Author: chromeder

  • NBA All-Star Power Rankings (1/2/22)

    NBA All-Star Power Rankings (1/2/22)


    Ladies and gentlemen, welcome back to another edition of my NBA All-Star Power Rankings series! Here, I’ll detail the current landscape of the league’s best players and condense my thoughts into one All-Star ballot. Players will be arranged into tiers based on their level of play, which is entirely based on the degree of impact the player provides by helping teams gain higher seeding and home-court advantage for the Playoffs. To add a final disclaimer:

    This list is not my “prediction” of the league’s actual All-Star teams lineups. This is a reflection of my evaluations of players, and where that would place them in the NBA’s award hierarchy.


    Within the league’s top-25 or so players is a group that has fully established itself as All-Star-caliber (or better). There’s little to no doubt in my mind that these players should be headed to Cleveland in February.

    • Giannis Antetokounmpo (East)
    • Jimmy Butler (East)
    • DeMar DeRozan (East)
    • Kevin Durant (East)
    • Joel Embiid (East)
    • James Harden (East)
    • Zach LaVine (East)
    • Trae Young (East)
    • Mike Conley (West)
    • Stephen Curry (West)
    • Anthony Davis* (West)
    • Luka Doncic (West)
    • Paul George* (West)
    • Rudy Gobert (West)
    • Draymond Green (West)
    • LeBron James (West)
    • Nikola Jokic (West)
    • Donovan Mitchell (West)
    • Ja Morant (West)
    • Chris Paul (West)
    • Karl-Anthony Towns (West)

    Because these are players whom I firmly believe are All-Stars, I won’t belabor any points. I will address the two asterisks next to Anthony Davis’s and Paul George’s names, which were added due to uncertainty surrounding their injury status come February. Davis and George are both currently out with a sprained MCL and a torn elbow ligament, respectively. Both will be re-evaluated in a few weeks’ time.


    The “Probably” group includes players I currently believe are All-Star-level, but I may not be entirely sold on their status. A lot of these players will make my final ballot, but whether it be injuries, a lack of signals, or general uncertainty about their playstyle, I distinguish them from those I wholeheartedly believe are All-Stars.

    • Bam Adebayo (East)

    A unique mold of player for the modern game, Adebayo is on track to replicate his All-Star success from the last two seasons. He provides a level of spacing as a threat from the mid-range (39% on 8.6 attempts per 75) to tie into a strong overall scoring package, which he pairs with elite defense that has remained on the perennial DPOY watch.

    • Bradley Beal (East)

    Beal’s outside shooting slumped out of the gate, which was an attribute of his that was crucially valuable to an elite off-ball package. Resultantly, I can’t view him as an All-Star lock, but his passing and shot creation have been trending upward, which boosts his value in a floor-raising role, also helping to mask his questionable defensive play.

    • Jrue Holiday (East)

    Holiday is a player that provides a ton of value that the box score doesn’t capture. Adjusted Plus/Minus models have always looked fondly upon his shooting, passing, and tough brand of point-of-attack defense. After a while, it becomes hard to ignore what the analytics are communicating.

    • Khris Middleton (East)

    Minutes played alongside the Greek Freak have depleted Middleton’s scoring punch so far, (Middleton averages 28.5 points per 75 on 59% True Shooting as the lone star.) but his skills have still carried over: spacing, passing, and shot creation. My only setback is how those skills map to his overall impact; the metrics are concerningly low on Middleton thus far.

    • Jayson Tatum (East)

    After a rapid ascension in 2020, Tatum seems to have stagnated slightly. His shooting and scoring have been in decline, and he doesn’t have the playmaking chops like Lillard to make up for some of that value. He’s otherwise adding some on defense. This is one of many “Playoffs will tell” cases.

    • Damian Lillard (West)

    Lillard feels like an obvious choice most other seasons. The only reason I put him here is his early-season shooting slump. He’s quickly picked up where he left off previously, but his struggles have dented his scoring effectiveness and have slightly offset the continued value he brings as an elite playmaker.


    The league’s talent pool is stacked, and as a result I nearly overwhelmed the nominal threshold of an All-Star player being within the sport’s top-25. Since there’s a numerous amount of other players that provide impact in similar vain to these “probable” stars, the “maybe” talents serve as high sub-All-Stars and potential injury replacements.

    • Jarrett Allen (East)
    • LaMelo Ball (East)
    • Darius Garland (East)
    • Fred VanVleet (East)
    • Devin Booker (West)

    Again, perhaps these players could be viewed as legitimate All-Stars. The 2022 season hasn’t fully taken shape yet, which could mean rearrangement among the previous two tiers. I’m on the absolute fence with some of these players (e.g. Booker and Conley), whether it be more lack of indicators or too little room in the actual ballot.

    Note: I’m omitting the “Not Quite There” tier from previous editions of this series due to the influx of information that comes as the season progresses.

    Final Ballot

    Once again, we reach the trickiest part of this exercise. It was difficult enough to sort the closest calls, but the task extends when putting these players into their All-Star slots. Similar to the previous editions, the ballots are structured to include two teams for either conference: five starters with two backcourt and three frontcourt players, five reserves (same restrictions), and two “wild cards” (no positional restrictions).

    Eastern Conference


    • G: James Harden
    • G: Trae Young
    • F: Giannis Antetokounmpo
    • F: Kevin Durant
    • C: Joel Embiid


    • G: DeMar DeRozan
    • G: Zach LaVine
    • F: Jimmy Butler
    • F: Jayson Tatum
    • C: Bam Adebayo

    Wild Cards:

    • W: Jrue Holiday
    • W: Khris Middleton

    The two closest calls here were 1) whether to give the last frontcourt reserves slot to Adebayo or Middleton and 2) whether to give the second wild-card slot to Middleton or Bradley Beal.

    Western Conference


    • G: Stephen Curry
    • G: Luka Doncic
    • F: LeBron James
    • C: Rudy Gobert
    • C: Nikola Jokic


    • G: Damian Lillard
    • G: Donovan Mitchell
    • F: Anthony Davis*
    • F: Paul George*
    • C: Karl-Anthony Towns

    Wild Cards:

    • W: Chris Paul
    • W: Draymond Green

    Given the injuries to Davis and George persist, the roster would be rearranged to bump Draymond Green up to a frontcourt reserve slot, give Mike Conley the vacant wild card slot, and move Kristaps Porzingis into the second frontcourt reserve slot.

    Data from:


  • Introduction to Cryptbeam Plus/Minus (CrPM)

    Introduction to Cryptbeam Plus/Minus (CrPM)

    I talk about NBA impact metrics a lot; and as most familiar with my content know, I’ve even created a few. Now, I’m ready to add another player to the mix: “Cryptbeam Plus/Minus” (CrPM). With the metric’s namesake being the title of this website, CrPM joins a long line of composite metrics that aim to identify the difference-makers of the sport through quantitative analysis. Why? As the creator of Player-Tracking Plus/Minus (PTPM), Andrew Johnson, once said: “Because what the world needs now is another all in one basketball player metric.” [1]


    CrPM draws most of its inspiration from two established impact metrics in Jacob Goldstein’s Player Impact Plus/Minus (PIPM) and Ben Taylor’s Augmented Plus/Minus (AuPM). The commonality of these three metrics is the shared “branch” of metric: I tend to differentiate between impact metrics by one of three types:

    • Box: a composite metric that is calculated using the box score only
    • Hybrid: a composite metric that is calculated using counting statistics outside the box score (e.g. player tracking and on-off data) — but may also include the box score
    • APMs: a composite metric that uses ridge-regressed lineup data as the basis of its calculation

    As for where CrPM falls under these categories, it’s formally a hybrid metric. The metric can be broken into two major component: a box score term and a plus-minus term. The box score “version” of CrPM can function as an impact metric on its own as an estimator of impact via traditionally-recorded counting stats: points, rebounds, assists, etc. Using Regularized Adjusted Plus/Minus (RAPM) as a basis, the box score is regressed onto this target to estimate a player’s per-possession impact on his team’s point differential.

    Two plus-minus statistics are then added to the box-score estimate to create CrPM: on-court Plus/Minus, which is a team’s per-100 point differential (Net Rating) with a player on the floor, and on-off Plus/Minus, which subtracts the team’s Net Rating with a given player off the floor from his on-court rating. The goal of the plus-minus component is to fill in some of the gaps left in the immeasurable, e.g. what the box score can’t capture. Testing of the model did later reinforce this idea.

    Regression Details

    The regressions for both the box score and plus-minus variants of the metric were based on fourteen years of player-seasons from Jeremias Engelmann’s xRAPM model. (This means that, in the RAPM calculation, a player’s score is pushed toward the previous season rather than zero.) This provided a more stable base for the regression to capture a wider variety of player efficacy in shorter RAPM stints. Additionally, the penalization term for each season was homogenized to improve season-to-season interpretability.

    The box score is not manipulated in the CrPM calculation outside of setting the stats as relative to league averages. The raw plus-minus terms, however, use minutes played as a stabilizer to draw results closer towards zero as playing time decreases. While some incorrectly label a larger sample size as more accurate, this adjustment serves to reduce variance in smaller samples to decrease the odds for larger error in these spots. These two branches of NBA statistics combine to create CrPM. [2]

    The regressions, especially the box score ones, were all able to explain the variability in the target RAPM with a surprising degree of accuracy. The R^2 values for combined in and out-of-sample RAPM ranged from 0.725 to 0.750 for the box-score metrics and bumped up to 0.825 with plus-minus included. A large concern for most ordinary linear regressions is heteroskedasticity, which is when error rates become larger as the predicted variable increases. The breadth of performance captured in the RAPM target mitigated this, and CrPM serves as an accurate indicator of impact for average players and MVP players alike.

    • Target response of RAPM was collected from Jeremias Engelmann’s website.
    • Box scores and plus-minus data were collected from Basketball-Reference.

    Current MVP Ladder

    Because CrPM serves as an indicator of a player’s impact, it can do a solid job of identifying viable candidates for the league’s MVP award. Through the 18th of December, here are the top-10 players of the 2022 season with at least 540 minutes played per the metric:

    1. Nikola Jokic (+11.8)

    The reigning MVP has started his follow-up campaign with a bang, and looks to be the frontrunner to snag the award again. His placement in the box-score component of the metric (+12.4 per 100) would be first among all players since 1997 with at least 1,500 minutes played during the season. Jokic’s overall score of +11.8 in CrPM is tied with LeBron James’s legendary 2009 seasons for the best regular season on record.

    2. Giannis Antetokounmpo (+9.4)

    Voter fatigue in recent seasons has downplayed the regular-season greatness of the Greek Freak, but he seems as good as ever according to CrPM. Each of his last three seasons are top-45 seasons since 1997 per the metric, with his dominating MVP run in 2020 ranking fourth (+10.8) among all high-minute players on record.

    3. Joel Embiid (+6.6)

    The metric suggests Embiid provides massive two-way value, with his marks on offense and defense being nearly identical in both the box-score and plus-minus versions of the metric. Despite a shooting slump to start the season that followed an exceptional mid-range campaign for the big man, he still adds a ton of value in Philadelphia. So far, the 76ers outscore opponents by +4.3 per 100 when Embiid is on the floor and are +9.2 points better with him in the lineup.

    4. Rudy Gobert (+6.5)

    It’s not an NBA regular season nowadays without the analytics looking upon Rudy Gobert with perhaps a little too much enthusiasm. Regardless, he’s still a surefire candidate for the DPOY Award and a probable finalist, if not winner. Almost all of his impact comes from the defense end, adding only +0.4 points per 100 in the offensive component of CrPM, with the remaining +6.1 points coming from his all-time-level rim protection and paint anchoring.

    5. Stephen Curry (+5.7)

    Curry’s plus-minus portfolio isn’t as transcendent as it was during his all-time seasons in the mid-2010s, but a revamped Golden State roster that amplifies his strengths boosts those numbers into the upper echelon of NBA superstars once more. The Warriors outscore opponents by +14.1 points per 100 with Curry on the floor and are +12 points better with him on the court. While the box score can’t capture all of the value he brings to the table, Curry still looks like one of the best players in the league according to CrPM.

    6. Kevin Durant (+5.5)

    Curry’s former teammate is another shooting savant who continues to string together legendary offensive seasons with league-best marks in both scoring volume and efficiency. He’s arguably the greatest mid-range shooter in NBA history and makes Brooklyn’s offense great with these shots alone. Speaking of, the Nets look like a surefire title contender with Durant on the floor, when they outscore opponents by +7.3 points per 100 possessions.

    7. Clint Capela (+4.6)

    While I don’t think Clint Capela has been a top-10 player in the league this year, his placement illustrates arguably the biggest sign of caution I’d address when using CrPM. Because the box-score component receives a whole lot of the weight in the plus-minus-included formula, the metric is overly sensitive to defensive rebounds and stocks. Especially in the modern league, when spacing affects statistics like rebounds to a higher degree than ever, Capela is a case of, while being a valuable player nonetheless, a stylistic disadvantage of CrPM.

    8. Jarrett Allen (+4.5)

    I’m similarly not as fond with Allen’s actual ranking among the league’s best, but he’s been sneakily good this season. The Cavaliers have clearly stocked up on Michael’s Secret Stuff for 2022, because they’ve been better than the Nets with Durant when they put Jarrett Allen in the game. Cleveland outscores its opponents by +8.4 points per 100 with Allen in the lineup! One of the sport’s emerging two-way talents receives well-deserved credit in the analytics.

