneuver around screens (and perhaps more importantly, ball screens)? Do they make strong rotations and anticipate ball movement well or is there some hesitation? (These are just a few examples. As stated earlier, the sport is much too complex to be solved through an ensemble of steals and blocks.)

    The simple answer is that it depends. A lot of people will say rim protection is generally more valuable, and in a broader sense, I would agree. The (generally) most efficient shots are taken in the paint, so to either contest, deflect, or deter these shots would certainly seem to have a greater positive effect on the team’s overall defensive performance. However, as the “truer” answer suggests, most of that value is dependent on the context of the game. During the Playoffs, we have seen a league-wide trend of non-versatile centers losing a certain degree of impact against certain postseason opponents. (I’ve discussed this a lot in recent weeks.) Versus great-shooting teams with a strong midrange arsenal, perimeter defenders will likely see an increase in value: defending some of the league’s best floor-raising offense (open midrange shots from elite midrange shooters) will put a cap on the opposition’s offensive ceiling.

    A total discussion wouldn’t even come close to ending here, but with this brief overview paired with other in-depth analysis, there are pretty clear indicators that rim protection will often be more valuable than perimeter defense. This explains why players like Rudy Gobert and Myles Turner will generally be viewed as stronger positive-impact defenders than ones like Ben Simmons and Marcus Smart. However, with the increasing rise in outside shooting efficacy and offensive development, defensive versatility ranging from multiple areas on the court may become more valuable than either of them.

    4. Building an RAPM prior

    Regularized Adjusted Plus/Minus is an all-in-one metric that estimates the effect of a player’s presence on his team’s point differential. I’ve written about the calculations behind RAPM before, but a topic I’ve never covered in-depth is how “priors” are constructed. For those unfamiliar with these processes, RAPM uses a ridge regression (a form of Tikhonov regularization) that reduces the variability among possible APM values, regressing scores toward average to minimize the higher variance in “regular” Adjusted Plus/Minus. A “prior” is used in place of an average (net-zero) to pair with pure APM calculations.

    Priors are often referred to as “Bayesian priors” because they align with the philosophy in Bayesian statistics that encourage pairing the approximations of unknown parameters with outside information known to hold value in the holistic solutions of these problems. The basketball equivalent to this would usually see APM regress toward the box score and past results, among others. Current examples include Real Plus/Minus, which regresses toward the box score. BBall-Index‘s LEBRON regresses toward PIPM’s box component. Estimated Plus/Minus regresses toward an RAPM estimator that uses the box score and tracking data (which the NBA started to track league-wide in the 2013-14 season).

    The composition of these priors has stood out to me, and during my research for an upcoming video podcast on ranking impact metrics, it become apparent the use of on-off ratings was often a significant hindrance to a metric’s quality. It’s long been clear the extreme variability of on-off data could limit a metric’s descriptive power in smaller samples because of its lack of adjusting for hot streaks, lineup combinations, and minute staggerings. These confounding variables can make an MVP-level player appear to be nothing more than a rotational piece, and vice versa. Because there’s simply too much on-off data doesn’t account for, even as the skill curves begin to smooth, it’s probably on a downward trajectory in its usage among modern impact metrics.

    Conversely, the more promising form of statistics seems to be tracking data. Although most of these stats weren’t tracked prior to the 2014 season, there’s a good amount of non-box data from resources like PBPStats, which could help in creating a prior-informed RAPM model that extends back to the beginning of the twenty-first century. These types of stats are estimated to have the least dependence on team circumstances among the “big” three that includes box scores and on-off ratings, which gives tracking data an inherent advantage. During his retrodiction testings of several high-quality NBA impact metrics, Taylor Snarr (creator of EPM) found evidence to suggest this pattern, and although this phenomenon hasn’t quite yet hit the mainstream, I expect the next generation of advanced stats is powered by tracking data.

    5. The statistical evaluation of defense

    Compared to the offensive side of the game, defense has always been a bit of a black box. It’s much harder to evaluate and even harder to quantify. (When the DPOY Award was instituted in the early 1980s, Magic Johnson would receive a good share of votes.) This is an even larger problem given the limitations of the current box score, which only extends to defensive rebounds, steals, blocks, and personal fouls. The majority of attentive NBA watchers knows the box score doesn’t track a lot of defensive information, so what statistical methods can be used to evaluate defense?

    One of the up-and-coming statistics in recent years has been opponent field-goal percentage; the proportion of defended field-goal attempts that were made. These marks are seen as especially useful by a community that mostly considers isolation defense; but as a measure of the quality of contests alone, these stats are often misused. Some will say a defender played exceptionally well against LeBron James because, in the two’s interactions, James made two of seven shots. (“Therefore, Andre Iguodala is the Finals MVP,” if you catch my drift.) Not only are these measures not a definitive representation of how well a defender contested a player’s shots (location and team positioning are big factors that affect these stats), but small samples are perennially mistreated.

    Anyone with some familiarity with statistical analysis knows the variability of a sampling distribution very often goes down as the sample size increases. (The common benchmark is n = 30 to satisfy a “Normal” condition for some types of stat tests.) Thus, when Kevin Durant shoots 21% on 12 attempts in a game versus Alex Caruso, it doesn’t mean Alex Caruso is therefore Kevin Durant’s kryptonite. The variability of opponent field-goal percentage, the lack of context surrounding the conditions of a field-goal attempt, and the infrequent instances in which they occur create a statistic that’s easy to abuse. If there should be one major takeaway from this post, it would be to KNOW AND UNDERSTAND YOUR DATA.

    Unfortunately, a lot of lower-variation and more descriptive defensive stats (defended FG% doesn’t confirm a cause-and-effect relationship) aren’t readily available to the public, but it’s worth noting some of the advancements in the subject. A more common statistic might be deflections, charges drawn, or total offensive fouls drawn (the latter two paired with steals created total forced turnovers). However, the most exemplary case of defensive measuring I’ve seen is through BBall-Index, whose data package comes with a multitude of high-quality defensive statistics, including box-out rates. rebounding “success rate,” loose ball recovery rate, rim deterrence, matchup data, among countless others. Seriously, if you’re looking to take your defensive statistical analysis up a notch, it’s the real deal.

    Impact metrics will always provide their two cents with their one-number estimates, and for the most part, they’ll be pretty good ballparking values. But intensive film studies (the building blocks for evaluating defense) may need to be paired with descriptive, intelligible defensive statistics to enhance the quality of analysis. This doesn’t make defense any easier to evaluate than offense, but relative to the alternative (steals + blocks), it’s a whole lot better.

    How important are skills like volume scoring and isolation defense? Are the right players credited with individual statistical increases? And how are the futures of RAPM and defensive measurements coming into play right? Leave your thoughts in the comments.


  • 5 NBA Thoughts [#1]

    5 NBA Thoughts [#1]

    (? The Ringer)

    Inspired by the likes of Sports IllustratedSB Nation, and Thinking Basketball among countless others, I’m introducing here a “5 Thoughts” series. Watching and studying the NBA means there’s a constant jumble of basketball thoughts in my head. However, I rarely touch on them in detailed articles or videos, so that’s where this series comes in: a rough, sporadic overview of five thoughts on the NBA!

    1. Curry’s offense vs. Jokic’s offense

    At this point, it’s safe to say the league’s two-best offensive players are Steph Curry and Nikola Jokic. But between the two, who’s better? The Playoffs will inevitably shed more light on this (while our knowledge of their postseason performances in the past is a positive indicator for Jokic), but with Jokic’s ascension, we may have enough to decipher a good amount of their skillsets.

    Curry functions in a high-movement offense that largely relies on finding him and open shot. That’s done primarily through Curry’s dynamic movement off the ball, darting through screens and coming up on pin downs, eventually culminating in an open jumper behind a ball screen. This style of offensive play may be considered a bit high-maintenance, but the potential it has to unclog other areas on the court (namely, the paint) is astronomical. Curry’s gravity was the main catalyst for a lot of Kevin Durant’s scoring bursts during the Playoffs, and that makes Curry one of the most adaptable offensive stars in the history of the game.

    Jokic is a passing savant with an off-ball repertoire of his own. His elbow game is perfectly designed for another style of high-activity offense. Rather than a long series of screening action, Denver uses an elaborate design of cutting to either unclog the paint or the corners, AKA prime real estate for Jokic’s passes and assists. The Nuggets’ offensive attack is so deadly in the half-court because of how distracting their cutters are. Defenses either collapse into the paint (leaving the main in the corner open) or maintain space (spacing out the paint). Pair that with Jokic’s midrange shooting, and you have the most electrifying team offenses in the game today.

    So which offensive game is better? Mentally projecting the Playoffs, I expect Jokic will be harder to gameplan against with his ability to pass out of traps inside the three-point line. (And those outlet passes are so phenomenal, half-court offense could be a contingency at times.) I don’t see Curry as poor in this regard, but his height definitely caps the ceiling in these types of possessions. I think they both fit alongside other star talents really, really well. I see Curry as the more “scalable” player considering Jokic’s defensive shortcomings and the increased difficulty in building a championship-level defense around a neutral-impact center.

    It’ll be extremely difficult to choose between Curry’s historical scoring and gravity and Jokic’s enigmatic passing and well-roundedness. I couldn’t sell myself on either one of them at this stage, but given out previous knowledge relating to their Playoffs adaptations, my have-to-make-a pick is Jokic.

    2. Is Harden being exposed in Brooklyn?

    I recently got around to eyeing Harden’s stint with the Brooklyn Nets, and one overarching thought put some concerns in my mind. During his day with the Rockets, he mastered spread pick-and-roll. He could create a ton of offense out of these spots with his stepback jumper, strength and finishing, and high-level passing and kick-outs, and this served as the primary source for his impact on offense. Now, if the last few seasons have taught us anything about Harden, a major sticking point has been that he provides nothing without the ball in his hands, and that may be a problem in Brooklyn.

    Because Harden absolved a decent amount of Durant’s and Kyrie Irving’s touches upon his arrival (refer to this graphic I made for a previous article on the Nets), his value in composite metrics and the box score seems fairly comparable to his level of play in Houston.

    A downward rate of change in their situational value for all three offensive stars is expected, but I wonder if there’s more cause for worry in the Playoffs. This is clearly a Harden-led offense, but his main offensive sets seem to have lost their big bite. Relative to his spread pick-and-roll possessions in Houston that I’ve watched this season, the Brooklyn counterparts seem like a notable downgrade. His handle has loosened and more point-of-attack defenders are poking the ball loose, fizzling out a lot of the action, and the aim and speed on his passes seem to have lost their touch. This may be a sampling issue, but the degree to which these plays declined seemed significant.

    As I let this thought simmer in my head for a while, I began to wonder if this was a game flow problem. With the Rockets, Harden could essentially call for these isolation possessions at will. But with the Nets, he has to concede a lot of those opportunities to Durant and Irving, which led me to believe the halt in constant ball-pounding left Harden in a bit of a funk. Does Harden absolutely need the ball in his hands throughout the game to exhibit his world-class value? Perhaps so, and perhaps not. Either way, this would indicate a really low ceiling on Harden’s fit alongside other perimeter isolationists.

    3. Are the Knicks legit?

    The New York Knicks have made one of the most sudden and unexpected team improvements in recent history. A season removed from a woeful -6.72 SRS and a seventh consecutive Playoff miss, they’ve made the astronomical leap to +1.90 through their 67th game of the season, very likely snapping their Playoff drought. (They did it for you, little Cody.)

    The 2021 season has been filled with unprecedented levels of confoundment (a trend that’s carried over from the 2020 bubble), and it’s made it a lot harder to separate lucky stints from tangible improvement. To me, that’s the biggest question with the Knicks. Are they a mere product of luck combined with a mild talent boost or one of the most improved teams in recent history?

    At this stage, it’s clear New York is thriving because of its team defense. At the time of this writing, their -1.5 relative Offensive Rating sits twentieth while their -3.7 relative Defensive Rating currently ranks as the fourth-best mark in the NBA. Because scoring and allowing points determine the winners of the games, the causal variables behind these ratings are crucial to simplifying the aforementioned “luck versus improvement” problem. The largest components of this will involve opponent free-throw shooting (as that’s something a team defense has no control over) and three-point shooting: the golden standard for noisy stats. To put this into perspective, take this quote from a Nylon Calculus study four years ago:

    “Let me begin this with some research background: open 3-point percentage is virtually all noise, and open three’s consist of a huge portion of the 3-pointers teams allow. There’s no pattern to individual 3-point percentage defense either — it’s noise too . Ken Pomeroy found that defenses had little control over opponent 3-pointer percentage in the NCAA as well.”

    From an intuitive perspective, this makes sense, especially on open three-point attempts. At that point, with no defender to dilute the quality of the shot, whether or not the shot is made is determined by the staggering variance in the bodily mechanics of the shot, which is influenced by factors almost entirely outside of the defense’s scope. Thus, these types of statistics will be used to ballpark the difference between shooting luck and systematic upgrades in the Knicks’ hardware.

    After looking at New York’s current statistical profile, I figured a lot of the data could be reasonably interpreted as noise. Last season, the Knicks shot 33.7% from three, ranking 27th in the whole league. That number has made the seemingly unparalleled jump to 39%, the fifth-best three-point percentage in the league. At the player level, there are a few data points that stood out in how drastic three-point percentage improvements were:

    • Julius Randle: 27.7% in 2020 | 41.7% in 2021
    • RJ Barrett: 32.0% in 2020 | 39.9% in 2021
    • Derrick Rose: 30.6% in 2020 | 38.3% in 2021
    • Kevin Knox: 32.7% in 2020 | 39.3% in 2021

    The Julius Randle uptick is the most prominent, not only because it was the largest change among moderate-volume shooters, but because he’s taken an extra 1.4 three-point attempts every 75 possessions compared to last season. Not only that, but BBall-Index‘s perimeter shooting data suggests Randle is taking pretty difficult shots (the 7th percentile in openness rating and the 2nd percentile in three-point shot quality). This is certainly good news for Randle and his MIP case, but it makes our questions about the Knicks even more difficult to answer.

    An even larger sticking point for me was how efficient their opponents were from three-point range. At the moment, this stands at 33.7%, good for the best opponent three-point percentage in the league. I like to use a ballparking tool in these types of scenarios by replacing the number of points the team limited in reality with a league-average result. So, for example, the Knicks’ opponents have shot 36.9 three-point attempts per 100 possessions at 33.9%, which means opponents generated 37.5 points every 100 possession from their perimeter shooting. A league-average percentage would have generated 40.6 points from these attempts in the allotted period.

    Namely, if the Knicks’ opponents were average three-point shooters, their new defensive rating would suggest they allow 111.7 points per 100, which would not be too far off from last season and would make the Knicks a net-negative team. If we use the same technique for their offense to estimate the effects of shooting luck (especially in this fan-free, short-schedule environment that’s seen a major spike in offensive efficacy), their new offensive rating would fall to 108.7. Using this stricter method, the Knicks would be a -3 team. I don’t think they’re quite that poor. There are positive signals for offensive shooting improvement and the defensive mind of Tom Thibodeau has really helped this team. But if I had to give my best guess, the Knicks are roughly an average team in 2021.

    4. The potential of Box Plus/Minus

    Box Plus/Minus (BPM) is perhaps the most popular plus-minus metric on the market aside from Plus/Minus itself. You don’t need to know anything about the metric other than its name to infer it’s calculated with the box score alone. Interestingly enough, a public that often doesn’t extend its thinking outside the box score will often criticize BPM for only using the box score. And that’s what I’ll discuss today, the “potential” of Box Plus/Minus.

    I’ve recently propagated the truest value from impact metrics comes from their ability to help us understand not necessarily who impacts the game most, but how much varying qualities of players can impact the game. BPM serves that purpose as well as any other one-number metric, but with an extra kick. Since BPM relies on counting stats alone, some of which quantify levels of skill, we can break down a player’s statistical profile to see which tendencies make up the bulk of his impact. More recent studies include Ben Taylor’s creations of ScoreVal and PlayVal, which estimate the plus-minus impact of scoring and playmaking as components of the Backpicks Box Plus/Minus model. Hybrid and APM metrics, which blend plus-minus data directly into the equation, can’t provide these types of analysis, giving BPM a grounded place among the major impact metrics.

    This is even more useful in career forecastings. While other impact metrics could use some type of role archetype extrapolated from its datasets or age to project careers, BPM allows for a much more granulated skills approach. For example, the Backpicks model uses shot creation and passing ability and teammate spacing and all other kinds of estimates based on the box score to help better the descriptive and predictive powers of the box-only metrics. So while some may see Box Plus/Minus as a dying art form, you could argue it’s actually ascending to its peak right now.

    5. A major analytics misconception

    For every analytical mind, there are five contrarians to oppose them. For the most part (emphasis on “the most part”), these oppositions don’t really know what they’re fighting against other than some vague advancement of NBA statistics. Due to this lopsided ignorance, there stem a lot of misconceptions as to how an analytical supporter interprets and use advanced stats.

    My experience conversing with the anti-analytics crowd has led me to believe they believe an analytical person will treat advanced stats as gospel, and that film study is some type of basketball sin that defies the analytics movement. The truth is really the exact opposite. Anyone who claims they can passively watch a game and then understand everything about it is overestimating themselves. It’s a simple function of cognition; we can neither track nor understand every single thing that’s happening on the court with our eyes alone. That’s where analytics comes in. (Because, honestly, if there weren’t a purpose for them, no one would have bothered to create advanced stats!)

    And that’s what I would like the major takeaway here to be. As someone who identifies as an analytics supporter, I can advocate on behalf of “us” and say the public eye is mostly wrong. Advanced stats aren’t treated as gospel. They’re estimates with varying error rates. Sometimes, advanced stats don’t capture players well at all! That’s why the fluidity of analytics and film is the actual driving force behind the analytics movement. As is with any other field, change causes pushback, and not everyone will be willing to evolve. But that’s the whole point of analytics, of advanced stats. They’re advancements.

    Who’s the better offensive player between Steph Curry and Nikola Jokic? Is Harden not serving the purpose in Brooklyn we’d all thought he would? Are the Knicks what their record says they are? Is Box Plus/Minus a dying breed? And how do analytical minds interpret advanced stats? Leave your thoughts in the comments.


  • Modeling NBA Scoring Proficiency

    Modeling NBA Scoring Proficiency

    (? The Ringer)

    The concept that diminishing returns on efficiency accompany an increase in scoring attempts has long existed, yet very few public models are available to showcase this. Recently, I tinkered with data from Basketball-Reference to estimate the effects of the context of a player’s shot selection with his shooting efficiency to create a few new statistics to help move the needle in quantifying these alternate approaches to “scoring proficiency.”

    The Goal

    With this project, I had one overarching goal in mind: to estimate the number of points a player scored “over expectation” based on the distances of his field-goal attempts, whether or not the shot was assisted (i.e. whether or not he is “creating” his own shots), and how often he shoots. This would hopefully take out some of the noise in pure rate stats like Effective Field-Goal Percentage and True Shooting to identify the most “proficient” scorers based on the context of his shooting attempts.

    The Method

    The first step in calculating this “Points Over Expectation” statistic is looking at how far away a player’s field-goal attempts were from the hoop. Using BBR as the data source, this split the court into seven different zones:

    • 0-3 feet from basket.
    • 3-10 feet from basket.
    • 10-16 feet from basket.
    • 16 feet from basket to 3P line.
    • Above-the-break 3P.
    • Corner 3P.
    • Heaves.

    The first building block to measuring scoring proficiency is comparing a given player’s efficiency and volume in these zones to league-average expectations and estimating a “Points Above Average” of sorts. For example, Luka Doncic has taken 215 attempts (through 4/21) within three feet of the hoop and made them at a 70.7% rate, which is slightly over 3% better than league-average; so based on the volume of his attempts, he “added” an estimated 14 points from this range. The process is repeated for all seven ranges, looking at how often and how efficient a player is from different zones on the court and comparing them to the expected output of an “average” player.

    To add some additional context to a player’s shot selection and produce more accurate results, there are two regressions incorporated here:

    • Efficiency based on how frequently a player’s field goals are assisted.
    • Efficiency based on how often a player shoots from the field.

    The firstmost regression occurs first, which looks at league-wide trends that estimate how efficiently a player will score based on how much help he would receive from his teammates. The results showed a significant positive trend between the two statistics. Namely, the more a player’s field goals are assisted, the more efficient he’s expected to score. The “PAA” results are adjusted to this context accordingly.

    The second regression is incorporated next. This repeats the same process for “shooting help,” but instead looks at location-adjusted efficiency compared to shooting volume, measured in total field-goal attempts. The results from this also showed a distinct negative relationship between efficiency and volume; the more a player shoots, the less efficient he’ll become. The results from the previous regression are then fitted to these data points.

    The Results

    I calculated the scores for every NBA player in the 2021 season through April 21st, the spreadsheet to which can be found here. First glancing at the scores for 2021, the player who immediately popped up was Luka Doncic leading the NBA with 285.3 “Points Over Expectation.” He’s certainly not the best scorer in the league, so what’s going on here? The approach this model takes love how often Doncic creates his own attempts; 16% of his field goals were the products of assists. He also shoots the ball a lot, then standing fifth among all players in field-goal attempts.

    Because of how the model works, the results will be slanted towards certain playstyles that demand the following:

    • Players who receive little “help.”
    • Players who shoot a lot.

    This confounds results for two big reasons: 1) The regressions used to model “luck” aren’t perfect measurements; in other words, there will be some level of variance with how players are rewarded or not depending on the adjustment factors the model uses. 2) Not all shot profiles are created equally. This means different players would, over thousands and thousands of chances, see varying changes in their efficiency based on help and volume. The above regressions use a “best fit” to estimate this change, but this means there will sometimes be large errors or outliers.

    The major takeaway here is that these results are mere estimates of a player’s scoring proficiency, not definitive measures. Because a heap of evidence shows Luka Doncic isn’t the NBA’s best scorer, we know we can treat his datapoint as the product of an error based on the calculations of the model.

    Discussion

    Although the primary goal of this project was the “POE” statistic, there were some other neat results that could be produced based on the data going into the calculations. To the right of the POE column in the spreadsheet is a column labeled “cFG%”, which stands for “creation-adjusted Effective Field-Goal %.” This simply converts POE to a rate stat (adjusted efficiency per shot) and converts it to an eFG% scale, meaning the league-average cFG% will always be set to the league-average eFG%. This acts as a brief perspective on adjusted efficiency on a more familiar scale, but one that gives some more leniency to lower-volume scorers.

    To the right of that is “xFG%,” which stands for “expected Effective Field-Goal %.” Because a player’s shot profile was the driver behind the main metric, the locations could also be used to determine how efficient a player is “expected” to be based on where he shoots the ball. This counterpart doesn’t look at the proportion of shots that are assisted or shooting volume, instead being based purely on location.

    So does this stat really measure the best scoring in the league? Of course not. There are a few kinks that can’t be shaken out; but for the most part, I hope this acts as a comprehensive and accessible measure to look at the effect of a player’s shot profile on how efficiently he scores, and how this influences the landscape of current NBA scoring.


  • The NBA MVP Voter Criteria is Deeply Flawed (Opinion Piece)

    The NBA MVP Voter Criteria is Deeply Flawed (Opinion Piece)

    (? Business Insider)

    Recently, I’ve scoured the internet for a clear and qualified description of what constitutes the definition of the NBA’s MVP Award, and unfortunately, these attempts have been fruitless. Perhaps this was done intentionally so that the ideas behind “value” could extend beyond thinking in the mass, but that still doesn’t stop people front searching for a universal criterion that can act as a “correct” interpretation of the “most valuable” player. However, in these efforts, there seems to be a widespread misunderstanding of what makes a player valuable. This post is admittedly and entirely an opinion piece, so while none of these ideas go without saying, I also won’t say the current state of the MVP voting rationale is without brokenness and deep flaw, and this is why.

    Current Voter Tendencies

    As discussed by a multitude of blogs, podcasts, and video before this, there are three main factors that go into how the voters will generally approach casting their MVP ballots:

    • Team success
    • Individual statistics
    • Narratives

    As evident from talk shows like ESPN‘s “First Take,” it’s not uncommon to see the “best player on the best team” notion thrown around. Namely, some will say the MVP is the best player on the best team; and from what I can gather, it’s because the “best” player on the “best” team is supposedly impacting the ability to win at the highest level. While I’m diametrically opposed to this idea, and I’ll explain why later, it’s an undeniable factor in media voting.

    Aside from knowing which teams are really good (which, in this case, takes a quick glance at the standings and nothing else), there also has to be some way to recognize the “best” players on those teams. This is where the box score comes in. While traditional box score statistics seem to be the most telling indicators of MVP winners (the historical MVP results that fueled Basketball-Reference‘s MVP tracking model found that points, rebounds, and assists per game were three of the four signaling variables in predicting voting outcomes, alongside team record), I will define this branch as more whole due to sparser but present references to advanced statistics like PER, Win Shares, etc.