    9. Karl-Anthony Towns (+4.4)

    Towns has played like an all-league star for a while, and now that his longtime home of Minnesota has found its footing in 2022, his value is more evident than ever. CrPM views Towns as a clear value-add on offense and defense, and this is enough to make him look like a candidate for the All-NBA second team this year. He’s one of the On-Off kings so far, posting a +13.1 Net Plus/Minus in a similar vain to other top-player candidates.

    10. Jimmy Butler (+4.4)

    If this list were box-score only, Butler would be several spots higher with his +6.3 score in Box CrPM; however, plus-minus doesn’t look upon him like the other players on this list entering 2022. Miami plays like a surefire postseason team with him on the court, but they actually perform +2.4 points better with him off the floor! While this is very, very likely just noise that accompanies most plus-minus data like this, it doesn’t serve as a very good indicator of his impact, thus compressing his score in plus-minus-included CrPM.

    Full 2022 Leaderboard

    Nikola JokićDEN247837.93.911.8
    Giannis AntetokounmpoMIL268495.53.99.4
    Joel EmbiidPHI196293.33.36.6
    Rudy GobertUTA299200.46.16.5
    Stephen CurryGSW289625.20.55.7
    Kevin DurantBRK2710005.30.25.5
    Clint CapelaATL298640.24.44.6
    Jarrett AllenCLE289131.92.64.5
    Karl-Anthony TownsMIN289633.01.44.4
    Jimmy ButlerMIA186074.20.24.4
    LaMelo BallCHO258283.21.24.4
    DeMar DeRozanCHI248464.9-0.64.3
    Trae YoungATL299906.2-2.04.2
    Montrezl HarrellWAS317993.30.94.2
    Myles TurnerIND30887-
    John CollinsATL299392.41.53.9
    LeBron JamesLAL186673.10.73.8
    Chris PaulPHO289063.60.33.8
    Jusuf NurkićPOR307520.63.23.8
    Dejounte MurraySAS289632.21.63.8
    Donovan MitchellUTA289104.1-0.63.5
    Jonas ValančiūnasNOP319801.52.03.5
    Domantas SabonisIND3110571.91.53.4
    Jrue HolidayMIL258193.00.43.3
    Kristaps PorziņģisDAL216341.41.93.3
    Jaren Jackson Jr.MEM297870.23.13.3
    Jayson TatumBOS3010952.30.93.2
    Andre DrummondPHI29571-
    Fred VanVleetTOR2810602.70.43.1
    Anthony DavisLAL279551.02.23.1
    LaMarcus AldridgeBRK255901.81.33.1
    D’Angelo RussellMIN247812.90.13.0
    Miles BridgesCHO3111351.91.02.9
    James HardenBRK269421.90.92.8
    Richaun HolmesSAC225961.51.32.8
    Al HorfordBOS247110.22.42.6
    Luka DončićDAL217352.30.22.5
    Bobby PortisMIL257110.52.02.5
    Alperen ŞengünHOU29538-
    Jarred VanderbiltMIN28682-
    Daniel GaffordWAS28601-
    Damian LillardPOR248733.9-1.62.3
    Patrick BeverleyMIN215521.30.82.1
    Ja MorantMEM196193.0-0.92.1
    Wendell Carter Jr.ORL308650.21.82.0
    Evan MobleyCLE25840-
    Mike ConleyUTA267273.2-1.21.9
    Deandre AytonPHO206250.51.51.9
    Malcolm BrogdonIND258832.7-0.81.9
    Devin BookerPHO216763.1-1.21.9
    Robert WilliamsBOS23638-
    Derrick RoseNYK266362.2-0.41.8
    Paul GeorgeLAC248610.61.21.8
    Darius GarlandCLE299913.0-1.31.8
    Draymond GreenGSW28849-
    Jakob PoeltlSAS216060.51.11.6
    Nikola VučevićCHI20663-
    De’Anthony MeltonMEM27654-
    Bam AdebayoMIA185920.41.11.5
    Ricky RubioCLE318801.20.31.5
    Brandon IngramNOP248552.3-0.81.5
    Cole AnthonyORL237851.9-0.51.4
    Alex CarusoCHI24685-
    Mo BambaORL27774-
    Monte MorrisDEN298752.4-1.11.3
    Zach LaVineCHI279483.1-1.81.3
    Shai Gilgeous-AlexanderOKC258731.9-0.61.2
    Jalen BrunsonDAL277952.7-1.51.2
    Pascal SiakamTOR175861.10.11.2
    Mitchell RobinsonNYK27653-
    Aaron GordonDEN299451.2-0.21.1
    Devin VassellSAS235590.11.01.1
    Tyus JonesMEM306341.8-0.71.1
    Cedi OsmanCLE255521.3-0.21.1
    Kevon LooneyGSW30564-
    Deni AvdijaWAS31672-
    Christian WoodHOU28888-
    Desmond BaneMEM308631.3-0.31.0
    Anthony EdwardsMIN2810060.50.51.0
    Khris MiddletonMIL216501.00.01.0
    Immanuel QuickleyNYK296331.8-0.90.9
    Andrew WigginsGSW299011.7-0.80.9
    Gary Trent Jr.TOR279330.60.20.8
    Ivica ZubacLAC30742-
    Kyle AndersonMEM26565-
    Alec BurksNYK297740.40.30.6
    Caris LeVertIND236681.3-0.70.6
    Cody MartinCHO297990.10.40.6
    Tyrese HaliburtonSAC289300.10.40.5
    Larry Nance Jr.POR30650-
    Scottie BarnesTOR279730.10.40.5
    Tyrese MaxeyPHI289691.9-1.50.5
    Josh HartNOP247560.10.30.4
    Gordon HaywardCHO3110521.4-1.00.4
    CJ McCollumPOR248481.4-1.10.3
    Mikal BridgesPHO289630.30.00.3
    Tobias HarrisPHI217200.7-0.40.3
    Lonzo BallCHI27958-
    Jordan ClarksonUTA297301.3-1.00.2
    Steven AdamsMEM30754-
    OG AnunobyTOR165880.5-0.30.2
    Marcus SmartBOS29991-
    Kelly Oubre Jr.CHO319031.1-1.00.1
    Lauri MarkkanenCLE226640.3-0.20.1
    Kyle LowryMIA289620.9-0.90.1
    Devonte’ GrahamNOP288761.3-1.20.1
    Will BartonDEN258250.6-0.60.0
    Grayson AllenMIL308750.7-0.70.0
    Derrick WhiteSAS288750.3-0.4-0.1
    T.J. McConnellIND245810.4-0.5-0.1
    Franz WagnerORL319940.3-0.4-0.1
    Jerami GrantDET24797-0.10.0-0.2
    Danny GreenPHI23558-2.01.8-0.2
    Russell WestbrookLAL3010780.2-0.4-0.2
    Mason PlumleeCHO22562-1.61.5-0.2
    Patty MillsBRK309051.6-1.8-0.2
    Luke KennardLAC308700.8-1.1-0.2
    Herb JonesNOP28766-1.71.4-0.3
    Bradley BealWAS2810051.6-1.9-0.3
    Jae CrowderPHO28789-1.51.2-0.3
    Nassir LittlePOR26603-1.61.3-0.3
    Keldon JohnsonSAS278290.1-0.5-0.4
    George HillMIL266860.1-0.5-0.4
    Royce O’NealeUTA27833-1.40.9-0.5
    Bojan BogdanovićUTA298641.8-2.2-0.5
    Jordan PooleGSW288600.8-1.2-0.5
    Reggie JacksonLAC309921.1-1.6-0.5
    Gabe VincentMIA275320.3-0.8-0.5
    Jae’Sean TateHOU30844-0.80.2-0.6
    Cade CunninghamDET23745-1.71.1-0.6
    Lonnie WalkerSAS27611-0.1-0.5-0.6
    Norman PowellPOR268251.0-1.6-0.6
    Terry RozierCHO227080.5-1.1-0.7
    Bogdan BogdanovićATL205640.5-1.2-0.7
    Josh RichardsonBOS225550.1-0.8-0.7
    Shake MiltonPHI256360.0-0.8-0.8
    Carmelo AnthonyLAL30828-0.3-0.5-0.8
    Georges NiangPHI286620.2-1.0-0.8
    Anfernee SimonsPOR266181.3-2.2-0.8
    Harrison BarnesSAC258360.2-1.1-0.9
    De’Aaron FoxSAC299930.5-1.4-0.9
    Matisse ThybullePHI23555-3.62.7-0.9
    Danilo GallinariATL26568-0.1-0.8-0.9
    Isaiah StewartDET26668-2.71.8-0.9
    Cameron JohnsonPHO28682-0.6-0.3-0.9
    Raul NetoWAS30607-0.2-0.8-0.9
    Seth CurryPHI279291.1-2.0-1.0
    Pat ConnaughtonMIL32929-0.4-0.6-1.0
    Dennis SchröderBOS278940.8-1.9-1.0
    Kevin HuerterATL287740.2-1.3-1.0
    Malik MonkLAL28666-0.2-0.8-1.0
    Tyler HerroMIA258220.5-1.5-1.1
    Buddy HieldSAC308570.0-1.1-1.2
    Julius RandleNYK301063-1.30.0-1.2
    Joe InglesUTA297180.2-1.5-1.3
    Spencer DinwiddieWAS267620.2-1.4-1.3
    Grant WilliamsBOS28618-1.0-0.3-1.3
    Tim Hardaway Jr.DAL28878-0.1-1.2-1.3
    Precious AchiuwaTOR22579-2.81.3-1.4
    Terance MannLAC29829-0.5-1.1-1.6
    Josh GiddeyOKC26779-2.20.6-1.6
    Chris DuarteIND29843-1.0-0.6-1.6
    P.J. TuckerMIA30856-1.2-0.5-1.6
    Bruce BrownBRK24539-2.50.9-1.7
    Kyle KuzmaWAS29937-2.30.6-1.7
    Dorian Finney-SmithDAL28899-1.80.0-1.8
    Davion MitchellSAC29744-0.3-1.6-1.9
    Robert CovingtonPOR30822-4.22.2-2.0
    Luguentz DortOKC26841-0.3-1.7-2.0
    Eric GordonHOU257450.0-2.0-2.0
    Furkan KorkmazPHI27600-1.0-1.1-2.1
    Nickeil Alexander-WalkerNOP31877-1.3-0.8-2.1
    Kevin Porter Jr.HOU19574-2.20.1-2.2
    Dwight PowellDAL28536-1.8-0.4-2.2
    Duncan RobinsonMIA30849-1.3-0.9-2.2
    Isaac OkoroCLE23663-1.3-1.0-2.3
    Jeff GreenDEN29732-0.9-1.4-2.3
    Eric BledsoeLAC30787-2.4-0.1-2.5
    Chuma OkekeORL25562-3.51.1-2.5
    Cam ReddishATL25558-1.5-1.0-2.5
    Landry ShametPHO27562-0.6-2.0-2.5
    RJ BarrettNYK25784-1.4-1.2-2.5
    Kentavious Caldwell-PopeWAS31906-2.0-0.5-2.6
    Justin HolidayIND25693-1.2-1.5-2.7
    Darius BazleyOKC28765-4.51.9-2.7
    Frank JacksonDET28620-0.6-2.1-2.7
    Killian HayesDET23602-2.90.1-2.9
    Facundo CampazzoDEN28567-1.9-1.0-2.9
    Jeremiah Robinson-EarlOKC28608-2.90.0-3.0
    Jalen SuggsORL21583-3.1-0.1-3.2
    Saddiq BeyDET28897-2.2-1.1-3.3
    Evan FournierNYK30857-1.6-1.8-3.4
    Jaden McDanielsMIN26646-3.90.5-3.4
    Malik BeasleyMIN29750-1.7-1.8-3.4
    R.J. HamptonORL29536-2.4-1.1-3.5
    Garrett TempleNOP29532-4.20.5-3.6
    Avery BradleyLAL26599-3.1-0.9-4.0
    Gary HarrisORL24651-2.1-2.2-4.3
    Terrence RossORL28715-2.4-2.3-4.8
    Reggie BullockDAL27646-3.1-1.7-4.8
    Jalen GreenHOU18555-3.9-2.6-6.5

    Updated Dec. 18, 2021

    [1] Read Johnson’s article, a primer on PTPM, here.

    [2] Because Basketball-Reference doesn’t report plus-minus for offense and defense as liberally as it does combined plus-minus, the offensive / defensive splits for CrPM are slightly less accurate than its total version.

  • NBA All-Star Power Rankings (11/8/21)

    NBA All-Star Power Rankings (11/8/21)


    As the dust of the early season starts to settle, albeit to a degree that leaves lots to be desired, it’s around the time we begin to think about how the upcoming All-Star teams will take shape. With twelve spots to fill in each conference, the following excerpts will detail my current selections for the teams based on how these players are providing material, observable impact that helps teams win basketball games.

    Similar to my previous All-Star post for last season, players will be sorted into tiers based on my evaluations of their degree of impact, with “better” players being more likely to make the final ballot while some players may be on the fringe, fighting with similarly valuable players for the final spots.


    The tier of “absolutely” consists of players for whom I have minimal doubt are playing at an All-Star level or better. Namely, if they either sustain strongly resemble their current level of play, they will continue to make my succeeding ballots.