    Narratives are perhaps a less decisive, but still influential, part of the equation. Because it’s difficult to tell exactly how much impact these have on voting, we do have the examples of the noise that surrounded Kobe Bryant in 2013 and LeBron James in 2020. Both of these players were approaching their twilight years and, due to their ages, were garnering much more praise in major media outlets. Among others is Russell Westbrook having averaged a triple-double in the 2017 season. Although this is more of a statistics-driven case, there was a widespread significance to these numbers as Westbrook would be breaking a record set by Oscar Robertson back in 1962, so there were still strong hints of story-telling in this instance.

    What does “value” mean?

    Because the MVP is an acronym for the “Most Valuable Player,” it makes sense to vote for the award as it’s defined and choose the “most valuable” player; but what does that really mean? This, of course, means value needs to be defined. Even in basketball nomenclature, “value” is a loosely defined concept, which often leads to lots of dissenting opinions. Most recently, I’ve seen these types of discussions in the comment sections of MVP ladders and a delicately placed one of my own that I issued recently. Let’s look at some of the interpretations expressed in these forums:

    • “It’s flawed but the logic behind it is that if you can’t lift your team to a top seed, you’re not impacting winning at an MVP level.”

    (This quote came from someone with a seemingly dissenting opinion, hence an “it’s flawed” beginning.) The logic outlined here suggests, for a player’s value to be validated, it has to materialize at the team level. But instead of that being a show of high lift, or larger differences in win pace or scoring margin with and without a player, it has to be the player’s team’s win percentage. This has been a concept I’ve struggled with for a long time, and that’s because it parallels a phenomenon I discussed in an earlier criticism of the work of the Instagram video podcast, “Ball Don’t Stop.”

    Without going into the nitty-gritty of this event, the podcast’s host drew an unsound connection between scoring on the player level and scoring at the team level. Namely, there are many more ways other than scoring through which a player can positively impact his team’s point differential. The same logic applies to the improper connection between winning at the player level and winning at the team level. (Winning “at the player level” would simply be represented by a hypothetical parameter of exactly how many wins a player contributes to his team.) All it takes is a damning example in recent history to disprove this: Anthony Davis in New Orleans. From the 2015 to 2019 seasons, he was arguably one of the ten-or-so best players in the league, yet his team only managed to barely surmount the “average” mark (in SRS) two of those five years.

    But does that mean, because the Pelicans were a sub .500 team, Davis’s ability to positively impact an NBA team is invalidated? By no means is this true. I’m not one to throw around impact metrics without attempting to make some adjustments for confoundment, but between those five seasons Davis clocked in at no less than 7.2 Win Shares in a season, making him an extremely likely candidate for the title of a “valuable player.” Contrary to popular belief, there is a lot of historical analysis that suggests a player becomes more valuable to a team at it becomes worse. The premise is that because the team becomes more reliant on the player and his skills are being put to more use in that situation, the increased role would mean a team’s win pace, barring confoundment from variance and/or team circumstance, would actually be impacted to a higher degree by any player as the remaining roster’s quality is weakened.

    • “I think it’s [team quality in MVP cases] a pretty large factor. You can’t be on a bad team and be the MVP, that shows a lack of leadership, even if ur team is dogsh*t. It’s the ‘Most Valuable’, u might be the most valuable person on your team, but when your team is meaningless, you’re not exactly valuable.”

    This argument implies an axiomatic truth that states a player, if he so bears the value of an MVP-caliber player, must be able to transform the worst team possible into a “good team” (as it’s stated an MVP can’t be on a “bad team.”) Leadership attributes aside, let’s design a method to determine the probability of We know that the most extreme cases of player impact, based on records of with-or-without-you data (which measures the difference between the team’s schedule-adjusted margin of victory with and without a player from game-to-game) and APM data (estimates of a player’s impact on his team’s Net Rating, controlling for the quality of teammates and opponents), would say a GOAT-level player can add no more than +10 points to his team’s scoring margin each game; and even that measurement is quite generous.

    So if the Basketball Messiah set foot on the court, we would expect him to be worth about +10 points to his team per game. Because, as an individual player, he’s about to embark on the greatest peak season in league history, he “should” in this case be able to transform any team into a “good” team. The worst team in history per Basketball-Reference‘s SRS was the 1993 Mavericks, posting a woeful -14.68 SRS, surprisingly in a full 82-game season. So if this amazing player, we’ll call him Cornelius, is worth +10 points per game and his cohorts are worth (about) -14.7 points per game, would the new team be a -4.7 SRS team? Perhaps, but a significant factor we need to account for is trade-offs in roles and how these teammates will scale alongside Cornelius.

    Most superstars will play about 75 possessions per game in the modern era (roughly 36 minutes per game), but because Cornelius is so good, let’s say he’s a bit more of a heavy lifter and plays 40 minutes per game, playing just over 83 possessions per game. Because he’s on the floor for 83% of his team’s games (league-average paces generally tend toward 100 possessions per 48 minutes) and there are five players on the court at a time, we can estimate Cornelius carves out roughly 2.44 points of influence from his teammates, which in this case, would be -2.44 points per game. That means the additive efforts of his teammates now equate to a -12.24 SRS team. Therefore, with the addition of Cornelius’s +10 points per game, the new team is now a -2.24 SRS team. This would equate to a 35-win pace in an 82-game season.

    But we don’t have to stop there; we can continue exploring the possibility that Cornelius does, in fact, make this historically-bad team a good team through a significance test. Namely, we’re trying to determine if the -2.24 SRS estimate is convincing evidence that Cornelius doesn’t turn the previous roster into a good team. Without going into the nitty-gritty of how this hypothesis test works, here’s a takeaway from the final result:

    • Assuming Cornelius would improve the ’93 Mavericks to average levels, the probability they would have a -2.24 SRS is 30.47%.

    We can alter the parameters of these experiments to account for even more scenarios:

    • Assuming Cornelius would improve the ’93 Mavericks to the quality of an eighth-seed team, the probability they would have a -2.24 SRS is 31.81%.
    • Assuming Cornelius would improve the ’93 Mavericks to the quality of a championship contender, the probability they have would a -2.24 SRS is 4.92%.

    These probabilities are obviously quite low. To increase the leniency of these situations, let’s look at how some of today’s players might fare in the current MVP race by plopping him on the worst team in the NBA right now: the OKC Thunder. Based on the latest APM data, a reasonable higher fence for a stable form of impact from the game’s best player is +6 points per game. Using the method from earlier, this new player (we’ll call him “Player B”) would alleviate 1.43 points of the Thunder’s SRS deficit en route to a -1.16 SRS team. While the higher quality of the current Thunder compared to the ’93 Mavericks allows for the lesser player to help them attain greater heights, no player in today’s game could lead the Thunder to a win-pace greater than a 9-seed team.

    Using the probability method from earlier, let’s once again lay out some of the likelihoods for Player B:

    • Assuming Player B would improve the OKC Thunder to the quality of a Playoff team, the probability they would have a -1.16 SRS is 40.79%.
    • Assuming Player B would improve the OKC Thunder to the quality of an average team, the probability they would have a -1.16 SRS is 39.55%.
    • Assuming Player B would improve the OKC Thunder to the quality of a “good” team (one SRS standard deviation above average), the probability they would have a -1.16 SRS is 10.29%.
    • Assuming Player B would improve the OKC Thunder to the quality of a title contender, the probability they would have a -1.16 SRS is 7.97%.

    Now, let’s take the whole landscape of “good” and “bad” teams for some final statistics. For context, Player B lifted each “bad” team to an average -0.25 SRS and no higher than an 0.37 SRS:

    • Assuming Player B improves a currently-existing “bad” team to the quality of a “good” team is 14.53%, the probability the currently-existing “bad” teams continue with a “bad” SRS is 14.53%.
    • Assuming Player B improves a currently-existing “bad” team to the quality of a championship contender, the probability the currently-existing “bad” teams continue with a “bad” SRS is 11.53%.

    As we can see, the odds are not in Player B’s favor, despite being the very best player in the game. So what does this mean for this year’s MVP race? Aside from the likely candidates, there’s a heap of very valuable players that play for teams that aren’t particularly good, such as Luka Doncic, Nikola Vucevic, Zion Williamson, and even two of the strongest MVP candidates right now: Stephen Curry and Damian Lillard. But do the qualities of these players’ teammates make them any better or worse, any more or less valuable, of a player? All the evidence suggests not. Even the greatest imaginable player in league history wouldn’t improve the current OKC Thunder to a “good” team!

    The major takeaway from today’s study:

    • DO NOT JUDGE THE QUALITY OF A PLAYER’S MVP CASE BY HIS TEAM CIRCUMSTANCES. SERIOUSLY, DO NOT DO THIS.

    I’ve seen some rebuttals to reforming the NBA MVP voting criteria, both of which qualify as logical fallacies. The first is the Appeal to Authority: i.e. the voters think this way, therefore it’s the “right” way. But, of course, the fact that the voters may sway one way doesn’t confirm or deny any qualifications of what makes a player valuable. The second is the Fallacy of Sunken Costs, i.e. the voting has gone on this way for so long, so why change it? Namely, the continuation of this flawed criterion is for the attainment of some unsound form of achievement. But, as these arguments are heavily fallacious, why not spur change in your next conversation to actually change the topic to… the most valuable players?

    The heavy inclusion of team success / three-pillar system as a focal point behind a player’s MVP case is deeply flawed, fallacious, and a massive embarrassment to the intellectual integrity of NBA basketball. To see such a complex topic be dumbed down to such measly levels is atrocious to me, and I hope this post helped reinforce the understanding of why I feel this way.


  • How to Interpret NBA Impact Metrics [Video & Script]

    How to Interpret NBA Impact Metrics [Video & Script]

    NBA impact metrics, despite acting as some of the best tools available to the public today, are frequently misinterpreted. What are some ways to look at impact metric scores and use the data to our best advantage? Are there cases in which largely lower-score players are “better” than higher-score players? As a relatively avid user of these stats, I dive into the tips and tricks I’ve gained over the past few months on how to make the best use of these metrics.

    Video Script:

    Good afternoon everyone, and welcome back to another discussion on NBA impact metrics. So recently, I’ve been talking and writing about impact metrics more than usual, and that’s because there’s still some level of mystery surrounding them in the public eye. Anyone can hop onto Basketball-Reference and see that Russell Westbrook had a league-leading +11.1 Box Plus/Minus in 2017, but what does that actually mean? For the more dedicated NBA fan, these numbers might be seen every day through an endless series of acronyms of BPM, EPM, RPM, PIPM, RAPM, RAPTOR, or whichever metric that happens to be perused that day. Because of this, I’ve decided to sit down today and discuss the interpretations of these impact metrics, not only to set some of the records straight on what they truly mean but as an aid to make more reliable conclusions based on these types of data.

    Before we begin, if you missed my discussion of how impact metrics are calculated, feel free to scroll down to the description box; I’ve linked that article as a precursor to this video as some optional context going into this.

    With that out of the way, let’s go over the definition of an impact metric that I laid out in that article, which goes as follows: “Impact metrics are all-in-one measurements that estimate a player’s value to his team. Within the context we’ll be diving into here, a player’s impact will be portrayed as his effect on his team’s point differential every 100 possessions he’s on the floor.” So when we refer back to Russell Westbrook’s Box Plus/Minus in 2017, we know that metric says he provided an estimated +11.1 points of extra impact every 100 possessions he played. Now, this understanding may suffice to recognize a score, but what we’re looking for here is a strong interpretation of these metrics because, unless the nuances of each metric remain present in the mind, some of the inferences drawn from these data points will lead to much poorer interpretations of what’s happening on the basketball court.

    Let’s begin with some universal rules that can be applied to nearly every widespread metric. They only capture a player’s value to his specific team in his specific role. And if that doesn’t sound like a problem at first, consider this example. Arguably the top-2 NBA point guards in 2016 and 2017 were Stephen Curry and Russell Westbrook, and they both had the best seasons of their careers within these two seasons. Curry had his mega-spike in the 2015-16 season while Westbrook followed that MVP case with one of his own in 2017 when he averaged a triple-double. Let’s look at their scores in Box Plus/Minus during these seasons. When Curry had his peak, he posted an Offensive Box Plus/Minus of +10.3 and an overall score of +11.9, which to this day stands as one of the highest marks since the merger. The following season, he had a very impressive yet significantly lower +6.7 Offensive Box Plus/Minus and a +6.9 total score. So was Steph really 5 points worse in 2017 than he was in 2016? Of course not. This phenomenon was created when the addition of Kevin Durant absolved some of Curry’s role in the effort to help the two stars coexist on the court together. If the logistics behind that alone doesn’t make sense, just look at some of Curry’s box score stats when he played without Durant in 2017 compared to his bigger role in 2016.