    • Giannis Antetokounmpo (East)
    • Jimmy Butler (East)
    • Stephen Curry (West)
    • Luka Doncic (West)
    • Kevin Durant (East)
    • Joel Embiid (East)
    • Paul George (West)
    • Rudy Gobert (West)
    • Nikola Jokic (West)
    • Donovan Mitchell (West)
    • Karl-Anthony Towns (West)
    • Trae Young (East)

    I pegged all of these players as All-Stars or better last year, meaning there are no newcomers so far. Compared to last year’s All-Star post (about a month into the season), this tier is thinned out, which is consistent with staying wary of the early season; the target of this exercise is to recognize tangible value that players provide to basketball teams, and each of these players provides established All-Star value.


    The “probably” tier is interesting. I’ve described many of these players as All-Star level or better in the past before, and will also likely remain All-Star-type players or better in my evaluations at the end of the season. However, there’s something to be missed in their performance so far, whether it’s aging, slumps, or uncertainties about their impact.

    • Bam Adebayo (East)
    • Devin Booker (West)
    • Mike Conley (West)
    • Anthony Davis (West)
    • James Harden (East)
    • LeBron James (West)
    • Zach LaVine (East)
    • Damian Lillard (West)
    • Ja Morant (West)
    • Chris Paul (West)
    • Jayson Tatum (East)

    The sore spot of this tier is clearly LeBron James. After nearly two decades of MVP-level play, we’re very likely partway through the beginning of the end of his reign of terror. Aging isn’t on his side, and thus he’s not pressuring the rim or attacking defenses through his passing in the same manner he would during his annual Playoff ascensions.

    A few of these names are mostly obvious All-Star performers, such as Anthony Davis and Damian Lillard. Whether it be rustiness due to injury or unlucky shooting, there’s that small degree of uncertainty that loosens their cases for the 2022 season. The remainder of the tier consists of either lower-level All-Star players or strong fringe members, such as Zach LaVine and Ja Morant.


    While some of these players are of comparable value to those in the tier above, most of these players are closer to injury replacements than legitimate All-Star contributors.

    • LaMelo Ball (East)
    • Bradley Beal (East)
    • Shai Gilgeous-Alexander (West)
    • Montrezl Harrell (East)
    • Tobias Harris (East)
    • Jrue Holiday (East)
    • Kyle Lowry (East)
    • Khris Middleton (East)
    • Domantas Sabonis (East)

    A name I feel the need to address here is Montrezl Harrell. With the benefit of hindsight that will come in the following months, I heavily doubt he will stay in this tier, but there are intriguing signals. He’s not overly dependent on perimeter creation as a finisher, and he’s had a significant spike in free-throw rate, drawing fouls and providing hyper-efficient scoring. It also doesn’t hurt that the impact metrics absolutely adore him.

    LaMelo Ball is a player I felt quite comfortable placing in this tier. I don’t think his outside shooting is sustainable, but his passing is off the charts and his shot creation has steadily improved from last season. As he continues to add value in the big-two skill sets of scoring and playmaking, he’ll develop into a viable offensive engine who can quarterback strong efforts in the Playoffs.

    “Not quite there”

    As the name suggests, this tier recognizes players that are more of honorable mentions that serious All-Star candidates. Namely, these are the players who I felt the need to consider in the process of creating my ballot; but after further research, decided they were more appropriately pegged closer to sub-All-Star level.

    • Miles Bridges (East)
    • Jaylen Brown (East)
    • John Collins (East)
    • DeMar DeRozan (East)
    • Draymond Green (West)
    • Brandon Ingram (West)
    • Dejounte Murray (West)
    • Julius Randle (East)
    • Russell Westbrook (West)

    Draymond Green is a player I’ve praised in the past for his heroic defensive efforts, snappy decision-making, and crafty transition passing, but I struggle to the see the confirmation that his impact is surely All-Star level. I suspect it’s probable he’s bumped up as the season goes on (even so far, his scoring has been somewhat adequate), but for now I’ll rank him as a very strong sub-All-Star-type player.

    Dejounte Murray was a player I was encouraged to stack up against Ja Morant in recent games, and while I see evidence that his passing and manipulation of the defense has grown, he doesn’t have the scoring punch and resulting threat to generate lots of offense for his teammates. I’ve also grown less fond of his defensive rotations and overarching off-ball defense. Regardless, Murray is a surefire candidate for a sub-All-Star team.

    Final Ballot

    Here’s the tricky part: condensing all of these tiers into the structure of an All-Star ballot. As stated earlier, there will be twelve players in each conference: five starters (two frontcourt and three backcourt players), five reserves (two frontcourt and three backcourt players), and two wildcards.



    • G: James Harden
    • G: Trae Young
    • F: Giannis Antetokounmpo
    • F: Kevin Durant
    • C: Joel Embiid


    • G: LaMelo Ball
    • G: Zach LaVine
    • F: Jimmy Butler
    • F: Jayson Tatum
    • C: Bam Adebayo


    • W: Kyle Lowry
    • W: Khris Middleton

    The hardest cut for me to make was the last guard slot on the reserves, which I gave to LaMelo Ball. The obvious candidates in his place were Bradley Beal and Kyle Lowry, the latter of which I gave a wildcard spot. I don’t think it’s impossible for Bradley Beal to rise on this ballot, but I’m concerned by his continuously declining outside shooting and lack of playmaking prowess next to players like Ball and Lowry.



    • G: Stephen Curry
    • G: Luka Doncic
    • F: Paul George
    • C: Rudy Gobert
    • C: Nikola Jokic


    • G: Damian Lillard
    • G: Donovan Mitchell
    • F: Anthony Davis
    • F: LeBron James
    • C: Karl-Anthony Towns


    • W: Ja Morant
    • W: Chris Paul

    Leaving Devin Booker and Mike Conley off my final ballot was a tough choice to make; the guard position in the West is simply too stacked for enough room to be made available. (And like I said, Booker and Conley are probably All-Star guys.) Aside from this debacle, I was pleased with my selections for the West. Gobert and Jokic as centers in the starting lineup felt slightly awkward, but a player like Gobert has way too much regular-season defensive value to leave off this type of ballot.

  • Top 10 NBA Players of 2021 (#1-3)

    Top 10 NBA Players of 2021 (#1-3)

    During the last post, I continued the top-10 series I introduced two days ago by covering the fourth through sixth rankings. Today, I’ll wrap up the “list” with spots one through three and discuss the skills and tendencies of the absolute very best basketball players in the game today. As a recap, here’s the criteria I laid out in the series’s introductory post:


    Consistent with my previous rankings, players are assessed based on how they impact success at the team level. Thanks to the revolutionary work from various basketball researchers, we have a great idea of not only which skills are most valuable, but also how much of an impact one player can have on a team’s success. I won’t belabor the topic, as I’ve engaged in many different conversations on it before, but this approach is antithetical to other, more common methods, which value skills next to one another based on the ranker’s personal belief system (a heuristic that isn’t guaranteed to be correct). To capture as much truth as possible, the value of different skills is viewed through my closest attempt to an objective lens.

    The next major part of the list concerns not the player, but the team around him. The endgame for every NBA team (as far as on-court performance is involved) is a championship. However, if we evaluated players based only on how he affects his own team’s title odds, a chunk of the league’s most talented players would lose their due representation. Paired with the fact that teammate synergies and coaching can actually cloud the strengths and weaknesses of a player’s value, the “title odds on a random team” criterion was adopted. (Note: The “economic” side of basketball isn’t included in these evaluations, e.g. contracts, salaries, enticement for free agents.)

    Perhaps the largest theme of this ranking, however, is how to react to single-season performances. Similar to the aforementioned factor of team construction around a player, the opponents a player’s team faces also play similar roles in augmenting, for example, box scores. Rudy Gobert received hearty criticisms for his ostensibly poor defensive performance against the Clippers in the second round, but more astute viewers noted the collapse of Utah’s perimeter defensive plan that led to an emphasized stress on Gobert to concede more long jumpers. The Clippers were a textbook “bad matchup” for a player of Gobert’s style, and while there are deeper conversations about drop coverage in the Playoffs, a lot of Gobert’s heavy scrutiny can be identified as an overreaction to results heavily influenced by situation.

    Because league-wide offensive efficacy has been shattering glass ceilings in the past two seasons, paired with the perceived psychological effects of zero fans in the stadium, larger-sample three-point shooting percentages are losing descriptive power. This is an example of where this list accounts for “good” and “bad” luck, and as the ultimate goal is to capture a player’s tangible skill and value, these rankings can be considered both retrodictive and predictive; meaning, there are instances in which the past sheds light on the present, and that reference points still hold value in these types of contexts. So while lucky or streaky box scores can be “appreciated,” that’s not the purpose of this list.

    Lastly, but certainly not least, this list ranks players at their fullest health, meaning players who suffered injuries won’t be penalized.

    The List

    10. James Harden (BKN)

    9. Joel Embiid (PHI)

    8. Luka Doncic (DAL)

    7. Kevin Durant (BKN)

    6. Kawhi Leonard (LAC)

    5. Anthony Davis (LAL)

    4. Nikola Jokic (DEN)

    3. LeBron James (LAL)

    During the preseason, my biggest concern with LeBron James is whether last season’s hiatus allowed for more time to replenish his athleticism, which then couldn’t be replicated in the following seasons. However, it seems James’s ability to pressure the rim largely carried over into 2021. He was in the 84th percentile with 10.5 drives per 75 possessions, 74% of which were unassisted, and these were comparable to his fully healthy stint last year. James’s reputation as one of the greatest basketball minds in history was as present as ever, constantly finding gaps and splitting defenses with his drives and slashing ability. This caused defenses to scramble, inadvertently allowing James to punish them with his other strong suit: passing. Nearly 11% of his drives resulted in a pass-out that led to an assist.

    James’s passing is so effective in the modern game because of his transcendent awareness and court-mapping. During my film study on him, he was consistently tracking the movements of his teammates on the perimeter and ready to instigate a high-leverage shot for an open shooter. Paired with his threat as a driver, which forces defenders down the baseline and unclogs the corner areas, James functions exceptionally well as the ball-dominant force surrounded by elite catch-and-shoot teammates. He was also in the 80th percentile or higher in both isolation volume and efficiency, and his ability to create offense for teammates and himself allows James to remain one of the very best offensive centerpieces in the league today.

    Similar to last year, James looked like a big positive on defense, and that was a large factor in why he ended up ranking higher than the NBA’s MVP Nikola Jokic. He was a versatile off-ball defender, using size to block driving and passing lanes while being able to guard a wide variety of players; he was in the 93rd percentile or higher in time spent guarding both “athletic finishers” and “stationary shooters” per BBall-Index matchup data. The largest reason I viewed his defense as slightly worse than last season was his rim protection, which started to regress closer to average. James wasn’t as present in the paint and deterred fewer shots, but he could still derail offensive sets before they culminated in these attempts, and that’s why I view James as a strong two-way player even at age thirty-six.

    Fun Fact: James was in the 96th percentile in the proportion of his half-court possessions in which he cut to the basket.

    2. Giannis Antetokounmpo (MIL)

    At the time of this writing, the Milwaukee Bucks are leading the Phoenix Suns 3-2 in the Finals, and Giannis Antetokounmpo is one win away from being an NBA champion. This is largely due to his perennially underrated capabilities as an offensive and defensive player, and his minor upgrade as a passer gives him the edge over a few players for me, as most of these decisions were made on very slim margins. Antetokounmpo seemed more comfortable with a wider variety of passes. While last season was characterized mostly by kick-outs and basic dump-offs, he’s now more likely to hit more players in more strenuating situations. He’s more effective as a skip passer and he’s hitting cutters a tad more frequently than before. Now that he’s surrounded by better shooters in Milwaukee, his paint and roll gravity are as valuable as they’ve ever been, and major catalysts to unlocking his passing.

    Antetokounmpo isn’t one of the very best on-ball threats in the league, particularly in the half-court when the paint is walled off, but his specialties as a driver and in transition offense are two feathers in his cap that add to a diverse and effective offensive portfolio. He’s an active lob finisher, which pairs well alongside strong passing, and he scored on a whopping 81% of his attempts at the rim in the regular season, and this number only fell to 78% on 10.7 attempts per 75 in the Playoffs. The major criticism of Antetokounmpo’s offense is that a system can’t be structured around him to win in the Playoffs, and there’s validity to this, which is why I fully endorse his transition to a more active off-ball role. He’s an extremely frequent cutter who sets formidable screens for teammates in a wide range of situations, while also being one of the most dominating roll men in the NBA.

    Arguably the main driver of Antetokounmpo’s mega-impact, however, is his game-changing defense. Milwaukee’s defense has been surprisingly effective in the Playoffs relative to their regular-season results, and Antetokounmpo has been the heaviest lifer. The Bucks’ defensive rating is nearly seven points better per 100 with him on the court, and this is largely because he’s an incredible defensive playmaker. He doesn’t function as a point-of-attack defender like some perimeter stars, but his hybrid role that takes him off the ball to stationary shooters or on the ball to versatile big men means he covers more ground than arguably any defensive star in the league. Antetokounmpo is among the hardest defenders to scheme around in a regular or postseason setting, and as a result, he’s super valuable in deep Playoff runs.

    Fun Fact: Despite troubled three-point shooting (30.3%) on very open shots (100th percentile in closeness to nearest defender), Antetokounmpo self-generates a ton of his shots, as he placed in the 97th percentile in the proportion of these shots that were unassisted.