    2017 (w/o KD): 39.5 PTS/100, 9.9 AST/100, 7.3 FTA/100

    2016: 42.5 PTS/100, 9.4 AST/100, 7.2 FTA/100

    The same events happened in reverse with Russell Westbrook, coincidentally enough because of the same player. With Durant in OKC in 2016, Westbrook had an Offensive BPM of +6.4 and an overall score of +7.8. After Durant left for Golden State that offseason, Westbrook posted an offensive score of +8.7 and an overall score of +11.1. So we ask again, was he really +3.3 points better a mere season apart? Of course, we answer again as we did with Curry: no. Westbrook simply took on a larger role; in fact, a much larger role. His usage rate increased a whopping TEN percent between the 2016 and 2017 seasons. That’s an unprecedented amount of change in such a short amount of time! Let’s use the same technique we did for Curry and compare Westbrook’s 2016 box scores when Durant was off the floor against his historically great solo act the following season.

    2016 (w/o KD): 40.7 PTS/100, 15.3 AST/100, 13.0 FTA/100

    2017: 44.8 PTS/100, 14.7 AST/100, 14.7 FTA/100

    The takeaway here is that impact metrics are extremely sensitive to a player’s role and only estimate what they’re doing in their specific situations. This means players who are poorly coached or are being assigned to a role that doesn’t fit their playstyle will always be underrated by these metrics while players who are utilized perfectly and play a role tailored to their style will always be a bit overrated. This type of significant confoundment will be found more often in box-only metrics than play-by-play informed ones; but star players on more top-heavy rosters will also see inflation in their on-off ratings, even after adjusting for some forms of luck.

    The next thing I’d like to discuss is how to interpret impact metrics in large groups. I’ve seen some claims that say one metric on its own isn’t entirely telling, but a healthy mix of a lot of metrics will be significantly more telling. Despite the fact that almost all notable one-number metrics attempt to estimate the same base measurement, RAPM, I still struggle with this idea; and that’s because every one of these metrics is created differently. Box Plus/Minus only uses the box score; PIPM uses the box score as well as luck-adjusted on-off ratings, RAPTOR uses both of those in addition to tracking data. I wouldn’t go so far as to call this an apples-to-oranges comparison, perhaps more along the lines of red apples to green apples. Averaging out five or so metrics might get closer to a true value, but it doesn’t necessarily move the needle as effectively as viewing each metric individually and considering the nuances. But I also won’t say this is entirely more useful, as these metrics still do use a lot of the same information. One form of confoundment for one metric will likely be present to some degree in another.

    The last main topic I’ll talk about here is how to interpret impact metrics within their sample size. At the time of this writing, NBA teams have played an average of 52 games so far, yet there have been cases of 50-game samples of these metrics treated just the same as a 250-game sample. This is where I’ll introduce the variance among these metrics. I’m a part of a biweekly MVP ladder ranking over at Discuss The Game, the profile to which I’ll also link in the description box, and in the discussion room filled by the panelists, I saw a lot of talk early on in the season that compared impact metric scores of the candidates. I only found this interesting because, as the panelist with arguably the highest usage of impact metrics in an overall sense, here I was the panelist with the least reliance on these stats. So why was this shift so significant? It paints a picture of how variance is often treated among basketball stats. NBA analyst Ben Taylor discusses “sample-size insensitivity” in his book, Thinking Basketball, which states most fans will often not consider the possibilities that lie beyond the scope of an allotted time period. This means that almost every team that wins the NBA championship is crowned the best team of the season. But what if the same teams replayed the same series a second time? Perhaps a third time? Hypothetically, if we could simulate these environments thousands of times, we’d have a much better idea of how good players and teams were during certain seasons. Because, after all, a lot of confounding results that don’t align with observable traits could be nothing more than random variance.

    So, with the bulk of this discussion concluded, let’s go over the biggest points in interpreting an impact metric score. When working with larger samples that span at least a season, perhaps the largest factor to consider is role sensitivity. Because these metrics only estimate how valuable a player is in his specific context, these aren’t estimates of how good a player would be across multiple environments. So in this sense, “value” versus “goodness” has some separation here. Look at these measures as ballparking values for how a team’s point differential shifts with versus without a player, subject to the inflations or deflations that come along with the circumstances of a player’s role and fit on that team. The next part of this relates back to assessing scores in groups. A simple averaging won’t suffice; each metric was made differently and should be treated as such. Instead, I prefer to use these different calculations of impact as a reference to which types of data prefer different types of players. So while almost all of Westbrook’s value can be detected by the box score, often with some overestimation, someone like Curry, who provides a lot of unseen gravity and rotational stress, won’t have a lot of his more valuable skills in consideration with these measurements. The last, and arguably the most important, is to interpret an impact metric based on its duration. Similar to how an RAPM model’s scores should be interpreted relative to its lambda-value, an impact metric score should be interpreted relative to its sample size. After ten or twenty games, they may be more “right” than they are “wrong,” but they aren’t definitive measures of a player’s situational value, and are even more confounded than the limitations of the data that goes into these stats. This means while one player can appear to be more valuable to his team, when in fact the counterpart in this example will prove to have done more in the long run.

    So the next time you’re on Basketball-Reference or FiveThirtyEight or wherever you get your stats, I hope this helps in understanding the values of these metrics and how to use them appropriately and in their safest contexts, Thanks for watching everyone.


  • MLB GOAT: Evaluating a Baseball Player

    MLB GOAT: Evaluating a Baseball Player

    My last post, which covered an introductory example of adjusting century-old stats for inflation in the MLB, was the first step is a larger goal, one that will be brought to life with the processes I’ll outline today: ranking the greatest MLB players ever. Many times before we have seen an attempt to do so, but rarely have I found a list that aligns with my universal sporting values. Thus, I have chosen to embark on a journey to replicate the results in a process I see to be more philosophically fair: a ranking of the best players of all time with the driver being the value of their on-field impact. However, as I am a relative novice in the art of hardcore analysis in baseball, I’ll be providing a clear, step-by-step account of my process to ensure the list is as accurate as possible.

    The Philosophy

    I’ve come to interpret one universal rule in player evaluation across most to all team sports, which relies on the purpose of the player. As I’ve stated in similar posts covering the NBA, a player is employed by a team for one purpose: to improve that team’s success. Throughout the course of the season, the team aims to win a championship. Therefore, the “greatest” MLB players give their teams the best odds to win the World Series. However, I’m going to alter one word in that sentence: “their.” Because championship odds are not universal across all teams (better teams have greater odds), that means a World Series likelihood approach that considers “situational” value (a player’s value to his own team) will be heavily skewed towards players on better teams, and that would be an unfair deflation or inflation of a player’s score that relies on his teammates.

    The central detail of my evaluation style will be the ideology behind assigning all players the same teammates, average teammates. Therefore, the question I’m trying to answer with a player evaluation is: what are the percent odds a player provides an average team to provide the World Series? This approach satisfies the two conditions I outlined earlier: to measure a player’s impact in the way that appeases the purpose of his employment while leveling the field for players seen as “weaker” due to outside factors they couldn’t control. Thus, we have the framework to structure the evaluations.

    The Method

    To measure a player’s impact, I’ll use a preexisting technique I’ve adopted for other sports, in which I estimate a player’s per-game impact (in this case, this would be represented through runs per game). For example, if an outfielder evaluates as a +0.25 runs per game player on offense and a 0 runs per game player on defense, he extends the aforementioned average team’s schedule-adjusted run differential (SRS) and thus raises the odds of winning a given game with the percent odds that come along with a +0.25 SRS boost. To gain an understanding of how the “impact landscape” works, I laid every qualified season from 1871 to 2020 out for both position players and pitchers to get a general idea of how “goodness” translates to impact. These were the results:

    Note: Offense and fielding use Fangraphs‘s “Off” and “Def” composite metrics scaled to per-game measures while pitching uses Runs Above Replacement per game scaled to “runs above average” – these statistics are used to gauge certain levels of impact. / I split the fielding distributions among positions to account for any inherent differences that result from play frequency, the value of a position’s skill set, and others.

    Offense (all positions)

    Fielding (pitchers)

    Fielding (catchers)

    Fielding (first basemen)

    Fielding (second basemen)

    Fielding (third basemen)

    Fielding (shortstops)

    Fielding (outfielders)

    Pitching (starters)

    Pitching (relievers)

    A large reason for the individual examination of each distribution is to gain a feel for what constitutes, say, an All-Star type of season, an All-MLB type of season, or an MVP-level season, and so on and so forth. The dispersions of the distributions are as listed below:

    Standard DeviationsPosition Players (Off)Starting Pitchers (Pitch)Relief Pitchers (Pitch)Pitchers (Field)Catchers (Field)First Basemen (Field)Second Basemen (Field)Third Basemen (Field)Shortstops (Field)Outfielders (Field)
    -4-0.554-1.683-0.582-0.305-0.262-0.255-0.256-0.258-0.258-0.286
    -3-0.402-1.262-0.437-0.233-0.183-0.202-0.185-0.188-0.178-0.221
    -2-0.250-0.841-0.291-0.162-0.104-0.149-0.115-0.118-0.097-0.157
    -1-0.098-0.421-0.146-0.090-0.025-0.096-0.044-0.048-0.017-0.092
    00.0540.0000.000-0.0180.053-0.0430.0260.0220.064-0.028
    10.2060.4210.1460.0530.1320.0100.0970.0920.1440.037
    20.3580.8410.2910.1250.2110.0630.1680.1620.2250.102
    30.5101.2620.4370.1970.2900.1160.2380.2320.3050.166
    40.6621.6830.5820.2690.3680.1690.3090.3020.3850.231

    These values are used to represent four ambiguous “tiers” of impact, with one standard deviation meaning “good” seasons, two standard deviations meaning “great” seasons, three standard deviations meaning “amazing” seasons, and four standard deviations meaning “all-time” seasons, with the negative halves representing the opposites of those descriptions. Throughout my evaluations, I’ll refrain from handing out all-time seasons, as these stats were taken from one-year samples and are thus prone to some form of variance. Therefore, an “all-time” season in this series will likely be a tad underneath what the metrics would suggest.

    There are also some clear disparities between the different fielding positions that will undoubtedly affect the level of impact each of them can provide. Most infield positions seem to be above-average fielders in general, with the first basemen showing greater signs of being more easily replaced. The second and third basemen share almost the same distribution while the shortstops and catchers make names as the “best” fielders on the diamond. I grouped all the outfielders into one curve, and they’re another “low-ceiling” impact position, similar to pitchers (for whom fielding isn’t even their primary duty). It’ll be important to keep these values in mind for evaluations, not necessarily to compare an average shortstop and an average first baseman, but, for instance, an all-time great fielding shortstop versus and an all-time great fielding first baseman.

    The Calculator

    Now that we have the practice listed out, it’s time to convert all those thoughts on a player to the numeric scale and actually do something with the number. The next step in the aforementioned preexisting technique is a “championship odds” calculator that uses a player’s impact on his team’s SRS (AKA the runs per game evaluation) and his health to gauge the “lift” he provided an average team that season. To create this function, I gathered the average SRS of the top-five seeds in the last twenty years and simulated a Postseason based on how likely a given team was to win the series, calculated with regular-season data in the same span.

    Because the fourth seed (the top Wild Card teams) is usually better than the third seed (the “worst” division leader), and the former would often face the easier path to the World Series, a disparity was created in the original World Series odds: in this case, a lower seed had better championship odds. To fit a more philosophically-fair curve, I had to take teams out of the equation and restructure the function accordingly. This means there is a stronger correlation to title odds based on SRS, separate from seeding conundrums; after all, we want to target the players with more lift, not the other way around. Eventually, this curve became so problematic I chose the more pragmatic approach: taking and generalizing real-world results instead of simulating them and found the ideal function with an R^2 of 0.977. (This method seemed to prove effective not only because of the strength of the fit, but the shape of the curve, which went from distinctly logarithmic (confusing) to distinctly exponential.)

    The last step is weighing a player’s championship equity using his health; if a player performed at an all-time level for 162 games but missed the entirety of the Postseason, he’s certainly not as valuable as he would’ve been if he’d been fully healthy. Thus, we use the proportion of a player’s games played in the regular season to determine the new SRS, while the percentage of Postseason games played represents the sustainability of that SRS for the second season. The health-weighted SRS is then plugged into the championship odds function to get Championship Probability Added!

    Significance

    With my new “World Series odds calculator,” I’ll perform evaluations on the best players in MLB history and rank the greatest careers in history. I’ll aim to rank the top-20 players ever at minimum, with a larger goal of cranking out the top-40. With this project, I hope to shed some light on these types of topics in a new manner while, hopefully, sparking discussion on a sport that deserves more coverage nowadays.