    1. Stephen Curry (GSW)

    The skills that lead me to believe Steph Curry is the greatest offensive player in NBA history were on full display this season. His three-point percentages slumped out of the gate, eventually settling around 42%, but Curry was by far and beyond the best long-range shooter in the league this year. He graded out in the 100th percentile in BBall-Index‘s composite shooting metric that incorporates shot location, type, and difficulty. Curry’s stepback aids him in generating a ton of these pull-up attempts; and his sharp release ensures the range on his shots remains effective in shorter spurts, meaning looks of the same quality in the Playoffs are much more likely to fall victim to the more pressing environment.

    As arguably the greatest scorer ever, Curry demands more defensive attention than, again, probably any player in NBA history. Highlights of teams deploying three or four-man trapping schemes versus Curry were popular this year, and because Curry played with as few offensive threats as he has in nearly a decade, his “situational” gravity was perhaps as massive as ever. However, without the basketball, Curry still creates a ton of shots for teammates. Golden State surrounded him with defensive-oriented teammates who could design a system relying heavily on pin downs and ball screens to find an open shot for Curry. This “off-ball” creation of sorts that results in his constant shooting threat maneuvering around the court amplifies the shooting of his teammates. All of these superb skills result in Curry being the most scalable offensive star to ever play in the NBA, meaning he can boost the star talent around him and potentially improve his own value.

    Curry’s all-time impact manages to hold despite elite defense because he’s not a liability on that end. I graded him out as neutral this year because it’s hard to argue his presence either strengthens or worsens a team’s defense. The major weakness in Curry’s defensive profile is his man defense; opponents can target him on the perimeter and he’s fairly vulnerable to strong-set screens, meaning ball-handlers will usually punish him. Conversely, Curry is kind of a good team defender. He has solid awareness and can clog driving lanes before opponents will leverage them, and this keeps his defensive value from bleeding into the negatives. While it’s hard to imagine Curry truly amplifies any defensive system, there’s also a hard argument to be made that he takes anything off the table.

    Fun Fact: Curry was expectantly in the 99th percentile in the proportion of his half-court possessions on which he scored off a screen.

    Up Next

    Before the series began, I asked community members from Discuss The Game to share their top-10 lists so I could compare our lists following the conclusion of mine. During the next post, I’ll go over the voting results and discuss trends, theories, and why we differ on rankings.

  • Top 10 NBA Players of 2021 (#4-6)

    Top 10 NBA Players of 2021 (#4-6)

    During my last post, I introduced a series in which I would rank the NBA’s ten best players of the 2021 season, starting with rankings seven through ten. Continuing the rankings now features the next clump of players, or the ones I believe account for the fourth through sixth spots. As a recap, here’s the criteria I laid out during the last post:


    Consistent with my previous rankings, players are assessed based on how they impact success at the team level. Thanks to the revolutionary work from various basketball researchers, we have a great idea of not only which skills are most valuable, but also how much of an impact one player can have on a team’s success. I won’t belabor the topic, as I’ve engaged in many different conversations on it before, but this approach is antithetical to other, more common methods, which value skills next to one another based on the ranker’s personal belief system (a heuristic that isn’t guaranteed to be correct). To capture as much truth as possible, the value of different skills is viewed through my closest attempt to an objective lens.

    The next major part of the list concerns not the player, but the team around him. The endgame for every NBA team (as far as on-court performance is involved) is a championship. However, if we evaluated players based only on how he affects his own team’s title odds, a chunk of the league’s most talented players would lose their due representation. Paired with the fact that teammate synergies and coaching can actually cloud the strengths and weaknesses of a player’s value, the “title odds on a random team” criterion was adopted. (Note: The “economic” side of basketball isn’t included in these evaluations, e.g. contracts, salaries, enticement for free agents.)

    Perhaps the largest theme of this ranking, however, is how to react to single-season performances. Similar to the aforementioned factor of team construction around a player, the opponents a player’s team faces also play similar roles in augmenting, for example, box scores. Rudy Gobert received hearty criticisms for his ostensibly poor defensive performance against the Clippers in the second round, but more astute viewers noted the collapse of Utah’s perimeter defensive plan that led to an emphasized stress on Gobert to concede more long jumpers. The Clippers were a textbook “bad matchup” for a player of Gobert’s style, and while there are deeper conversations about drop coverage in the Playoffs, a lot of Gobert’s heavy scrutiny can be identified as an overreaction to results heavily influenced by situation.

    Because league-wide offensive efficacy has been shattering glass ceilings in the past two seasons, paired with the perceived psychological effects of zero fans in the stadium, larger-sample three-point shooting percentages are losing descriptive power. This is an example of where this list accounts for “good” and “bad” luck, and as the ultimate goal is to capture a player’s tangible skill and value, these rankings can be considered both retrodictive and predictive; meaning, there are instances in which the past sheds light on the present, and that reference points still hold value in these types of contexts. So while lucky or streaky box scores can be “appreciated,” that’s not the purpose of this list.

    Lastly, but certainly not least, this list ranks players at their fullest health, meaning players who suffered injuries won’t be penalized.

    The List

    10. James Harden (BKN)

    9. Joel Embiid (PHI)

    8. Luka Doncic (DAL)

    7. Kevin Durant (BKN)

    6. Kawhi Leonard (LAC)

    Similar to his predecessor on this list, Kawhi Leonard is one of the most proficient isolation scorers in the NBA. During the regular season, he was in the 96th percentile in isolations per possession on roughly one point per shot, which made for extremely efficient offense in the half-court despite rapidly increasing league-wide offensive ratings. However, Leonard’s case as the league’s best isolationist would come from his scoring’s resiliency in the Playoffs. Because he’s a prolific three-level scorer, he can’t be contained by most trapping schemes, and this leads to dazzling productivity as a scorer. During the Playoffs, he averaged an outstanding 30 points per 75 on True Shooting +10% better than the league.

    Leonard provides offensive floor-raising, but he continues to add to his scalability. Three-point shooting percentages are wonky this season, but Leonard was in the 95th percentile in catch-and-shoot efficiency at 47%. Paired with his growing frequency off the ball, as 16% of his half-court possessions featured a scoring opportunity off screens, and there are indicators that Leonard would fit well alongside other great offensive teammates. Although his offensive playstyle has changed drastically since his trade to Toronto, now calling for frequent pick-and-roll and evolving into a true offensive quarterback, there are remnants of the skills that once made Leonard one of the more scalable players in the league.

    The other big driver of Leonard’s value is his playmaking. I’ve never been too high on Leonard as a passer. For a primary ball-handler, his reads were fairly basic, and he never exhibited the passing aggression that most on-ball creators do. But in 2021, I saw some minor leaps forward. Leonard is starting to act more out of the pick-and-roll, and while most of these are corner reads that many other players could make, he’s leveraging the Clippers’ spacing more than he would have in previous seasons. However, that also sets forth the question of how diverse his passing locations would be outside of Los Angeles, perhaps alongside teammates who don’t stretch the floor like Nic Batum and Luke Kennard.

    To my eye, and some changes in his statistical profile, Leonard is losing ground as a defender. Los Angeles will still stick him onto some of the opponents’ better players; he spent the highest proportion of his defensive possessions against the “shot creator” archetype. But he was also generally less involved on defense this year, to my film study on him alongside some statistical signals; he spent the second-most defensive possessions against stationary shooters. Leonard clogged passing lanes less often and was beaten off the dribble more often, but his face-up and rearview games are enough for me still view him as a big positive on defense.

    Fun Fact: There was an almost even split between the percentage of Kawhi’s isolation possessions on the perimeter (55%) and the post (45%).

    5. Anthony Davis (LAL)

    The consensus on Davis is that he regressed in 2021 due to injuries that bled into his on-court play; and while there may be some rightful gripes with his unhealthy performances, there were more than enough signals that indicate a healthy Anthony Davis is still one of the very best players in the league. During the past three seasons, he’s slowly upgraded his passing arsenal; and during his incredible regular-season stretch in 2019, he was a serviceable primary facilitator on a weaker offense in New Orleans. While he’s taken the more suitable backseat role alongside offensive juggernaut LeBron James, this is also where Davis adds a ton of his value.

    He spent roughly half of his 2021 playing time without James on the floor, and in these 561 minutes, he generated 12.4 points from assists per 100 possessions as opposed to 10.2 per 100 with James on the floor. While there isn’t nearly enough evidence that suggests Davis could shoulder the load of a primary playmaker on a good offense, his secondary passing increases his scalability. He’s certainly active and attentive as a passer, often receiving the ball inside the arc and hunting for cutters fi facing the basket, and his back-to-the-basket game alleviates some of his mechanics on kicking out to one of Los Angeles’s shooters. However, the range of his assists is limited, as the “Passing Versatility” stat referenced in the last post placed Davis in the 31st percentile during the regular season.

    Anthony Davis is one of the best defensive players in the league, which paired with his abilities off the ball, makes him one of the league’s most valuable players to a contending team. It’s well known that Davis makes a compelling case as the greatest lob finisher in NBA history, and this pairs extremely well alongside the drivers that would quarterback those elite offenses (one of the reasons Davis and James function so well together). More than half of his drives were assisted in 2021, suggesting that while he’s not a classic self-generating offensive star, his ability to capitalize on his better teammates’ passing is incredibly valuable. Davis was in the 96th percentile in field-goal percentage at the rim in the regular season. Coupled with his diverse screening action, which includes flex screens, pick-and-roll action, pin downs, and ball screens for shooters, as well as his frequent cutting (98th percentile), Davis is one of the most scalable offensive stars in the league.

    Last season, Davis was the best defensive player in the Playoffs due to his unmatched combination of versatility and rim protection that punished all types of offensive constructions. This season, he didn’t lose much of a step outside of fatigue and health issues. During the regular season, Davis was less eager to close out (although he was still in the 84th percentile in three-point contests per possession) and seemed to attempt to conserve some energy, but all of his previous defensive skills stood out. His vertical contests are among some of the greatest ever, he’s an extremely cerebral and patient isolation defender, and his rim protection was characteristically great. Davis’s nail defense stood out to me in 2021, where he would frequently get a foot into lanes to absorb passes, and as a result, he was in the 84th percentile in the sum of bad pass turnovers and deflections per possession and the 92nd percentile in steals per possession.

    Fun Fact: Davis was dead-last in the league in drawing fouls on three-point shot attempts in the regular season.

    4. Nikola Jokic (DEN)

    Don’t get me wrong; Nikola Jokic was, and still would be, my pick as the NBA’s MVP. Perhaps the greatest offensive big man from a center occurred in 2021, rivaled only by the likes of the legendary Kareem Abdul-Jabbar and Shaquille O’Neal. Jokic was the most dynamic and versatile passer of any player in the league. He constantly found high-value shots with his passes in the paint and behind the stripe, leveraging Denver’s cutting threats to unclog various areas on the court. If his half-court game seemed effective, his transition passing extended to transcendence. Jokic could throw fastballs from the opposite block after one-handing an offensive rebound; but unlike most other similar passers, he was never overzealous with his velocity, having mastered his passing’s north-south movement.

    There also appeared to be a permanent improvement to Jokic’s shot. During the regular season, he was actually more efficient on above-the-break shots than catch-and-shoot attempts relative to the league. The 38% three-point shooting he displayed in last year’s Playoffs carried over at 39%, and I think his shot mechanics have improved. As he undertook less of a catapulting motion, the variability of his motions and the trajectory of his attempts decreased. This was the ceiling-shattering upgrade to Jokic’s offensive package, forcing defenses to react more attentively to his mid-range game while Jokic could continue to punish the opposition with his own shot to greater reward outside the paint. Although he didn’t fit the mold of a traditional isolation scorer who would function out of triple-threat, the middle of the floor served as the stomping ground for Jokic’s insane volume (97th percentile) and efficiency (88th percentile) on isolation possessions.

    Jokic makes a truly compelling case as the league’s best offensive player, but I was more concerned with his defense than in previous seasons. A lot of his strengths carried over from previous seasons: great hands, anticipation, and solid awareness. But his off-ball repertoire doesn’t offset his troubled face-up defense for me. Jokic’s lack of athleticism makes it easy for slower guards to beat him off the dribble; and for a near seven-footer, he provides virtually no rim protection. The concern with this is that, contrary to disengaged guards like James Harden, defenses can’t scheme around these types of weaknesses in the Playoffs. While it’s unlikely that Jokic is anything worse than a slight negative on defense, the deficiencies that come with his playstyle suggest there may be a cap on this end of the floor.

    Fun Fact: Jokic was in the 99th percentile in points scored from pops per possession in the regular season.

    Up Next

    My next post will continue this series with profiles for the first, second, and third-best players on my top-10 list. I’ll discuss the “high” and “low bands” for which I could reasonably see players swapped in later editions; the final rankings can be thought of as the point estimates. Comment down below any disagreements, surprises, or thoughts on these players!

  • Top 10 NBA Players of 2021 (#7-10)

    Top 10 NBA Players of 2021 (#7-10)

    Every year, I embark on the self-destructive journey of ranking the NBA’s very best players. Anyone who regularly consumes basketball content will likely have seen others attempt to answer the same question, perhaps to varying degrees of success and failure. But, in truth, the success or failure of a player ranking lies more in the process than in the results. A major criticism of a lot of lists is how one’s personal biases and incomplete heuristics are blended into the selection process. Namely, a ranker may feel their list is correct, but not necessarily why the list is correct. To avoid human error and misconception, the following strict criteria acted as the guideline to creating this year’s list:


    Consistent with my previous rankings, players are assessed based on how they impact success at the team level. Thanks to the revolutionary work from various basketball researchers, we have a great idea of not only which skills are most valuable, but also how much of an impact one player can have on a team’s success. I won’t belabor the topic, as I’ve engaged in many different conversations on it before, but this approach is antithetical to other, more common methods, which value skills next to one another based on the ranker’s personal belief system (a heuristic that isn’t guaranteed to be correct). To capture as much truth as possible, the value of different skills is viewed through my closest attempt to an objective lens.