  • How Different Would Hugh Duffy’s 1894 Batting Title Look in 2020? – MLB Stat Inflation

    How Different Would Hugh Duffy’s 1894 Batting Title Look in 2020? – MLB Stat Inflation

    During the 1894 MLB season, Hugh Duffy of the Boston Beaneaters set a new precedent for contact hitters, posting an outstanding .440 batting average. This record has yet to be broken and will likely never be. Naturally, this sets forth the idea of questioning how valuable Duffy’s average truly was. What would a .440 hitter in 1984 have looked like if he played at the same level during, say, 2020? Here, I’ll use a technique to prorate Duffy’s batting average to an environment closer to the one batters play in today as an introductory example to accounting for stat inflation in the MLB, as well as to gain some more insight as to how impressive Duffy’s 1894 campaign really was.

    The Method

    To standardize batting average across eras, we need to set a baseline for the hitting environment. Because we’re adjusting stats closest to the 2020 season, I’ll choose values that are very similar to today’s to allow for more intelligible comparison. Last season, the MLB’s cumulative batting average was .245, a mere half-percent less than the “conventional average” of .250, so for these standardized values, we’ll set the typical batting average as such. The next point of consideration is the dispersion of our ideal batting averages, which will be measured with a conceived standard deviation. There are two options for us here:

    • Measure the standard deviation using all players with at least one at-bat.
    • Measure the standard deviation using all qualified hitters ( 3.1+ plate appearances per team game).

    It may seem there wouldn’t be a significant change, but in taking one of the other, the standard deviation will vary by roughly 10%. For example, in 2019, the standard deviation of batting average using the first method would draw a value of roughly 13.5%. The second method garners a typical variance of 2.6%. Because the distribution of batting average looks approximately normal, I’m inclined to use the second method. It also makes sense to think a “good” hitter (one standard deviation above the mean) would hit roughly .280, a “great” one would hit about .310, and a .340 hitter would be in contention for the batting title. Thus, we’ll set the parameters of our standardized batting curve to a mean of .250 and a standard deviation of 3%.

    There was also one more variable that I suspected would play a role in a fair cross-era comparison. (This is concerning cumulative stats such as hits or home runs). League offenses were far more efficient on a per-game basis in 1894 (7.38 runs per game) than in 2020 (4.65 runs per game). This could potentially mean a quicker flow of offense during 1894 granted its players far more opportunities per game than in 2020. Thus, I calculated a figure I’ll call “pace,” the number of plate appearances every nine innings. (I chose to use nine innings rather than one game because per-game stats will be affected by extra-inning games.) During the 1894 season, there were about 43.0 plate appearances every nine innings whereas, in 2020, there were 39.8. This may not seem to be a significant factor, but it could be the difference between four and five plate appearances in a game for the cleanup hitter.

    Duffy’s New Average

    During the 1894 season, the “placeholder” standard deviation was absurdly high compared to its 2020 counterpart, making Duffy’s .440 batting average less impressive on our standardized scale. By taking the z-score of his batting average, we obtain a value of +3.825, which on the standardized scale, is…

    *drum roll please*

    … a new average of .365! This means that if Duffy were to have played at the same level in a roughly 2020-esque environment, just under 36.5% of his at-bats would have resulted in a hit. This is still a very impressive feat, and Duffy would still claim the batting title among the 2020 contenders, but his hitting proficiency is closer to that of DJ LeMahieu last season (.364 average) than an outlier among outliers in MLB history.

    Significance

    It’s often well-known that batting averages in baseball will fluctuate over time, explaining why the superstars of the late 19th and early 20th centuries will post some averages greater than .400 while the very best of today will rarely exceed .350. However. there have been few attempts (that I’ve seen) to adjust for these changes to create a “Standardized Scale.” (From here on out, I will refer to these adjusted baseball statistics with a “z” abbreviation (alluding to the notation of the standardized test statistic)). So Duffy’s 1894 batting average of .440 correlates to a “z” BA of .365. My goal with these values is to help evaluate MLB players of the past in fair comparison to players of the present, to shed more light on the true capabilities of the greatest baseball players of all time.


  • Are the Brooklyn Nets the Title Favorites?

    Are the Brooklyn Nets the Title Favorites?

    After the minor blockbuster deal that relieved Blake Griffin of his athletic duties in Detroit and eventually landed him in Brooklyn, the world started to ask if his acquisition moved the needle even more for the Nets’ championship hopes. Naturally, this sets forth the question of Brooklyn’s Finals likelihood before the signing, and whether or not Griffin actually changes those odds.

    The Raw Numbers

    The aggregate Brooklyn Nets team so far, meaning the inclusions of stints with and without the later additions like James Harden, is not on track to win the championship. With an SRS of +4.65 through their first 37 games, the Nets would be on track for 54 wins during a regular 82-game season (corresponds to a rough 65.5% win percentage). Compared to their actual win percentage of 64.9% (24 – 13), a small argument could be made that Brooklyn’s record is currently understating them, although the difference isn’t even enough to add an extra win to their “Pythagorean” record.

    Historically speaking, NBA teams don’t enter legitimate title candidacy with an SRS below +5. According to Ben Taylor’s CORP overview on Nylon Calculus: “Since Jordan returned in 1996, no healthy team has hung a banner with an SRS differential below 5.6 and only one (the ’03 Spurs) was below 6.6.” (This was written before the Raptors hung their own banner in 2019). This means, assuming Brooklyn doesn’t obtain some major catalyst for the second season, either in terms of roster development or team chemistry, they aren’t viable pick as the “title favorites.” However, these figures aren’t totally representative of how good the Nets are right now, as they included games before the addition of James Harden and all of them exclude the efforts that Griffin will bring to the table.

    Brooklyn with Harden?

    Because Griffin, a very good player in his own right, will make a lesser impact on the Nets than James Harden, the latter player is the more important focus when gauging the team’s championship likelihood. Harden’s larger role and greater influence on the scoreboard will resultantly have a more significant impact on whether or not Brooklyn eclipses the cluster of “good-not-great” teams and into championship contention.

    During the past, we’ve seen that bringing in more star talent is not additive. When the Golden State Warriors won 73 games in 2016 they were evidently a super-team, posting a +10.38 SRS and nearly claimed the title as the greatest team ever before falling to LeBron James’s Cavaliers in seven games (although I don’t think the Finals loss necessarily topples Golden State’s case, either). When they replaced (mostly) Harrison Barnes’s minutes with a peak Kevin Durant, they clocked in as a +11.35 SRS team in 2017. (We’re controlling for low-minute, replacement-level additions and subtractions as near negligible). Based on the historical distribution of Adjusted Plus/Minus data, a +1 player wouldn’t even be an All-Star level contributor. Does this mean Kevin Durant wasn’t even as good as a “sub” All-Star in 2017? Of course not. But his value to the Warriors was likely closer to that number than the same figure if he were on an average team.

    My “portability” curve estimates in which players are grouped into five tiers – the graph shows the change in per-game impact for a +4 player across all tiers and team SRS (x-axis) differentials greater than zero.

    This is why there were so many concerns surrounding James Harden’s arrival in Brooklyn. Would the immersion of so many offensive superstars, especially ones that lack some of the “portable” traits we saw succeed in Golden State, it was perfectly reasonable to suggest that diminishing returns would eventually kick in with the Nets and their offense would nearly plateau. But has this been the case? Through Harden’s first 23 games in Brooklyn, the offense has been scoring 123.3 points every 100 possessions with him on the floor, which would comfortably finish as the greatest team offense of all-time, as well as being a mark comparable to Curry and Durant’s team offenses in Golden State. But similar to those Curry-Durant lead teams, having a historically-great offense with stars on the floor doesn’t guarantee a championship (plus, Golden State fared very well in a department in which Brooklyn severely lacks: defense).

    With Harden off the floor, Brooklyn’s offense scores 116.3 points every 100 possessions: still a very good team offense, but not nearly as good when the Beard is checked in. Does this mean Harden contributes +7 points every 100 possessions to the Brooklyn Nets? Not necessarily. On-off ratings are highly influenced by how a team staggers its playing time, i.e. a player may spend all his minutes with the team’s stars or the team’s scrubs. However, if we comb through the Nets’ n-man lineups, we can gain insight as to how the additions and replacements of one of Durant, Harden, and Kyrie Irving would increase the team’s offensive heights.

    (? PBP Stats)

    It’s no surprise that the Nets’ offense is at the peak of its powers when Durant and Harden, the team’s two best offensive players, are on the court together, posting a whopping 126.4 offensive rating. Now let’s look at how Durant and Irving-led offenses fare: a similarly outstanding 121.8 points per 100. A five-point SRS difference could be the difference between near-locks and playoff contention; however, we’re already seeing a declination in Harden’s supposed influence on Brooklyn’s offense. But wait, there’s more! Let’s look at the Nets’ four-man units to further gauge Harden’s offensive value in Brooklyn.

    (? PBP Stats)

    There are some really interesting implications here. Using five of Brooklyn’s regulars, take a look at the Brooklyn offense without Kyrie Irving: still a great 120.1 offensive rating. If we take DeAndre Jordan, the worst offensive player, out of the lineup and replace him with Kyrie Irving, the offense only improves by +1.1 points every 100 possession. Even giving Irving the easier route using Jordan as the control rather than, say, Joe Harris, the diminishing returns effect is perfectly clear. Replicating the same exercise for Harden – looking at how good his offenses are compared to Jordan’s – we get an estimate of +5.7 points of offensive impact every 100 possessions. This is similar to what has been suggested so far and is thus no surprise. However, what is surprising is where Kevin Durant stands in this approach.

    With Brooklyn’s four best (healthy?) offensive players on the floor (the Big-3 and Joe Harris), they score an astronomical 126.9 offensive rating. Once again, with DeAndre Jordan in Durant’s place, we see that mark take a minor toll to a 126.7 offensive rating. Does this mean Durant is only worth +0.2 points every 100 possessions to the Nets’ offense? Of course not. It doesn’t only defy the rational suppositions we have on Durant’s value, but there is some level of confoundment here. The extenuating circumstances do permit leniency, but lots of observed basketball trends still hold here. However, this does relate to later ideas we’ll explore. Lastly, the most damning piece of evidence in favor of the “portability” conundrum is how Joe Harris falls into the equation. A low-demand, high-efficiency shooter – an ideal mold for a complementary offensive piece – would have some of these diminishing returns alleviated, right? It turns out that’s more than true.

    (? Backpicks – Do Joe Harris’s more “scalable” traits make him even more valuable to the Nets’ high-powered offenses than their stars?)

    Without Joe Harris in the lineup among these five players, Brooklyn’s offense hits a low at a 118.1 offensive rating. Similar to the “replacement-level” route used for the previous three players, let’s look at the “Big-4” offense once more: the same astounding 126.9 offensive rating. That means, relative to the game setting and substitution, Joe Harris was worth +8.7 points more to Brooklyn’s high-level offenses relative to DeAndre Jordan. Perhaps let’s even the playing field out more. With Kyrie Irving as the replacement player, Harris’s offenses are +2 points more efficiency every 100 possessions. This is a very significant indicator of Harris’s “portability” in the Nets’ lineups. Does this mean he’s a more valuable offensive player than Irving? Not necessarily, but it suggests Harris’s main department (scalability) raises the ceiling for these high-level offenses more than Kyrie Irving’s skills, which start to blend in after so much offensive talent is thrown into the mix.

    This is supported by single-year RAPM (Regularized Adjusted Plus/Minus). Most of the time, players like Durant (+2.17 ORAPM) and Irving (+2.37) are more valuable offensive players than Harris (+1.99), but the relatively small gap paired with our previous knowledge on the subject corroborates even more: once Brooklyn’s offense becomes astronomically good, using players’ scalable traits will raise the ceiling even more. This is antithetical to a player like Allen Iverson (AKA a “floor raiser”). But there’s still one unanswered question: why was James Harden seemingly a more valuable offensive player than Durant and Irving (but especially Durant). If Harden is the player being added to the preexisting roster, why doesn’t he experience many diminishing returns? The answer: load and role trade-offs.

    James Harden is comfortably the most ball-dominant of Brooklyn’s offensive stars, holding the ball for an average of 5.42 seconds per touch on 93.3 touches per game according to Synergy tracking data. Although there is a reduction from last season, as implied through the “portability” construct, this change wasn’t unexpected. Meanwhile, his teammates Durant and Irving clock in at 3.11 seconds per touch / 69.5 touches per game 4.44 seconds per touch / 75.1 touches per game, respectively. When Harden takes the load off Durant and Irving, he’s absorbing a significant amount of their offensive impact. So while Harden’s offensive impact didn’t change a whole lot, Durant’s and Irving’s did.