    The next major part of the list concerns not the player, but the team around him. The endgame for every NBA team (as far as on-court performance is involved) is a championship. However, if we evaluated players based only on how he affects his own team’s title odds, a chunk of the league’s most talented players would lose their due representation. Paired with the fact that teammate synergies and coaching can actually cloud the strengths and weaknesses of a player’s value, the “title odds on a random team” criterion was adopted. (Note: The “economic” side of basketball isn’t included in these evaluations, e.g. contracts, salaries, enticement for free agents.)

    Perhaps the largest theme of this ranking, however, is how to react to single-season performances. Similar to the aforementioned factor of team construction around a player, the opponents a player’s team faces also play similar roles in augmenting, for example, box scores. Rudy Gobert received hearty criticisms for his ostensibly poor defensive performance against the Clippers in the second round, but more astute viewers noted the collapse of Utah’s perimeter defensive plan that led to an emphasized stress on Gobert to concede more long jumpers. The Clippers were a textbook “bad matchup” for a player of Gobert’s style, and while there are deeper conversations about drop coverage in the Playoffs, a lot of Gobert’s heavy scrutiny can be identified as an overreaction to results heavily influenced by situation.

    Because league-wide offensive efficacy has been shattering glass ceilings in the past two seasons, paired with the perceived psychological effects of zero fans in the stadium, larger-sample three-point shooting percentages are losing descriptive power. This is an example of where this list accounts for “good” and “bad” luck, and as the ultimate goal is to capture a player’s tangible skill and value, these rankings can be considered both retrodictive and predictive; meaning, there are instances in which the past sheds light on the present, and that reference points still hold value in these types of contexts. So while lucky or streaky box scores can be “appreciated,” that’s not the purpose of this list.

    Lastly, but certainly not least, this list ranks players at their fullest health, meaning players who suffered injuries won’t be penalized.

    Honorable Mentions

    There was a number of other players I considered as top-10 candidates for this list, although I’d slightly struggle to see one of the following players bumped from the final cut. Namely, my reasonable floor for these top-10 players will still hold more impact than my reasonable ceilings for the remainder of the top-15. The best of the rest for me were, in alphabetical order, and are not limited to: Jimmy Butler, Paul George, Rudy Gobert, and Damian Lillard.

    The List

    10. James Harden (BKN)

    Despite having been traded to arguably the league’s best offensive team partway through the season, Harden once again carved out another ball-dominant role highlighted by his operation in spread pick-and-roll. Although he wasn’t the statistical outlier he was in previous seasons, Harden possessed the ball for 8.6 seconds per possession in his stints with both Houston and Brooklyn, which was good for third in the entire league during the regular season. And, thanks to the wondrous spacing capabilities from teammates like Kevin Durant and Joe Harris, Harden had even more room to work with. This led to one of Harden’s best-scoring postseasons in recent history in which he scored 22 points per 75 possessions on +11.5% relative True Shooting.

    The most glaring statistical trend in Harden’s profile this season has been his volume scoring, which, two years removed from posting the highest regular-season scoring rate in league history, settled at a more pedestrian 25 points per 75 in the regular season. While comparable numbers in his first few games in Houston can be attributed to off-court issues leading up to opening night, Harden’s volume scoring still seems elite. During 301 minutes with Kevin Durant on the floor, Harden averaged an uncharacteristic 17.6 points per 75 as opposed to 26.9 points per 75 in 1,017 minutes spent without Durant. Evidently, there was some clash between the two as on-ball scorers during their shared time, but these minutes also combined to produce an offensive rating of 125 during the regular season.

    A lingering question with Harden had always been whether he could adopt a more movement-heavy role alongside more ball-dominant teammates, as his off-ball efficacy has drawn strong comparison to cacti in the past. This season served as an indicator, and although Harden played a similarly ball-dominant role relative to his other star teammates, there was a slight uptick in general activity off the ball. However, his movement never took off as some of his stronger believers had hoped for, as he ranked in the 8th percentile among players in his percentage of offensive possessions that involved scoring off screening action and cutting to the basket.

    Defensively, there wasn’t a whole lot of change for Harden. To my viewing, his perennial lack of true engagement held, and that led to very little value as a help defender. While Harden does have strengths on that end, he seemed to lack the anticipatory recognition that would make him a clear positive. His “gambling” style also carried over from previous seasons; as, despite his aforementioned lack of good awareness, he was in the 66th percentile of “Passing Lane Defense” (bad pass steals + deflections per 75) and deflections per 75 possessions. Harden’s stout frame still allowed him to function well as an interior defender. He was actually in the 65th percentile in block rate and the 90th percentile in block rate on contests.

    Fun Fact: According to BBall-Index matchup data, Harden spent the largest proportion of his defensive possessions (14.6%) against the “stretch big” archetype.

    9. Joel Embiid (PHI)

    It was painfully difficult to slide Harden to the back end of the list this season, but that’s in part due to the unique, outlier-ish effectiveness of Joel Embiid. Last season, there was evidence that suggested big men who primarily play drop coverage in the Playoffs are more likely to be met by bad matchups; and more specifically, excellent shooting teams who can punish space inside the arc with their midrange shot. However, Embiid seems to be a bit of an exception here. I noted that he contested very few threes and was reluctant to close out during his film study, and this is corroborated by the stat sheet, as he only contested two of these shots every 75 possessions he was on the floor.

    I view Embiid as special because, despite this style that baits great shooters, he still seems to be an elite defender in the Playoffs. Embiid doesn’t stand up to the interior heavyweights like Rudy Gobert, but Philadelphia’s defense was a modest two points better per 100 with him on the floor. Paired with his clear improvements on offense, and Embiid is starting to look more and more like a legitimate MVP candidate. Granted, he’s still not a great or even good passer, but there are some positive signals. Looking at the diversity of the locations of his assists along with the play types on which they were accrued, Embiid almost looks like an above-average passer in spurts. To my eye, his vision is also continuing to improve, and his increased clarity of the corners gives him a strong outlet when met with trapping schemes to leverage Philly’s excellent shooting teammates.

    Meanwhile, there’s also a lot of positives about his movement off the ball. He would constantly hunt for offensive rebounding positions, mimicking what made ’50s stars like Bob Pettit great by resetting possessions for his team. Embiid spends a lot of his off-ball possessions as a roll man as well, placing in the 94th percentile in the proportion of his team’s likewise possessions in which he was the roller. And, relative to league-average efficiency, Embiid’s per-75 impact as a roller was also in the 94th percentile among players this season. He’s also making strides as a cutter, with about 27% of his half-court possessions characterized by a cut, but his efficiency on these plays was particularly worse.

    Fun Fact: Embiid was at the top of the league this season with 14.5 isolations per 75 possessions, 25% of which were on the perimeter and 75% in the post.

    8. Luka Doncic (DAL)

    The Slovenian superstar is quickly ascending to MVP levels as the quarterback of one of the NBA’s most promising offensive teams. While the Mavericks couldn’t replicate last season’s offensive heights in an increasingly competitive offensive landscape, Doncic got even better. It’s possible he’s currently shouldering the largest offensive load of any player in the history of the sport! During the regular season, his time of possession of 8.9 seconds led the entire league, and that number skyrocketed to 12.1 seconds in the postseason. (Trae Young was second in the Playoffs at 9.6 seconds.) As one of the league’s defining heliocentric stars, almost all of Dallas’s offense runs through Doncic.

    His passing and shot creation are his strongest attributes, and they go hand-in-hand while Doncic will continue to unlock historical offensive heights. Similar to Harden, Doncic runs a lot of spread pick-and-roll with high-set screens, and all the space this creates allows him to inflict a lot of damage on Dallas’s opponents. When the Mavericks send a roller to the paint, Doncic leverages his incredible anticipation to place a pass at the apex of his teammate’s jump. Perhaps Doncic drives to the basket. His scoring threat and unique finishing capabilities are enough to collapse some defenses, and this leads to his excellent passing. Doncic loves to hit the corners for high-value shots, and 43% of his drives ended with pass-outs while 11.2% of his drives led to assists.


    Doncic may have the most effective on-ball offensive package in the league right now. The limiting factor for me is his activity off the ball. To my viewing, he never quite exhibited the ability to create offense without the ball and mostly resorted to catch-and-shoot and post-up movements. However, Doncic is not a great catch-and-shoot scorer (43rd percentile) but he is effective in the post, able to score efficiently and draw fouls at league-leading rates. Doncic’s lack of a true off-ball repertoire is one of the reasons I don’t rank him as highly as others may, and these types of skills are especially important in being able to provide value to contending teams. It’s clear that Doncic is more of a floor raiser than a ceiling raiser, but can he provide the same mega-value alongside another perimeter star who demands the ball?

    The other big reason I drop Doncic down a few spots is that he concedes impact on the defensive end. He’s certainly a relatively skilled defender. Although he doesn’t face these types of players often (8% of his defensive possessions), Doncic is an abled man defender against athletic finishers and shifty guards who pressure the rim. He shuffles his feet quite well and provides a big body in the post versus smaller guards like Steph Curry or Damian Lillard. There are also signals that he could potentially grow into a cerebral off-ball defender. Doncic is an engaged defender when his man doesn’t have the rock, making clear attempts to cover open ground to prevent a high-value shot. He also uses his uncanny physical strengths to navigate screens fairly well, going over the screen while minimizing contact with the opponent.

    Fun Fact: During the seven-game series against the Clippers in the first round, the Mavericks’ offense was 30 points per 100 more efficient with Doncic on the floor than off.

    7. Kevin Durant (BKN)

    Earlier in the season, I assumed James Harden’s larger offensive load would result in him being the driver of Brooklyn’s elite offense. But now, I’m starting to think that it’s actually been Kevin Durant. During 1,017 minutes with Harden on the floor and Durant off the floor, the Nets put up a spritely 120 points per 100 possessions. But during 855 minutes with Durant on and Harden off, that number improved to an even-greater 125 points per 100. If we include the Playoffs in that sample size, the gap narrows, but it creates enough uncertainty that I wonder whether Durant’s mixture of on and off-ball play is more valuable to the Nets than Harden’s heavy isolation frequency and ball-pounding.

    Despite a devastating Achilles tear in the 2019 Finals, Durant has lost very little offensive ground to his younger self. He remained one of the league’s very best scorers, averaging 30 points per 75 on True Shooting +10% ahead of the league. His isolation game also held strong, averaging 5.6 isolations per 75 on 1.2 points per shot. But I’m also wondering if his playmaking has taken a tiny leap forward. A large part of it may be the expansive space Durant has to work, but he seemed generally willing to throw touchdown passes every once in a while. He passes well out of traps, not just by using his height, but by splitting two defenders with his bounce passes. Paired with a great passing gig with Brooklyn’s cutters, Durant was a versatile passer this season. He placed in the 93rd percentile in the “Passing Versatility” statistic that looks at the variability of his assist locations.

    Durant was slightly more fragile this season with his vertical leaping, but intelligent play and great lateral movement lead me to believe he adds positive value on that end. And at the end of the day, this positive defense is what separates him from other offensive stars like Doncic and Harden. Durant covered most of his rotations, exhibiting the same ability to track his matchup and the movement of the ball similar to lots of other smart team defenders in history. He was also an effective interior defender. Durant didn’t deter these attempts like the league’s defining paint protectors, but he was in the 98th percentile in block rate on shot contests and the 85th percentile in his opponent’s field-goal percentage at the rim over expectation.

    Fun Fact: Durant was in the 36th percentile in one-year adjusted offensive rebounding rate but the 94th percentile in adjusted defensive rebounding rate.

    Up Next

    My next post will continue this series with profiles for the fourth, fifth, and sixth-best players on my top-10 list. I’ll discuss the “high” and “low bands” for which I could reasonably see players swapped in later editions; the final rankings can be thought of as the point estimates. Comment down below any disagreements, surprises, or thoughts on these players!

  • Wilt Chamberlain and the Dunning-Kruger Curve of Statistical Analysis

    Wilt Chamberlain and the Dunning-Kruger Curve of Statistical Analysis

    Proposed by social psychologists David Dunning and Justin Kruger in 1999, the Dunning-Kruger effect explains a form of cognitive bias by describing the stages of a person’s progression in a field. The premise is that someone will often overestimate their abilities as they dip their toe into the field because they lack the introspection to assess the quality of their knowledge. As they become more exposed to the field, they begin to recognize that they lack key information to identify “high” knowledge. What follows is a continuously gradual period of growth in which the person attains both increasingly more knowledge in the field and the self-evaluation skills they once lacked. The “curve” that documents this journey is pictured below.

    As is with many other fields, the Dunning-Kruger effect is present in learning about basketball statistics. Having undergone a similar journey myself, there’s no other player in NBA history that exemplifies the Dunning-Kruger effect than Wilt Chamberlain. His individual statistics are treated as unprecedented, reigning high and above any other player ever. Perhaps there’s some validity there, but the larger theme here is how these stats should be interpreted. Using Wilt the Stilt as the guideline, here is the Dunning-Kruger curve of basketball statistics.

    The Peak of “Mount Stupid”

    As labeled on the above graphic, “Mount Stupid” acts as a representation of the first stage of the Dunning-Kruger effect. The person believes they are equipped with enough knowledge to proclaim expertise despite an introductory level of proficiency in the field. This is the stage in which, clearly, statistical analysis is the most limited, strictly adherent to the box score. Additionally, there is the false belief that all notable statistical information is captured in the box score. Active basketball watchers know there’s a whole lot more going on outside of what’s recorded in the box score; hence, the peak of “Mount Stupid.”

    For these reasons, some may see Wilt Chamberlain as the greatest NBA player of all time due to his unmatched combination of volume scoring, rebounding, and assisting prowess. Chamberlain’s career average of 30.1 points per game has only ever been challenged by Michael Jordan, and his rebounding average of 22.9 rebounds per game is the highest mark in league history. This type of statistical dominance was held in his peak seasons, one of which is commonly seen as the 1962 season in which he averaged 50.4 points per game. The Stilt holds the top-four seasons in points per game in league history, and the next-closest player ever since was Michael Jordan’s 37.1 points per game in 1987.

    Chamberlain’s aforementioned assisting dominance trickled in as his scoring went down and he undertook more of a facilitating role in Philadelphia. Even today, his 8.6 assists per game in 1968 leads all centers in NBA history. This level of raw statistical dominance is incredibly captivating, characterizing the Stilt as arguably the most well-rounded and commanding player in league history. But, again, as some of us know, the implications of Chamberlain’s historical statistical profile run far deeper than how they are taken at face value. Additionally, these crude box score statistics miss out on a lot of the advanced techniques developed over the years, which we’ll dive into later.

    Key Takeaways of Stage 1:

    • Wilt Chamberlain averaged a lot of points, rebounds, assists, etc., and his unprecedented per-game statistics mean he’s the most statistically dominant player in NBA history.
    • Box score stats are taken purely at face value, e.g. a 23 points per game scorer with a field-goal percentage of 50% is a better scorer than a 21 points per game scorer with a field-goal percentage of 47% because of these numbers.
    • The entire lack of consideration for how different statistics, box score or not, have an effect on the team levels. This “Stage 1” mindset also glosses over the much-needed contextualization methods of today.

    The Valley of Despair

    After a while, it becomes much clearer that the box score is a mere fraction of what should make up the totality of a player’s “statistical” impact. Recognizing the box score fails to track such crucial information is a trademark quality of the “Valley of Despair,” which occurs when the person becomes aware of how little they know. For example, the assist is the universal proxy for playmaking talent, recorded each time a player’s pass leads directly to a teammate’s made shot attempt. Disregarding the philosophical disparities between stat-trackers, the assist is entirely dependent on the teammate making the shot; meaning a player’s assists figures can either be inflated or deflated based on the quality of the players around him. Namely, comparing assists between players will never be an apples-to-apples comparison. [1]

    While Stage 2 is similarly characterized as one when the person still lacks a significant amount of knowledge, the questioning of the Stage 1 methods acts as the catalyst to unlocking a broader understanding of statistics. Because this usually accompanies an increased awareness of how teammates and coaching influence a player’s statistics (e.g. the assists example), questions will naturally arise that ask whether a more stuffed stat line is truly better than another. The previous case of two scorers exemplifies this well. If “Player A” averages 23 points per game on (let’s use a more sophisticated measure of efficiency) 57% True Shooting, is he automatically a “better” scorer than Player B and his 21 points per game on 54% True Shooting?

    Wilt Chamberlain’s revered 1962 season is a campaign that should similarly evoke these questions. We know he averaged an absurd 50.4 points per game, but could those points have come at the expense of something else? The Stilt averaged a mere 2.4 assists per game, which heavily suggests he was heavily slanted towards scoring as opposed to creating for teammates. Questioning the value of Chamberlain’s “black hole” signature style connects the player to the phenomenon.

    Key Takeaways of Stage 2:

    • The questioning of whether box score stats should be taken as absolute measures; the increased awareness that stats like points, rebounds, and assists are accrued in different environments, setting forth the concepts of inflated and deflated statistical profiles.
    • Although the exact countermeasures to the box score’s inherent flaws aren’t to the person’s knowledge yet, they recognize the need to search for them, meaning they’ve reached the point at which they understand they lack proficient knowledge.

    The Slope of Enlightenment

    Referring to the Dunning-Kruger effect graphic above, the Valley of Despair is immediately followed by the continuous increase of knowledge in the field. As the previous recognition of one’s own inexperience sets in, they begin to search for alternative methods to the ones they had once misused. This creates a continuous period of growth in which new information is constantly made to be readily available for the person to absorb. Pertaining to the subject of Wilt Chamberlain, there are multiple of the aforementioned “contextualization methods” that shed light on the value of his juggernaut scoring and whether or not it made him the greatest individual (or “statistical”) player of all time.

    Perhaps the most common of these tools is the pace-adjusted statistic, which was introduced to a more even playing field to compare players across eras. For example, using Basketball-Reference‘s pace estimates, Wilt Chamberlain’s Warriors of 1962 accumulated 131.1 offensive possessions per 48 minutes. Because Wilt Chamberlain played every minute of every game, including overtime, he had roughly 132 chances to rack up stats every game during this season. For reference, the fastest-paced team of the 2021 regular season (the Washington Wizards) averaged 104 possessions per 48 minutes. This huge disparity in opportunities is used to add context to Chamberlain’s scoring averages in the following fashion:

    Because we like to express statistics in a modernized fashion, box score stats are often represented as “per 75” measures, calculating the number of stats a player accrues every 75 possessions he’s on the floor. [2] Using Chamberlain’s 1962 scoring total with the previous pace estimate, we know the Stilt scored a total of 4,029 points in roughly 10,597 possessions. This means his “per-75” scoring average is a more realistic 28.5 points rather than 50.4 points. For reference, the closest player to Chamberlain’s scoring rate in 2021 was Zach LaVine (28.3 points per 75) of the Chicago Bulls, who ranked tenth among all qualified players.

    Key Takeaways of Stage 3:

    • The countermeasures for the concerns expressed in Stage 2 are put into action, with the person continuously gaining knowledge on enhanced statistical practices and implementing them to discover new information on players and teams.
    • The use of more sophisticated measures to quantify player actions, e.g. points per 75 instead of points per game (in addition to even savvier inflation-adjusted measures), True Shooting percentage (or relative True Shooting) instead of field-goal percentage.

    The Plateau of Sustainability

    While the word “plateau” suggests a lesser growth in knowledge after Stage 3 (this is not the case), the fourth stage is more the product of the previous three having laid the groundwork for further analysis. The person is now able to independently function as proficient in the field and continue to research these phenomena and add onto insightful reasonings. This is when even more of the advanced work happens, and there’s a whole lot of thought-provoking stuff on Chamberlain that counterbalances the extremities of his raw box scores.

    (? Backpicks)

    As it turns out, the previous questioning of whether Chamberlain’s scoring offset other important offensive actions was valid. The above chart plots the relationship between Chamberlain’s per-game scoring averages by season and his teams’ offensive ratings (points scored per 100 possessions). Clearly, there exists a massively negative correlation between these two variables. How do we interpret this? Well, there’s the unavoidable confounder of team changes and teammate development, so some of this relationship should be taken with a grain of salt. But this career-long trend is a damning piece of evidence that tells us something.

    Because Chamberlain was not an elite shot creator (Box Creation, and estimate of shot creation, said Wilt created roughly 2 to 3 shots for teammates every 100 possessions throughout his career), his tendency to take a ton of shots held back some of his higher-level teammates, bolstering his individual scoring statistics at the cost of the team’s overall efficiency. The disparity between his individual statistics and his team-level impact holds true in impact estimates like WOWYR (With Or Without You, Regressed). As perhaps the most robust measure of historical impact we have, WOWYR divvies credit for a healthy lineup’s success among the heart of its lineup.

    Chamberlain’s prime seasons estimated his impact as worth +5.2 points per game, which would still make him one of the very best players in the history of the sport. But a player with “poorer” individual statistics, Bill Russell, had a mark of +6.7 points per game. So while Chamberlain is still an all-time great basketball player, one of the ten very best to my estimation, the rawest forms of his stats are not reflective of how “good” of a player he was, and therefore, his statistical efficacy.

    Key Takeaways of Stage 4:

    • The increased understanding the statistical analysis does not decrease the breadth of information to analyze; i.e. rigorously adding context to a player’s statistics.
    • Establishing more connections between a player’s actions and presence and team performance. Because players are employed to help teams win games, this is what we really care about.
    • Leveraging more robust data to ballpark not only how valuable a player is to a team, but how valuable any player can be, e.g. how much closer can a role player, All-Star, or MVP take a team to a championship.

    [1] There’s also the larger, overarching debate of the differences between assist qualities. The “Rondo Assist” was coined to identify assists that were barely the product of the passer, meaning the shooter did all the work.

    [2] We use the “per 75” measure because a typical NBA game nowadays lasts roughly 100 possessions and some superstars will play roughly 36 minutes per game. (36 minutes is 75% of the 48-minute game.)

  • The NBA’s Top 10 Offensive Players of 2021

    The NBA’s Top 10 Offensive Players of 2021

    (? The Ringer)

    Nearing the end of the 2021 Playoffs, with a whole new season of information on the league’s top players, we cycle around to yet another series of rankings. Rather than evaluating a player based on his overall impact, today’s edition starts with ballparking the value a player adds on offense alone. Because the rules and practices of the NBA are currently slanted toward offense, the best offensive players have a significantly greater impact on the scoreboard than the league’s best defensive players. And because offensive skills and tactics continue to develop and grow, ranking these players becomes an even more complex task. So what are we looking for here?


    Unlike some lists, this will not rattle off the league’s top volume scorers. While teams win by scoring more points than the opposition, there is a multitude of other ways a player can influence his team’s scoring than taking the final shot. Keep that in mind if these rankings appear to be less fond of players like the Greek Freak, Bradley Beal, or Joel Embiid. While the conversation of exactly how valuable certain offensive skills are is a much larger one than today’s, there will be some themes that pop out during the list.

    Contrary to popular opinion, volume playmaking will be viewed in a slightly rosier lens, and that’s because a shot created has a greater expected value than a shot taken. Because an offensive possession is all about generating the most efficient shot, these mega-shot creators who can also score themselves will be ranked higher than the more flashy, self-generated scoring type of stars that historically receive a lot of praise. I’ve written on the topic of volume versus efficiency before, and while there’s more to a player’s scoring value than these two measuring sticks, they’re valued as roughly (key word: roughly) equal.

    Because offense is so often reduced to volume scoring, this list may appear to excessively praise great passers and off-ball players, but this is because they both contribute toward high-value offensive possession. Passing exploits the mishaps in a defense while off-ball cutting or offensive rebounding pressure the rim and generate a ton of second-chance opportunities. The overarching point here is that all offensive skills are at play here, and they’ll be weighed appropriately based on evidence of how valuable they are and, even more important to how they affect bad teams, how much they affect good teams.

    Honorable Mentions

    Before diving into the list, let’s go over some honorable mentions, and why the list caps off at ten players. The first two players out, and the ones I saw as making the strongest arguments to slide in at the back end of the top-ten, are Giannis Antetokounmpo and Karl-Anthony Towns. While they may raise the floor for teams are well as a few players on this list, they were lacking in major offensive categories that made the final cut just a bit easier. Players that were also in contention for the top-fifteen include but are not limited to: Devin Booker, Bradley Beal, Joel Embiid, Paul George, Donovan Mitchell, and Zion Williamson.

    The last main sticking point for this list is that it is extremely fluid. Meaning, players who are close to one another are, for the most part, interchangeable to a reasonable degree. This list is also meant to act as more of a starting point than an ending one. A “part one” of sorts that can be added onto alongside a new influx of information and the benefit of hindsight. So, without further ado, I present my estimation of basketball’s ten-best offensive players today.

    The List

    10. Trae Young

    During the past two seasons, Trae Young has evolved into one of the league’s premier shot creators, posting some of the highest estimates on record. He led the league with an estimated 18.5 shots created for teammates in the regular season, which held at a steady 16.4 through 15 Playoff games. Young’s passing was the catalyst to unlocking the value from his shot-creating. An astounding 85% of his assists in the regular season led to layups or three-pointers. While he doesn’t have the catch-and-shot or off-ball proficiency to optimize his fit alongside other perimeter talents, Young’s floor-raising style has proven him to be one of the NBA’s most dangerous offensive weapons.

    9. Kyrie Irving

    Despite the off-court drama, Kyrie Irving continues to string together some of the more underrated offensive campaigns in recent history, and there are a ton of positive indicators for him: He was +4.6 in offensive Estimated Plus/Minus, +4.1 in offensive LEBRON, and +3 in offensive Real Plus/Minus. Unlike his predecessor on this list, Irving is a great catch-and-shoot scorer, converting on 43% of these attempts in the regular season. Paired with elite finishing that takes advantage of the spacing created by the star talent around him, Irving can maintain a lot of the impact he’d use to strengthen the heights of poorer teams on championship-level offenses. That was the differentiator between him and a floor-raising stud like Trae Young.