    “Portability” usually observes the “internal” changes, or how individuals fares in different environments, but the other half of that coin of how traits like ball-dominance affect the portability of teammates. These phenomena explain why Harden’s offensive impact is comparable to his role in Houston and why Joe Harris is arguably more valuable to extremely high-octane offenses than Kyrie Irving.

    So what about Griffin?

    A part of the beauty of interpreting the Blake Griffin trade is that, no matter how good he is with the Nets, his impact will become redundant. Whether he lets his injuries define his post-thirty era or transforms back into 2019 Blake Griffin, there’s simply a limited amount of offensive impact to go around. If Griffin were reminiscent of his early-2010s self, perhaps he’ll show notable ability to fit well alongside star talent; but based on his time with the Pistons, Griffin isn’t a very high-portability player. Thus, if I were Steve Nash and the Nets’ coaching staff, I wouldn’t slot Griffin into the starting lineup or into the lineup early on in the first quarter (because, contrary to popular belief, games are often won by building suitable leads in the first quarter). Instead, Griffin would better serve his purpose as an anchor of the second unit, depending on how good he is again because we still don’t have a very clear picture of that.

    Conclusively, regardless of the “goodness” Griffin brings to the table, he’ll be spending too much time alongside too many offensive superstars with too little defensive equity, and his value to the Nets won’t be especially significant given his minutes aren’t drastically staggered against the starters’ playing time. With all this information processed, there’s now a clearer picture as to where they stand in the current playoff picture. Given the trade-offs between Durant’s, Harden’s, and Irving’s offensive impact, we can’t expect Brooklyn’s offense to be that much better. (The loss of defensive shares in the Harden trade is why I still think Brooklyn would’ve been better off refraining.) Due to the unstable state of the team defense (looking to approach well-below-average), the team’s regular-season SRS will likely max out at +5, and I could see a top-three seed as perfectly reasonable – Brooklyn is still a very good team!

    And the Playoffs?

    During the postseason, Kevin Durant will have the same luxury he did with the Warriors: acting as the secondary offensive star. The stress taken of his load between OKC and Golden State explains a lot of the stat inflation during the 2017 and 2018 title runs, and thus, his scoring could thrive to a similar level. But then there’s Harden. As his load hasn’t changed too much, and his skills become more redundant in the second season, he’ll likely pose a similar threat compared to previous seasons (although the eased burden with more stars alongside him could open up more catch-and-shoot opportunities). Irving is just one more offensive threat to add to this equation and will continue to woo defenses away from overplaying one of the stars.

    The prospect of Brooklyn’s offense in the Playoffs is intriguing; however, the results we’ve seen so far make those ideas more of an “on paper” scenario. The applicability of this style has yet to materialize into firm action. The inevitable threat of facing above-average offenses will continue to deconstruct the Nets’ defense, and I don’t see a ton of evidence to suggest Brooklyn will notably improve from its +5 SRS caliber player during the regular season. Depending on how the Bucks and Sixers pan out in the second season, I could reasonably see the Nets in the NBA Finals, although this is more due to a subpar Eastern Conference than actual Finals-caliber play on their part. However, I’d really have to squint to see Brooklyn topple either of the healthy Los Angeles teams, and even teams like Phoenix would pose a legitimate threat.

    (? ClutchPoints)

    When all is said and done, I don’t expect to see the Nets lift the Larry O’Brien trophy. Based on the current landscape of the East, a Finals berth is not out of reason. Milwaukee and Philadelphia are legitimate threats, and although I favor the Nets over the 76ers, I think Milwaukee is entirely capable of pushing through. Based on my expectations for the Brooklyn Nets (+5 SRS), the odds they win the title would clock in at roughly 2.6%. But because the East is so depleted and I’m not 100% confident in that evaluation, my reasonable range for the Nets’ championship odds is between 3% and 7%. The lesson to preach: bet on the field.


  • How Do NBA Impact Metrics Work?

    How Do NBA Impact Metrics Work?

    The introductions of player-evaluation metrics like Player-Impact Plus/Minus (PIPM) and the “Luck-adjusted player estimate using a box prior regularized on-off” (yes, that is actually what “LEBRON” stands for) peddled the use of these metrics to a higher degree than ever. Nowadays, you’ll rarely see a comprehensive player analysis not include at least one type of impact metric. With a growing interest in advanced statistics in the communities with which I am involved, I figured it would serve as a useful topic to provide a more complete (compared with my previous attempts on the subject) and in-depth review of the mathematics and philosophies behind our favorite NBA numbers.

    To begin, let’s first start with an all-inclusive definition of what constitutes an impact metric:

    “Impact metrics” are all-in-one measurements that estimate a player’s value to his team. Within the context we’ll be diving into here, a player’s impact will be portrayed as his effect on his team’s point differential every 100 possessions he’s on the floor.

    As anyone who has ever tried to evaluate a basketball player knows, building a conclusive approach to sum all a player’s contributions in a single notation is nearly impossible, and it is. That’s a key I want to stress with impact metrics:

    Impact metrics are merely estimates of a player’s value to his team, not end-all-be-all values, that are subject to the deficiencies and confoundment of the metric’s methodologies and data set.

    However, what can be achieved is a “best guess” of sorts. We can use the “most likely” methods that will provide the most promising results. To represent this type of approach, I’ll go through a step-by-step process that is used to calculate one of the more popular impact metrics known today: Regularized Adjusted Plus-Minus, also known as “RAPM.” Like all impact metrics, it estimates the correlation between a player’s presence and his team’s performance, but the ideological and unique properties of its computations make it a building block upon which all other impact metrics rest.

    Traditional Plus/Minus

    When the NBA started tracking play-by-play data during the 1996-97 season, they calculated a statistic called “Plus/Minus,” which measured a team’s Net Rating (point differential every 100 possessions) while a given player was on the floor. For example, if Billy John played 800 possessions in a season during which his team held a cumulative point differential of 40 points, that player would have a Plus/Minus of +5. The “formula” for Plus/Minus is the point differential of the team while the given player was in the game divided by the number of possessions during which a player was on the floor (a “complete” possession has both an offensive and defensive action), extrapolated to 100 possessions.

    Example:

    • Billy John played 800 possessions through the season.
    • His team outscored its opponents by 40 points throughout those 800 possessions.

    Plus/Minus = [(Point Diff / Poss) * 100] = [(40/800) * 100] = +5

    While Plus/Minus is a complete and conclusive statistic, it suffers from severe forms of confoundment in a player-evaluation sense: 1) it doesn’t consider the players on the floor alongside the given player. If Zaza Pachulia had spent all his minutes alongside the Warriors mega-quartet during the 2017 season, he would likely have one of the best Plus/Minus scores in the league despite not being one of the best players in the league. The other half of this coin is the players used by the opposing team. If one player had spent all his time against that Warriors “death lineup,” then his Plus/Minus would have been abysmally-low even if he were one of the best players in the game (think of LeBron James with his depleted 2018 Cavaliers).

    Adjusted Plus/Minus

    “Adjusted” Plus/Minus (APM) was the first step in resolving these issues. The model worked to run through each individual stint (a series of possessions in which the same ten players are on the floor) and distribute the credit for the resulting team performances between the ten players. This process is achieved through the following framework:

    (? Squared Statistics)

    The system of linear equations is structured so “Y” equals the Net Rating of the home team in stint number “s” in a given game. The variables “A” and “B” are indicators of whether a given player is on the home or away team, respectively, while its first subscript (let’s call it “i”) categorizes a team’s player as a given number and the “s” (the second subscript) numbered stint in which the stint took place.

    To structure these equations to divvy the credit of the outcome of the stint, a player for the home team is designated with a 1, a player for the away team is given a -1, and a player on the bench is a 0 (because he played no role in the outcome of the stint).

    The matrix form of this system for a full game has the home team’s Net Rating for each stint listed on a column vector, which is then set equal to the “player” matrix, or the 1, -1, and 0 designation system we discussed earlier. Because the matrix will likely be non-square it is non-invertible (another indicator is that the determinant of the matrix would equal zero). Thus, the column vector and the player matrix are both multiplied by the transpose (meaning it is flipped across its diagonal, i.e. the rows become columns and the columns become rows) of the player matrix, which gives us a square matrix to solve for the implied beta column vector!

    An example of how a matrix is transposed.

    The new column vector will align the altered player matrix with the traditional Plus/Minus of a given player throughout the game while the new player matrix counts the number of interactions between two players. For example, if the value that intersects players one and six has an absolute value of eight, the two of them were on the floor together (or in this case, against each other) for eight stints. Unfortunately, the altered player matrix doesn’t have an inverse either, which requires the new column vector to be multiplied by the generalized inverse of the new player matrix (most commonly used as the Moore-Penrose inverse). I may take a deeper dive into computing the pseudoinverse of a non-invertible matrix in a future walk-through calculation, but the obligatory understanding of the technique for this example is that it’s an approximation of a given matrix with invertible properties.

    Multiplying by the “pseudoinverse” results in the approximation of the beta coefficients and will display the raw APM for the players in the game. Taken over the course of the season, a player’s APM is a weighted (by the number of possessions) average of a player’s scores for all games, and voila, Adjusted Plus/Minus! This process serves as the foundation for RAPM and, although a “fair” distribution of a team’s performance, it’s far from perfect. Raw APM is, admittedly, an unbiased measure, but it often suffers from extreme variance. This means the approximations (APM) from the model will often strongly correlate with a team’s performance, but as stated earlier, it’s a “best guess” measurement. Namely, if there were a set of solutions that would appease the least-squares regression even slightly less, the scores could drastically change.

    Thanks to the work of statisticians like Jeremias Engelmann (who, in a 2015 NESSIS talk, explained that regular APM will often “overfit,” meaning the model correlates too strongly to the measured response and loses significant predictive power, a main contributor to the variance problem), there are viable solutions to this confoundment.

    (? Towards Data Science)

    Regularized Adjusted Plus/Minus

    Former Senior Basketball Researcher for the Orlando Magic, Justin Jacobs, in his overview of the metric on Squared Statistics, outlined a set of calculations for APM in a three-on-three setting, obtaining features similar to the ones that would usually be found.

    (? Squared Statistics)

    Although the beta coefficients were perfectly reasonable estimators of a team’s Net Rating, their variances were astoundingly high. Statistically speaking, the likelihood that a given player’s APM score was truly reflective of his value to his team would be abysmal. To mitigate these hindrances, statisticians use a technique known as a “ridge regression,” which involves adding a very mild perturbation (“change”) to the player interaction matrix as another method to approximate the solutions that would have otherwise been found if the matrix were invertible.

    We start with the ordinary least-squares regression (this is the original and most commonly used method to estimate unknown parameters):

    This form is then altered as such:

    Note: The “beta-hat” indicates the solution is an approximation.

    The significant alterations to the OLS form are the additions of the lambda-value and an identity matrix (a square matrix with a “1” across its main diagonal and a “0” everywhere else; think of its usage as multiplying any number by one. Similar to how “n” (a number) * 1 = n, “I” (the identity matrix) * “A” (a matrix) = A). The trademark feature of the ridge regression is its shrinkage properties. The larger the lambda-value grows, the greater the penalty and the APM scores regress closer towards zero.

    (? UC Business Analytics – an example of shrinkage due to an increase in the lambda-value, represented by its (implied) base-10 logarithm)

    With the inclusion of the perturbation to the player interaction matrix, given the properties listed, we have RAPM! However, as with raw APM, there are multiple sources of confoundment. The most damning evidence, as stated earlier, is that we’re already using an approximation method, meaning the “most likely” style from APM isn’t eliminated with ridge regression. If the correlation to team success were slightly harmed, the beta coefficients could still see a change, but not one nearly as drastic as we’d see with regular APM.

    There’s also the minor inclusion of bias that is inherent with ridge regression. The bias-variance tradeoff is another trademark in regression analysis with its relationship between model complexity. Consequently, the goal will often be to find the “optimal” model complexity. RAPM is a model that introduces the aforementioned bias, but it’s such a small inclusion it’s nearly negligible. At the same time, we’re solving the variance problem! It’s also worth noting the lambda-value will affect the beta coefficients, meaning a player’s RAPM is best interpreted relative to the model’s lambda-value (another helpful tidbit from Justin Jacobs).

    (? Scott Fortmann-Roe)

    My concluding recommendations for interpreting RAPM include: 1) Allow the scores to have time to stabilize. Similar to points per game or win percentage, RAPM varies from game-to-game and, in its earlier stages, will often give a score that isn’t necessarily representative of a player’s value. 2) Low-minute players aren’t always properly measured either. This ties into the sample-size conundrum, but an important aspect of RAPM to consider is that it’s a “rate stat,” meaning it doesn’t account for the volume of a player’s minutes. Lastly, as emphasized throughout the calculation process, RAPM is not the exact correlation between the scoreboard and a player’s presence. Rather, it is an estimate. Given sufficient time to stabilize, it eventually gains a very high amount of descriptive power.