    8. Damian Lillard

    Lillard is one of the most special on-ball talents in the league right now. As the clear-cut primary ball-handler for Portland, he runs a lot of high pick-and-roll that unlock: 1) his elite floor spacing and shooting gravity that pulls defenses far beyond the three-point line, and 2) open driving lanes that allow Lillard to pressure the rim. Because he pairs two extremely effective methods of scoring with the byproduct of high-level shot creation, Damian Lillard is very close to players multiple spots ahead of him on this list. His offensive impact metrics may have been even higher than his represented level, such as his +6.7 in the offensive component of EPM and +8.3 O-RAPTOR. Despite an elite Playoff series on paper: 32 points per 75 possessions on +8% True Shooting, there are still some lingering questions that ask how defenses can effectively scheme around Lillard in the Playoffs; so if forced to choose, he’s a notch under…

    7. Kawhi Leonard

    I’m splitting hairs between Leonard and Lillard, but the main sticking point with Leonard is that his scoring is more resilient in the postseason. His 48% shooting from the midrange in the regular season (57% in the Playoffs) gives him the classic three-level scoring reprtoire that Lillard (38% in the regular season and 15% in the Playoffs) doesn’t quite have. As the lead ball-handler with the Clippers, Leonard’s playmaking has shined as bright as ever. He doesn’t have the high-leverage assist power of the game’s very best, but his respectable passing keeps defenses at bay for him to punish drop coverages and unlock his incredible scoring repertoire.

    6. Kevin Durant

    We’ve had the benefit of viewing Kevin Durant through the lenses of various different roster constructions. The only problem: stints have been spaced far apart from one another. There are continuous questionings of whether he could handle the load as a primary ball-handler against elite defenses in the Playoffs, but he provides a ton of value as a secondary star as well. Durant’s all-time-level shooting and isolation scoring allow his scoring to fit well on most types of teams. And because he adds smaller amounts of value through passing and gravity as a roller, Durant still remains an All-NBA player due to offense alone. My confidence level is smaller with Durant, mostly because I wish there were more of him for us to see, but my “most likely” spot for him ends up being sixth.

    5. Luka Doncic

    A second consecutive player who’s very hard to rank, Luka Doncic. There’s a good argument that Doncic is currently shouldering the largest offensive load in NBA history, and he’s handling it extremely well. His creation estimates were second only to Trae Young in the regular season, and he placed first in the quick scoring proficiency model I whipped up some time ago. Because he creates so much offense through his individual actions, Doncic might be the best floor raiser in the league today. But because he can much up possessions by holding the ball later in the shot clock, and due to a lesser-developed off-ball game, my only concern is how well he could maintain that value if he were playing alongside another ball-dominant guard. This is the lowest I could see Doncic based on how incredible he’s been. (If it isn’t already obvious, these rankings are really hard.)

    4. LeBron James

    Once again, another player with lingering question marks. Last season, James made a great argument as the best healthy offensive player in the league with how well his motor was repaired for the Playoffs, allowing him to punish teams at the rim. His passing still continues to peak, but we saw his regular-season Passer Rating dip from historical heights to 8.3, suggesting he’s lost a bite of his passing value from a statistical perspective. There are also concerns of health and aging, so it’s difficult to fully assess healthy LeBron’s offensive prowess. But because I think he still fits on a good amount of teams, I’ll slot him in at fourth, but this is a bit of an optimistic outlook. Lower rankings are perfectly justified.

    3. James Harden

    Harden isn’t a traditionally scalable player, but he’s shown time and time again that he can provide oodles of impact on good teams. The only question with this is how much of his teammates’ roles are being sacrificed to incorporate Harden and his perennially league-leading times of possession. However, it has become clear his high-level shot creation will remain effective alongside other perimeter stars. Harden’s scoring took minor tolls from both a volume and efficiency standpoint, but he still averaged a steady 25 points per 75 on +4% relative True Shooting. I’ve gone back and forth between him and mate Durant for the past few months, but I went with Harden because Durant’s raw performances are far more likely to be the results of his being the beneficiary of optimal roster construction.

    2. Nikola Jokic

    The razor-sharp battle for the top spot is ever-so-slightly lost by Jokic in my eyes. (I’ll explain more later.) He carried over his all-time passing capabilities from the 2019 and 2020 seasons, but managed to perfect the craft even more. Jokic’s half-court passing and creation reached career highs, enhancing the Nuggets’ offense through the layups-and-threes shot selection, panning out countless assists to the paint and the corners. The full-court was his tapestry, and Jokic painted it with his passes as he hit leaking teammates as if it were target practice. When he wasn’t fighting for open position in the middle of the floor or screening for teammates, which added to his off-ball value, Jokic’s increased scoring kick took his offense toward historical levels. With a cleaner form and positive signals that accompany his shooting spikes, Jokic’s three-level scoring and league-leading passing create a combination that led to one of the greatest offensive seasons in history and a deserving MVP.

    1. Stephen Curry

    Narrowly edging out the MVP for the top spot on this list is Steph Curry, who manages to rack up more and more MVP-caliber seasons in Golden State. The argument that 2021 was his peak season is valid in that this very well might have been the best season of Curry’s career in a vacuum. While he loses some three-point dominance as the outside shot continues to evolve, Curry’s insane gravity unclogs the middle of the floor unlike any player ever. The classic images of teams sending traps on the perimeter early into the shot clock are great representations of the difficulties surrounding defenses scheming around Curry. Statistics like Box Creation underrate players who aren’t outliers as floor spacers on paper (Shaquille O’Neal), and while Curry doesn’t pass out of traps exceptionally well, his floor-spacing might be the most effective catalyst for a championship-level offense.

    Content Update

    To end the list, I’ll give a quick update on the content drought as of late. It’s been 40 days since my last NBA article, so while there hasn’t been the same writing frequency as of late. there are more types of content in the works. I’ll likely have some video content rolling out in the near future related to some cognitive phenomena in evaluating players and individual breakdowns of current and historical player seasons. Until then, I hope today’s article was a solid exchange of information on the league’s top offensive players.

  • How Matt Chapman’s Two-Way Play Makes Him an All-Star

    How Matt Chapman’s Two-Way Play Makes Him an All-Star

    Matt Chapman burst onto the scene in 2018 as an All-Star level player, proving strong abilities as both a hitter and a fielder, resulting in two consecutive years finishing at least seventh in AL MVP voting. As his batting began to stabilize, Chapman remained the anchor of one of the MLB’s best defensive teams and consistently providing value to Oakland that would rank him among the very best third basemen in the game. But as of late, Chapman’s performances have seemed more streaky and less effective. His overall statistical profiles on both sides of the ball have been declining since the 2019 season, so is this truly an indicator of a declining talent, or is Matt Chapman still on track to become an All-League baseball player?


    Chapman’s value as a hitter has been a bit puzzling over the last four seasons. During his first full season in 2018, his batting profile spiked at very desirable heights. His 2017 hard-hit rate (EV > 94 MPH) of 43.6% jumped to 53.8%, and he consistently fared well in hitting line drives while limiting ground balls and fly balls. Weighted Runs Created (wRC), which estimates a player’s value as a batter using box score statistics in conjunction with run expectancy values for various events, pegged Chapman in its standardized counterpart at 139 up from 110 the previous season. A season later in 2019, that value dropped to 126. A season later, in a mere 37 games, Chapman was still above league-average at 117. However, in 60 games played in 2021, he’s fallen to 88.

    Baseball can be a streaky sport, with even season-long runs of statistics not being totally indicative of a player’s “true” value, so has Chapman’s offensive skill dropped off in recent years, or is there an element of luck at play?

    The immediate eyesore in Chapman’s statistical profile is his batting average, which has dropped at least 17 percentage points in each season since 2018, and this statistic seems to have some type of relationship with his batting average on balls in play. Chapman’s .278 season saw 33.8% of batted balls result in hits, which immediately fell to .270 the following season without any major change in his zone swing portfolio.

    We actually see his tendency to chase low balls decline in the following season, suggesting he almost certainly received the benefit of chance with his batting average in 2018. That means, while we see a significant decline in the raw numbers, his skill level is very likely more stable than these numbers indicate. However, there is one prominent aspect of Chapman’s pitch selection that can explain his shortcomings in the batter’s box as of late: massive changes in run value in certain swinging areas.

    There has basically been no change in how Chapman attacks various qualities of pitches, with the pattern of an ever-so-slight increase in overall swing rate evolving over the past four seasons. However, as stated earlier, some of these areas of Chapman’s swings appear to be bleeding value. The approximated run value in certain listed zones have been fluctuating:

    A degree of instability across zones is clear, but the exact degrees vary across zones. Chapman’s estimated run value from pitches in the shadow zone, which envelops the heart of the strike zone while extending slightly beyond it, has been relatively stable over the past four seasons. However, Chapman appears to have lost a considerable amount of impact as a hitter in each of the other zones. The largest yearly drop-off in a zone was between the 2019 and 2020 seasons, during which his value in the chase zone severely declined, but it is worth noting a lot of flattened trends in the last two seasons are in some form byproducts of shorter or incomplete seasons.

    An important skill of Chapman’s to recognize is how he provides most of his value as a hitter; and interestingly, it’s not necessarily by his ability to hit the ball, but to take pitches. Expectantly, in zones outside the heart of the strike zone, Chapman usually loses runs for his team when he doesn’t take the pitch. (It’s worth noting Chapman added an estimated 20 runs through swings in the heart of the strike zone, followed by three seasons of 9, 4, and -8 runs, which serve as indicators of the potential “luck” factor in Chapman’s batting output.) However, Chapman’s selectivity with pitches outside the strike zone actually adds a considerable amount of value to his team’s offense.

    The aforementioned -8 run value from the pitches Chapman faced in the heart of the strike zone is a compelling figure alongside the previous three seasons, and likely signals some type of change in either Chapman’s hitting tendencies or opposing defense’s reactions to such hits. While his proportion of batted balls hasn’t changed much, other aspects of his batting portfolio have. Matt Chapman has always been a great hard hitter, hitter 53% or more of his batted balls leaving at an exit velocity of 95 MPH or higher from 2018 to 2020. But in 2021, that percentage has fallen below the 2017 to 2021 league average of 39%, settling at 36.2%.

    As his other hitting tendencies are functionally similar, there seems to be a sneaky good chance a large proportion of Chapman’s hits in the heart of the strike zone are inadvertently resulting in pop-ups. Since these pitches aren’t positioned at angles that provide an inherently greater or less chance of the resulting hit being a pop-up, the increased fly ball percentage has a promising likelihood of being a product of poorer luck. Thus, I’m a bit higher on Matt Chapman’s slugging ability than the number suggests, and perhaps if all the weird recent circumstances hadn’t come into play, his batting profile would have regressed to values that are more indicative of his true value as a hitter.


    During the past four years, Chapman has been awarded two Gold Gloves as an AL third baseman and two Platinum Gloves, seemingly on the track to become one of baseball’s all-time great fielders at the position. His renowned defensive game is centered around Chapman’s all-world fielding range.

    Chapman is known to strictly play the roles of a left-side infielder, spending heavy innings at third base while seldom moving to shortstop. The above chart shows Chapman’s starting positions from the 2018 to 2021 seasons (through June 6, 2021), displaying a healthy diet of movement and adjustments that would be expected from an everyday third baseman; but the more interesting aspect of his fielding is where he finishes.

    Chapman’s estimated 41 outs above average were surprisingly dispersed across the geometry of the field. He stays within the distinct vicinity of the third-base territory but extends his reach out past the foul lines and a considerable way into the outfield along with his bunt protection and coverage versus shorter batted balls. As explored in his film study, Chapman pairs elite abilities as a fielder with absurd levels of versatility in how he protects such large areas of the field for the Athletics.

    His ability to protect the area of the field extending out to the foul line is the focal point of his fielding, and it makes ground ball hits extremely difficult to convert on for opposing teams. Chapman’s fielding on film exhibits some of the most impressive glove precision in the game today, eliminating the need to provide a lot of value through a quicker recovery time.

    Unlike other third basemen, Chapman shows a consistent effort between the catch-to-throw transition to effectively block the ground ball and square his body for the out to first. His aforementioned recovery time is shown to be split into two parts: one, the shorter one, involves his play during hits that extend his range. The time between his interception of the ball and when he’s back on his feet is among the quickest in the league, alleviating the stress for the period that follows. Chapman is shown to take slightly more time to position himself for the throw than other infielders, but it mitigates some of the wildness that comes with an arm as strong as his.

    However, Chapman displays a strong tendency to augment his fielding motion to adapt to a given play. Here, he blocks the ground ball a significant portion to his right and splits the time between recovery and throw roughly equally. This defensive versatility allows Chapman to function at an elite level in many types of run situations. Paired with his incredible arm speed and maintenance, and Chapman demonstrates a clear All-League skill in his fielding.

    Chapman adds to his bag of tricks as a ground-ball fielder with the spin move. The fluidity of his hips paired with his glove placement makes him one of the best defensive playmakers in baseball. Here, he turns a relatively difficult ball in play into a safe out through his full rotation upon fielding the ball, clearly shortening the time necessary to make the throw and furthering the idea that Chapman protects a larger area of the field than arguably any other player at his position.

    A strength of Chapman’s that separates him from other third basemen is how well he protects foul territory. He makes similar plays on line drives or looping hangers that would clearly appear to be in unattainable descent, yet the value Chapman adds from converting on these plays saves a considerable number of runs over the course of a season. This play demonstrates his ability to travel into the seating area, but as long as the batted ball is within the horizontal range of his third base positioning, he’s a consistent candidate to make the catch.