    Regression Models

    RAPM may be a helpful metric to use in a three or five-year sample, but what if we wanted to accomplish the same task (estimate a player’s impact on his team every 100 possessions he’s on the floor) with a smaller sample size? And how does all this relate to the metrics commonly used today, like Box Plus/Minus, PIPM, and LEBRON? As it turns out, they are the measurements that attempt to answer the question I proposed earlier: they will often replicate the scores (to the best of their abilities) that RAPM would distribute without the need for stabilization. Do they accomplish that? Sometimes. The sole reason for their existence is to approximate value in short stints, but that doesn’t necessarily mean they need some time to gain soundness.

    Similar to our exercise with a general impact metric, which uses any method to estimate value, let’s define the parameters of a “regression model” impact metric:

    A regression model is a type of impact metric that estimates RAPM over a shorter period of time than needed by RAPM (roughly three years) using a pool of explanatory variables that will vary from metric to metric.

    The idea is fairly clear: regression models estimate RAPM (hence, why scores are represented through net impact every 100 possessions). But how do they approximate those values? These types of impact metrics use a statistical technique named the multiple linear regression, which fulfills the goal of the regression model by estimating a “response” variable (in this case, RAPM) using a pool of explanatory variables. This will involve creating a model that takes observed response values (i.e. preexisting long-term RAPM) and its correlation with the independent variables used to describe the players (such as the box score, on-off ratings, etc.).

    (? Cross Validated – Stack Exchange)

    Similar to the “line of best fit” function in Google Sheets that creates forecast models for simple (using one explanatory variable) linear regressions, the multiple linear regression creates a line of best fit that considers descriptive power between multiple explanatory variables. Similar to the least-squares regression for APM, a regression model will usually approximate its response using ordinary least-squares, setting forth the same method present in the RAPM segment that is used to create the perturbation matrix. However, this isn’t always the case. Metrics like PIPM use a weighted linear regression (AKA weighted least squares) in which there is a preexisting knowledge of notable heteroscedasticity in the relationship between the model’s residuals and its predicted values (in rough layman’s terms, there is significant “variance” in the model’s variance).

    (The WLS format – describing the use of the residual and the value predicted from the model.)

    WLS is a subset of generalized least squares (in which there is a preexisting knowledge of homoscedasticity (there is little to no dispersion among the model’s variance) in the model), but the latter is rarely used to build impact metrics. Most metrics will follow the traditional path of designating two data sets: the training and validation data. The training data is used to fit the model (i.e. what is put into the regression) while the validation data evaluates parts like how biased the model is and assuring the lack of an overfit. If a model were trained to one set of data and not validated by another set, there’d be room to question its status as “good” unless verified at a later date.

    After the model is fitted and validated, an impact metric has been successfully created! Unfortunately (again…), we’re not done here, as another necessary part of understanding impact metrics is a working knowledge of how to assess their accuracy.

    Evaluating Regression Models

    While the formulations of a lot of these impact metrics may resemble one another, that doesn’t automatically mean similar methods produce similar outputs. Intuitively speaking, we’d expect a metric like PIPM or RAPTOR, which includes adjusted on-off ratings and tracking data, to have a higher descriptive power compared to a metric like BPM, which only uses the box score. Most of the time, our sixth sense can pick apart from the good from bad, and sometimes the good and the great, but simply skimming a metric’s leaderboard won’t suffice when evaluating the soundness of its model.

    The initial and one of the most common forms of assessing the fit of the model includes the output statistic “r-squared” (R^2), also known as the coefficient of determination. This measures the percent of variance that can be accounted for in a regression model. For example, if a BPM model has an R^2 of 0.70, then roughly 70% of the variance is accounted for while 30% is not. While this figure serves its purpose to measure the magnitude of the models’ fit to its response data, a higher R^2 isn’t necessarily “better” than a lower one. A model that is too reliant on its training data loses some of its predictive power, as stated earlier, falling victim to a model overfit. Thus, there are even more methods to assess the strength of these metrics.

    (? InvestingAnswers)

    Another common and very simple method could be to compare the absolute values of the residuals of the model’s scoring between the training data and the validation data (we use the absolute values because ordinary least-squares is designed so the sum of the residuals will equal zero) to assess whether the model is equally unbiased toward the data it isn’t fitted to. Although this may be a perfectly sound technique, its simplicity and lack of comprehension may leave the method at a higher risk of error. Its place here is more to provide a more intelligible outlook on evaluating regression models. Similarly, we’ll sometimes see the mean absolute error (MAE) of a model given with the regression details as a measure of how well it predicts those original sets of data.

    There’s also the statistical custom of assessing a metric’s residual plot, which compares the model’s predicted value and its residual (observed value minus predicted value) on the x and y-axes, respectively, on a two-dimensional Cartesian coordinate system (AKA a graph). If there is a distinct pattern found within the relationship between the two, the model is one of a poorer fit. The “ideal” models have a randomly distributed plot with values that don’t stray too far from a standardized-zero. Practically speaking, the evaluation of the residual plot is one of the common and viable methods to assessing how well the model was fit to the data.

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    However, as seen in works from websites like Nylon Calculus and Dunks & Threes, the most common form of impact metric evaluation in the analytics community is retrodiction testing. This involves using minute-weighted stats from one season used to predict the next season. For example, if Cornelius Featherton was worth +5.6 points every 100 possession he was on the floor during the 2019 season and played an average of 36 minutes per game in the 2020 season, his comparison score would equate to roughly +4.2 points per game. This would be used to measure the errors between a team’s cumulative score (i.e. an “estimated” SRS) against the team’s actual SRS. Evidently, this method suffers from the omission of ever-changing factors like a player’s improvements and declinations, aging curves, and yearly fluctuations, it does hold up against injury and serves a purpose as a measure of predictive power. (“A good stat is a predictive stat” – a spreading adage nowadays.)

    Basketball analytics and impact metrics may appear to be an esoteric field at times – I certainly thought so some time ago – but the comprehension of its methodologies and principles isn’t full of completely unintelligible metric designs and reviews. Hopefully, this post served as a good introductory framework to the models and philosophies of the numbers we adore as modern analysts or fans, and that it paints a somewhat clear picture of the meanings behind impact metrics.


  • The Psychology of Basketball (Part 2 – Dissecting Traditional Values)

    The Psychology of Basketball (Part 2 – Dissecting Traditional Values)

    Nowadays, you’re either an eye-test guy or stats guy, right? There seems to be no acceptable middle ground, especially to the side I’ll take a deep-dive into today, the “traditionalists.” The use of any intelligible statistic beyond the box score signals someone who skims a Basketball-Reference page to evaluate a player, a common notion set forth by some. I haven’t absorbed the entirety of the traditionalist standpoint; so, to gain insight on what it entails, I turned to Ekam Nagra, the face of the “Ball Don’t Stop” Instagram page, a platform he uses to host a podcast. He will often use his posts to share his ideas on how analytics are poor tools to evaluate players, at times to interview former and current NBA players with similar opinions.

    Through my time spent learning the tendencies of his methods, I believe I’ve found a reasonable set of pillars that provide the structure for his evaluations, rankings, or any other process that requires player assessment:

    • Because the rules of basketball dictate the value of a possession to rely on whether or not the ball is scored, the most valuable individual trait is also scoring.
    • The previous view can be further defined to focus on volume scoring (although Nagra has expressed a distaste for the term in the past), with a crucial context of efficiency being the difficulty of the defensive scheming and the type of shot.
    • Defense, on the player and team levels, is less of an individual quality than offense because the latter dictates the momentum on the defensive end (offense “creates” defense in a way).
    • Statistics and analytics, in essence, lack context and are watered-down interpretations of court actions used as a flimsy replacement for “true” explanation.
    • Lastly, basketball analysis is an esoteric field. It requires direct, firsthand experience as a competitive basketball athlete to attain a higher ability to comprehend game actions.

    Anyone familiar with my previous work knows my evaluation tendencies, ones because of which Nagra would almost certainly dub me an “analytics boy” or a “stat fan.” I consistently use statistics and impact metrics in my end-of-season evaluations, so as a potential disclaimer, I am writing from a “progressive” perspective (i.e. in support of the analytics movement). Thus, I’ll dissect the meaning of Nagra’s explicit and implicit rationale to provide an analytical alternative, which will hopefully take the series an extra step further in the truer understanding of the psychology behind basketball.

    Scoring Blindness

    As I discussed in the first installment of the series, as defined by the Thinking Basketball book, “scoring blindness” is the tendency of a critic to overrate the contributions of a team’s highest-volume scorer (i.e. the player who leads his team in points per game). Although I don’t agree with the employment of such a method, I understand the concept behind it: if the point of a possession on offense is to score the basketball, then the best players will likely score most often. (This is something I generally agree with). However, Nagra takes it a step further in Episode 91 of the “Ball Don’t Stop” podcast, from which the following quote is derived:

    “… It just drives me crazy when I hear this, and I laugh, and it’s usually people that never played basketball saying this, or people that never really scored when they did play basketball, saying, ‘Oh, he’s just a scorer.’ … ‘You know, he’s the best scorer, he’s not the best player.’ … Scoring isn’t everything in basketball, but I’ll be the first to tell you it is by far the main thing. The name of the game is getting buckets.” (Ekam Nagra – Episode 91 of the “Ball Don’t Stop” podcast)

    I understand the train of thought behind Nagra’s beliefs. A team’s efficacy on offense is entirely dependent on how frequently they score the ball. This is why a team’s Offensive Rating is so widely used; it measures how good a team was at performing its offensive duties. Therefore, the “best” offensive players make the largest scoring contributions. However, I think it’s a misstep to connect scoring on the team level to individual scoring on the player level. This claim relies on the belief that individual scoring is not the only way to positively influence a team’s offense. High-level shot creation that unclogs the floor and opens more efficient attempts is, in fact, usually more effective to the team compared to consistent “hero-ball” and isolation possessions.

    Scoring blindness is, as stated earlier, the propensity to rate players based on favorable points per game figures, and we see it in practice with the criteria Nagra uses the evaluate players:

    “The number one thing in basketball, the foundation of the game is putting the ball in the basket. The guys that did that the best are the guys that shined the brightest in the history of the game. They’re the ones that moved arenas, they’re the ones that sold jerseys, they’re the ones put teams on their back, the guys that are, you know, making sh*t happen on the basketball court.” (Ekam Nagra – Episode 91 of the “Ball Don’t Stop” Podcast)

    I’ll return to the tendency later, but Nagra consistently attributes questionable factors to a player’s “goodness,” such as the roar of the crowd, merchandising, and a touch of the “Lone Star Illusion” (the tendency to undervalue the effects of a supporting cast, another topic invoked by Thinking Basketball). A self-proclaimed former player, Nagra often relates the demanding environment of the NBA to street-ball or pick-up preferences:

    “It’s… it’s simple, you know, common f*cking sense. If me and you were to walk into a court today and, er, open run or tryout or whatever, the first guy that would stand out, the first guy we’d look for if we were smart, is the guy that’s putting the ball in the hoop.” (Ekam Nagra – Episode 91 of the “Ball Don’t Stop” Podcast)

    This reminds me of the mentality of middle or high-school roster selection, or the mindset of the young players, which pose the ultimate goal to be the best and brightest scorer. After all, almost everyone wanted to be the ones to hit the game winners and the clutch shots when they were young, and that means you would want to become the best scorer. As I dive deeper into Nagra’s evaluation style, I’ve become more convinced a lot of his rationale is based on his time as a player: who stood out and who appeared to be the best.

    Nagra gives another opinion that provides insight on how he relates scoring to team performance later on in the episode used for the aforementioned quotes:

    “But those teams that win, and these teams that are led, and teams that go far in the Playoffs, they’re the ones that have the best scorer on the floor… or the second-best scorer on the floor… at all times.” (Ekam Nagra – Episode 91 of the “Ball Don’t Stop” podcast)

    Because he doesn’t give any specific examples, we could investigate this claim to create a “stepping-off” point to see whether or not his claims are based on facts or the internal, intuitive feelings he conveyed earlier in the episode. To either confirm or deny this claim, we can look at the league-leaders in points per game in recent history and connect them with which round their teams advanced to in the second season. (He doesn’t give a specific round or the number of postseason games played to constitute teams that “go far in the Playoffs,” so I’ll assume the lower fence is a conference championship appearance.)

    If a (qualified) top-two finisher in points per game was on a team that advanced to the conference championship or further in the same season, he will receive a “Yes.” If a player’s team did not manage to reach the semi-finals, he will be denoted with a “No.”

    • 2019-20: James Harden (No) and Bradley Beal (No)
    • 2018-19: James Harden (No) and Paul George (No)
    • 2017-18: James Harden (Yes) and Anthony Davis (No)
    • 2016-17: Russell Westbrook (No) and James Harden (No)
    • 2015-16: Stephen Curry (Yes) and James Harden (No)
    • 2014-15: Russell Westbrook (No) and James Harden (Yes)
    • 2013-14: Kevin Durant (Yes) and Carmelo Anthony (No)
    • 2012-13: Carmelo Anthony (No) and Kevin Durant (No)
    • 2011-12: Kevin Durant (Yes) and Kobe Bryant (No)
    • 2010-11: Kevin Durant (Yes) and LeBron James (Yes)
    • 2009-10: Kevin Durant (No) and LeBron James (No)
    • 2008-09: Dwyane Wade (No) and LeBron James (Yes)
    • 2007-08: LeBron James (No) and Allen Iverson (No)
    • 2006-07: Kobe Bryant (No) and Carmelo Anthony (No)
    • 2005-06: Kobe Bryant (No) and Allen Iverson (No)

    During the last fifteen seasons, only 26.7% of either conference final series has sported one of the top-two finishers in points per game in the same season. Admittedly, this isn’t the largest sample there is, but it disproves that having one of the top-two volume scorers in the league guarantees a deep Playoff run. We’ve actually seen more of the opposite; teams seem to be more likely to appear in the conference finals without, say, a thirty points per game scorer. This isn’t to say a team’s leading scorer hurts his team (although he sometimes does), but that a dominating half-court “assassin” is not a prerequisite to a deep run in the postseason.

    Defensive Ignorance

    With the current state of information available at the hands of most, there was bound to be a lopsided partiality to offense compared to defense. Box scores will track the number of points, rebounds, assists, field-goals, and turnovers a player records in a given period, but defense is restricted to steals and blocks (personal fouls are usually associated with the defensive box score but also include offensive fouls). Nagra is no exception to this tendency, expressing a clear opinion in Episode 34 of his podcast, which covered the validity of the terminology given to “two-way players.”

    He immediately provides insight on how he distinguishes the best players:

    “You know, the foundation of this game, since day-one, will always be scoring. The defense, all that other stuff is a bonus.” (Ekam Nagra – Episode 34 of the “Ball Don’t Stop” podcast)

    As discussed earlier, this relates to the connection Nagra established between scoring on the team level with individual scoring on the player level. We have already concluded this connection is mostly false and overlooks the larger expanse of offensive contributions that leads to scoring output among teams, so it’s safe to say this mindset is setting up all further opinions that build on this principle for some level of failure.

    However, it seems the prioritizing of high-volume scorer extends further than the structure of the game Nagra lays out:

    “The most feared thing in basketball, till this day, is a guy that can walk into a game and effortlessly get you thirty, forty, and fifty [points].” (Ekam Nagra – Episode 34 of the “Ball Don’t Stop” podcast)

    “I’ve never seen a coach break his clipboard because of two-way players just being a two-way player.” (Ekam Nagra – Episode 34 of the “Ball Don’t Stop” podcast)

    “You know, those are the guys [scorers] that people remember forever…” (Ekam Nagra – Episode 34 of the “Ball Don’t Stop” podcast)

    The common denominator of each sentiment is the reactivity to surroundings, especially emotionally-driven ones: fear, anger, and remembrance. Yet, Nagra uses these elements to evaluate on-court impact. The individual perceptions of these game actions may not even roughly correlate to value as a player, but he continually treats them otherwise. This relates to my earlier inferences that suggest Nagra structures his knowledge of basketball around his experiences as a player. However, as we explore later, having played basketball at even the highest level does not guarantee a higher ability to evaluate players.

    During the same segments, Nagra explores what he believes to be an inherent disparity between offensive and defensive contributions, the former of which drastically outweighs the latter:

    “Carmelo Anthony on the Knicks… top-four player in the game. You know, I didn’t care if he played defense or not. The fact that he could walk into a game and singlehandedly change the outcome, and… you know, have an impact on the game with just his scoring ability – that right there is it for me.” (Ekam Nagra – Episode 34 of the “Ball Don’t Stop” podcast)

    “Hey, if you’re a good defensive player, you’re a good defensive player. If you can score the hell out of the ball, you know, you’re a killer, you’re an assassin out there.” (Ekam Nagra – Episode 34 of the “Ball Don’t Stop” podcast)

    “You know, Michael Jordan and Kobe Bryant were the same way [skilled on offense and defense]. Like, I never saw anyone dub them as ‘two-way players.’ They were just the best players in the game… Them playing defense was a bonus.” (Ekam Nagra – Episode 34 of the “Ball Don’t Stop” podcast)

    Defense is consistently treated as a secondary trait, a bonus, to offense. Nagra suggested no other skill in basketball matters if, at the end of the day, the ball wasn’t going in the basket. He doesn’t hold this to be self-evident; rather, the rules of basketball (which require a bucket to be had) make it so. This is more antithetical to how basketball is played than Nagra gives credit for. Through the entirety of his segments that cover scoring or defense, he doesn’t address that the magnitude of a two-point basket on offense is equal to that of a two-point basket allowed on defense. If the world’s greatest offensive player is worth 1.3 points per team possession but allows 1.3 points per possession on defense, he’s not helping his team win at all!

    “Correctness”

    The last revealing quotation from Episode 34 comes with his disagreement on the soundness of dubbing “two-way” play:

    “What the f*ck is a two-way player? Like, who came up with this concept? You know, if you look back at it, like… I never heard this in the ‘90s. I never heard this in the 2000s.” (Ekam Nagra – Episode 34 of the “Ball Don’t Stop” podcast)

    Nagra displays a clear bias toward styles of basketball that align with the styles of play that were most prevalent in his youthhood, with a strong emphasis on jump shots. During Episode 36, he provides this excerpt on a tendency he observed upon LeBron James’s arrival in Miami:

    “I didn’t like it when he [LeBron James] went to the Miami Heat and he was like, ‘Hey, I’m not gonna shoot threes anymore; or, I’m gonna shoot less jumpers.’ … I didn’t feel like that was pure. You know, you can’t really cheat the game. You can’t be… like, it is what it is. You gotta make jump shots. In basketball, the foundation is ‘get a bucket,’ score a jump shot, all these things. You know, they matter.” (Ekam Nagra – Episode 36 of the “Ball Don’t Stop” podcast)

    During his discussion on why he believed Kawhi Leonard was the second-best player in basketball, Nagra heavily implies a “proper” or “correct” version of basketball exists that some of the league’s players have violated. He, again, refers to his foundation of the game (to get a bucket), the misinterpretation of which already dilutes the quality of any appendages, but then extends it to: “You gotta make jump shots.” To improve the team’s offense, it would be undeniably more effective for the unit to score fifty-five easy layups (if those were somehow available) than to score thirty, forty, or even fifty-four of the most difficult mid-range shots in league history. After all, the team that scores the most wins!

    Nagra’s inclinations toward his most prized styles of play signal heavy biases, and ones that cloud the truth behind “effective” basketball play as ones that are flashy, memorable, and visually remarkable. Thus, I don’t immediately absorb the opinions he states as ones of proper consideration, rather ones driven by personal preferences that don’t relate to the “true” topic at hand, which makes these claims nothing more than opinions in a sea of truth and falsehood.

    We’ll fast-forward to Episode 211 of the Ball Don’t Stop podcast, in which Nagra an All-Rookie and All-Defensive former NBA player in Josh Smith. When Nagra asks Smith what the latter’s reaction was upon the arrival of the analytics revolution, Smith replies with:

    “It [the analytics revolution] felt weird because… you know, when you start playing basketball, you’re taught the game the right way. You know, like, you know, mid-range, layups, three-pointers, you know, like… getting your teammates the ball… You gotta start inside out.” (Josh Smith – Episode 211 of the “Ball Don’t Stop” podcast)

    There’s a recurring theme in the “Ball Don’t Stop” podcasts that distinguish a “proper” way to play the game, one that paves the way for Nagra’s (and former players alike) distaste of basketball analytics and advanced statistics.

    Authority

    Among the pillars of traditional values stated earlier was the extreme value of having experienced the competitive and rigorous environment of professional or semi-professional basketball play. If such a trait doesn’t reside within the individual, he or she is automatically less able to discuss the evaluations of a player at a higher level.

    During Episode 211, he interviews an All-Rookie and All-Defensive former NBA player in Josh Smith. Nagra wastes no time in expressing disinterest in the analytics revolution and modernized statistics:

    “I feel like the game now, as talented as it is, as athletic as it is, they’ve [analytics and its supporters] kind of dumbed it down, the way it’s played, man; and like, it’s just weird to me.” (Ekam Nagra – Episode 211 of the “Ball Don’t Stop podcast)

    As we’ll explore later, Nagra sees the analytics revolution and its associated forthcoming as having deteriorated the play of the game, crucial context for later excerpts. Smith follows later in the episode with his own take on how players approach analytics:

    “As a player, how can you listen to a person that never played the game of basketball? ‘Cause most of those analytical guys… have never played a game of basketball, so they don’t have a feel of… what’s really going on… and time and situation and… the mental aspect of the game… You can’t put that in the analytics.” (Josh Smith – Episode 211 of the “Ball Don’t Stop” podcast)

    Smith certainly doesn’t speak for all players, especially the recently-employed more familiar with the analytical setting (Smith played his last full season in 2015-16), but there seems to be some notable stigma towards the analytics departments of NBA teams among players. They feel, as few to none of the analysts were players themselves, the analysts are not as qualified to dictate the tendencies and playstyles of those that are or were experienced as NBA players. Smith said that the lack of hands-on experience prohibited analytics developers from comprehending and incorporating the necessary elements.

    I’ve never played in the NBA, so perhaps there’s something that I’m missing, but no matter who you are or what your experience with basketball is, the exact same forty-eight minutes of play (barring overtime) is available to any and all who can watch. At the end of the day, all of the court actions that a player is involved in can be absorbed by an outside observer. Granted, the comprehension of these court actions is a skill, and one that requires great knowledge and practice; but the only aspect of the game that a non-player can’t directly recognize is the “mental” aspect: what flows through the players’ minds. The ability to experience these may add context to the triggers behind varying neurological patterns in certain moments; but as Nagra continuously states, victory is crowned by scoring more than the opponent. No aspect of a player’s impact is exclusive to former or current players.

    As Nagra and Smith continue their conversation, the latter gives more of his thoughts on how analytics is changing the game and, more specifically, how it affects the NBA as a show business:

    “It’s sad, because… I feel like it’s gonna eventually take… the ratings are gonna start going down because… like, the exciting part of the game was dunking on motherf*ckers… like, putting that sh*t in the rim, putting they *ss in the rim… It’s like, all these threes and layups and floaters and sh*t… It’s taking the excitement out of the game.” (Josh Smith – Episode 211 of the “Ball Don’t Stop” podcast)

    Smith clearly connects his distaste of analytics to how it affects the style of the game, an aspect for which Nagra also expressed concern. It’s not unreasonable to say that the pace-and-space style of basketball spurred by analytics makes the viewing experience less exciting, but then again, analytics were not created to improve game ratings. Analytics were created to give players and teams the highest odds to win. Advanced statistics and impact metrics aim to quantify and structure a player’s or team’s impact, not either’s likelihood of increasing viewer count. Thus, I see Nagra and Smith’s concern with analytics as not only misguided but untrue to the nature of its creation. Advanced statistics are not boosters of the NBA as a show business; they aim to provide explanatory and predictive power to help players and teams understand what happens on the court and to improve for the future.

    I went into this examination of “traditional” thinking with an open mind, even hoping to add a piece or two of its process to my own if I were to find the right evidence. Unfortunately, I don’t feel I’ve been given any more reason to revert to traditionalism given the alternatives (i.e. analytics). Nagra does not speak for all traditionalists and Smith doesn’t speak for all players, but the brief taste I had of their ideologies was nothing more than unimpressive. They aspire for a desirable style of play that, along with the growth of data and information, became obsolete. Now, there’s certainly nothing wrong with deprecating the current style of play as it pertains to the watching experience, but the same practice in evaluating players and teams is a method doomed for failure.

    Nagra peddles the belief that experience, or the lack thereof, is the problem in today’s game. To me, it’s less an issue stemming from experience, but the unrelenting tendency to hold onto ideals and the inability to adapt to an evolving game.