    There are only two prominent weaknesses in Chapman’s game, both of which are rarely at play. Because he has the tendency to shield the ball with mainly his glove rather than blocking it with his entire body, the angle at which his glove is positioned proves crucial. This means a downturned glove will allow more hard grounders to sneak by, and his torso won’t be in positioning to halt its movement.

    Chapman has one of the strongest arms among position players in the MLB. During his time with the U.S. national college team, he threw pitches that were tracked at a velocity up to 98 miles per hour and was perennially recognized as having one of the strongest arms in the Minor Leagues before his rookie year. With that, however, comes the greater risk of an overthrow. Chapman appears to actively combat this, meaning more of his throwing errors actually require first basemen to scoop his throw rather than leap for it. Although a testament to Chapman’s defensive mind and awareness, there isn’t an immediate remedy for his short-arm throws.

    Impact Evaluation

    Even everyday watchers of the Athletics during Chapman’s first few seasons were taken aback at how quickly he was able to ascend to elite territory among the MLB’s best players. All-in-one estimates of aggregate value, mostly Wins Above Replacement models, thought very fondly of Chapman during the 2018 to 2019 stretch, which was still likely the peak of his actual abilities as both a batter and a fielder.

    Chapman peaked at elite heights, which suggested he had even surpassed the typical All-Star electee and was entering All-League territory, which would put him among the top-16 or so players in the MLB. Because there still a certain number of question marks with his offense (is his pop-up spike a function of skill loss or bad luck?) and how much slack his fielding can pick up, I’m not quite ready to name him to my All-MLB teams. But there’s simply too much evidence that suggests he’s a bonafide All-Star, and when he’s healthy, perhaps even more.

  • The 10 Best NBA Impact Metrics

    The 10 Best NBA Impact Metrics

    It’s been a long, windy journey to get here, one that started with plans for a video. (That wouldn’t have been enough time to discuss all ten metrics.) Then I recorded a podcast that ended up being just under an hour and a half long. I’m hoping to fall somewhere in the middle here, to provide as much information possible in a digestible amount of time. Ladies and gentlemen, I present to you (finally…), the 10 best NBA impact metrics.


    Ranking impact metrics proved to be no easy task. To limit errors that would come from an arbitrary approach, I chose to run with a very strict criterion:

    • Descriptivity

    To qualify for the list, the impact metric had to (at the very least) be a measure of the past, or what has already happened. There will be some metrics in the rankings that enlist predictive techniques as well. But as long as past data is used to also measure the past, it checks this box. It’s also worth noting most metrics that aren’t strictly predictive don’t inject themselves with predictive power for traditionally “predictive” purposes. Model overfitting is a consistent problem among pure Plus/Minus metrics, meaning scores can severely change from team to team even if the quality of the player stays the same. Combatting these phenomena will actually create some clearer images of the past.

    • Type of Measurements

    Because almost every “good” modern metric is based in some way on Adjusted Plus/Minus (RAPM), which employs philosophically fair principles, I figured it would be “fairest” to evaluate metrics based on their adherence to the original “ideology” of RAPM: to measure a player’s impact on his team in a makeshift vacuum that places him alongside average teammates while facing similarly average opponents. Because this approach would, in theory, cancel out a lot of the noise that stems from extreme team circumstances to measure the player independent from his teammates, impact metrics are judged on how they align with these ideas. (Impact metrics are distinct measures of value to only one team, but some will be able to move the needle more in overcoming problems like these.)

    • No Sniff Tests

    A lot of NBA critics or fans who aren’t mathematically inclined will often skim leaderboards for a metric to see how it aligns with their personal lists or player rankings. Because this approach places too much stock in prior information, and a lot of the critics may not actually evaluate players well, the sniff test is not really going to help anyone judge a metric. For this list, all specific player placements are set aside to only view the metric from a lens that focuses on how they perform in the aforementioned criteria.

    • Availability

    This doesn’t concern how the metric is judged itself, but the last qualification for a metric to appear on this list is its current availability. A metric I reviewed for this list called “Individual Player Value” (IPV) may have held a spot on the list, but there were virtually no opportunities to view the metric’s results from recent seasons. Thus, all metrics on this list were available (not necessarily free to the public but in the public knowledge) through the beginning of the 2021 season. If it isn’t clear, I really wanted to include PIPM here.

    • Modern Era Metrics

    Not all metrics on this list can extend as far back in the past as others. Most will be available from the 2014 season (when the NBA first started recording widespread tracking data) onward, while some can be calculated as far back as turnovers can be estimated (basically as far back as the institution of the shot clock). Because this really takes a “modern era” approach to evaluating these metrics, only a metric’s performance and value in the 2014 season and beyond will be in consideration during these rankings. So, for example, PIPM’s shaky nature in season predating Plus/Minus data is out of the equation here.

    • Disclaimer

    People can use impact metrics improperly during a debate all the time, but the most specific case I want to show can be explained by the following example. Let’s say, hypothetically, LeBron James finished as +7 in LEBRON in 2021 and +8 in BPM. If someone instigates a conversation with the BPM score, the interlocutor may provide the +7 LEBRON as a “better” or “more meaningful” representation of James. This is not a good way to go about comparing scores in impact metrics. Different metrics sway toward various playstyles, team constructions, etc. Just because LEBRON is a “better” metric (this shouldn’t really be a spoiler),  it won’t measure every player better than, say, BPM.

    List Structure

    If only this were as simple as only needing one list… Because different metrics treat different sample sizes differently, and the time period during which a metric is taken affects its accuracy relative to other metrics, I’ll split this list into two. The first, which will include the condensed metric profiles, assesses the metrics’ performances across three (full) seasons or more. Three years is the general threshold for stability, a point at which scores aren’t significantly fluctuating. The second list will evaluate metrics in a sample taken within a single season. Since players will often be analyzed using single-season impact metrics, this distinction will hopefully separate some of the metrics’ strengths and weaknesses in various environments.

    10. Luck-adjusted RAPM

    Developer: Ryan Davis

    Based on the original works of Regularized Adjusted Plus/Minus (RAPM), Ryan Davis added a prior to his calculations as a “luck adjustment.” It’s not a traditional prior that would, for example, use counting or on-off statistics to bring in outside information we know to hold value. Rather, the adjustment normalizes a player’s three-point shooting to his career average based on the location of the shot. Free-throw shooting is also normalized to career average. I’m particularly low on the function of the prior because, to me, it would make more sense to adjust teammate and opponent performance instead (what is done in luck-adjusted on-off calculations).

    My largest concern is that long-term samples of LA-RAPM will struggle to capture improvements over time. And if someone were to map out a player’s career, it would probably be too smooth, and not in a good way. Because the career averages are used, it might be a bit better in evaluating career-long samples as a whole, but it’s not going to measure individual seasons or even long samples much better than RAPM with no prior. The ideology and the processes behind the metric are impressive, but their applications seem a bit wonky to me.

    9. NPI RAPM

    Developer: Jeremias Engelmann

    The predecessor to every single other metric on this list, non-prior-informed RAPM was Jerry Engelmann’s improvement on Daniel Rosenbaum’s Adjusted Plus/Minus (APM), an estimate of the correlation between a player’s presence and the shift in his team’s Net Rating. Although a promising metric, APM was never truly built to be used in practice because of its inherent noisiness and high-variance solutions to linear-system appeasements. Englemann employed ridge regression, an equal-treatment form of Tikhonov regularization in which a perturbation form of traditional OLS appeasement uses various degrees of lambda-values (nowadays found through cross-validation) that suppress the variance of APM coefficients and draw all scores toward average, or net-zero.

    A lot of great analytical minds will say long-term RAPM is the cream of the crop of impact metrics. However, as was with APM, it’s still unavoidably noisy in practice. And since players are treated entirely as dummy variables in the RAPM calculations, devoid of any causal variables, my confidence in the accuracy of the metric is lower than others. RAPM is built to provide strong correlations between the players and their teams, but due to a lack of any outside information creates a greater level of uncertainty regarding RAPM’s accuracy, I’m going to rank it near the back end of this list. However, I have it higher than Davis’s luck-adjusted version for the aforementioned reasons relating to career mapping.

    8. Basketball-Reference Box Plus/Minus

    Developer: Daniel Myers

    The signature metric of Basketball-Reference and probably the most popular Plus/Minus metric on the market, Daniel Myers’s BPM 2.0 is arguably the most impressive statistical model on this list. There are some philosophical qualms I have with the metric, which I’ll discuss later. BPM continues the signature Myers trademark of dividing the credit of the team’s success across the players on the team. However, this time, he updated the metric to include offensive role and position on his team to add context to the environment in which a player accrued his box score stats. This means assists are worth more for centers, blocks are worth more for point guards, etc.

    BPM incorporates a force-fit, meaning the weighted sum of BPM scores for a team’s players will equal the team’s seasonal Net Rating (adjusted for strength of schedule). However, a team’s NRtg/A uses a “trailing adjustment,” which adds a small boost to good teams and a downgrade for poor teams based on how teams often perform slightly better when they are trailing in the game. The aforementioned gripes are mainly based on how BPM treats offensive roles. The metric will sometimes treat increments in offensive load as actual improvements, something we know isn’t always true. There are also some questions I have on the fairness of measuring offensive roles relative to the other players on the team.

    7. Backpicks Box Plus/Minus

    Developer: Ben Taylor

    I’ve gone back-and-forth between the two major Box Plus/Minus models for some time now, but after learning of some new calculation details from the creator of the metric himself, I’m much more comfortable in leaning toward Ben Taylor’s model. He doesn’t reveal too much information (in fact, not very much of anything at all), even to the subscribers of his website, but he was willing to share a few extra details: BPM uses two Taylor-made (double entendre?) stats: Box Creation and Passer Rating, estimates of the number of shots a player creates for teammates every 100 possessions and a player’s passing ability on a scale of one to ten. This is a very significant upgrade over assists in the metric’s playmaking components and certainly moves the needle in overcoming team-specific phenomena that don’t represent players fairly.

    Backpicks BPM also trains its data on more suitable responses, something I didn’t mention in the Basketball-Reference profile. Myers’s model uses five-year RAPM runs, notably decreasing the metric’s ability to measure stronger players. Conversely, Taylor’s two-to-three-year runs include stronger levels of play in the training data, meaning All-NBA, MVP level, and beyond caliber players are better represented. Teammate data is also toyed with differently. Rather than measuring a player strictly within the confines of his roster, the Backpicks model makes a clear attempt to neutralize an environment. To put this into perspective, Myers’s model thought of Russell Westbrook as a +7.8 player in 2016 (with Durant) and a +11.1 player in 2017. Taylor’s model saw Westbrook as a +7 player in both 2016 and 2017.

    6. Player Impact Plus/Minus

    Developer: Jacob Goldstein

    As was with me when I was first learning about impact metrics, introductory stages to basketball data will often lead people to believe PIPM is arguably the best one-number metric in basketball. It combines the box score with on-off data and has very strong correlative powers relative to its training data. But when I started to look under the hood a bit more, it was clear there more issues than immediately met the eye. Compared to other box metrics, PIPM’s box component is comparatively weak. It uses offense to measure defense, and vice versa. It doesn’t account for any positional factors and the response is probably the most problematic of any metric on this list. I’ll discuss this more.

    Recently, I’ve been leaning away from on-off ratings. They’re inherently noisy, perhaps even more so than RAPM, easily influenced by lineup combinations and minutes staggerings, which can make an MVP level player look like a rotational piece, and vice versa. The luck adjustment does cancel out some noisiness, but I’m not sure it’s enough to overcome the overall deficiencies of on-off data. PIPM is also based on one fifteen-year sample of RAPM, meaning the high R^2 values are significantly inflated. Again, this means very good players won’t be well-represented by PIPM. This excerpt may have sounded more critical than anything. But the more I explore PIPM, the most I’m met with confounders that weaken my view of it. Perhaps the box-only metrics are slightly better, but I’ll give PIPM the benefit of the doubt in the long term.

    5. Augmented Plus/Minus

    Developer: Ben Taylor

    Augmented Plus/Minus (AuPM) similarly functions as a box score / on-off hybrid. It incorporates the Backpicks BPM directly into the equation, also roping in raw Plus/Minus data such as On-Court Plus/Minus and net on-off (On-Off Plus/Minus). It includes a teammate interaction term that measures the player’s Plus/Minus portfolio relative to other high-minute teammates, and the 2.0 version added blocks and defensive rebounds per 48 minutes. There’s no direct explanation as to why those two variables were included; perhaps it included the regression results a bit more, despite having likely introduced a new form of bias.

    Pertaining to the AuPM vs. PIPM debate, it should be abundantly clear that AuPM has the stronger component. And while PIPM bests its opponent in the on-off department, the inclusion of shorter RAPM stints in the regression for AuPM means more players will be measured more accurately. So, despite arguably weaker explanatory variables, the treatment of the variables leans heavily in favor of Augmented Plus/Minus.

    4. RAPTOR

    Developers: Jay Boice, Neil Paine, and Nate Silver

    The Robust Algorithm using Player Tracking and On-Off Ratings (RAPTOR) metric is the highest-ranked hybrid metric, meaning every metric higher uses RAPM calculations in its series of calculations, not just as a response for the regression. RAPTOR uses a complex series of box scores and tracking data paired with regressed on-off ratings that consider the performances of the teammates alongside the player and then the teammates of those teammates. The regression surmounts to approximate one six-year sample of NPI RAPM. My high thoughts of it may seem inconsistent with the contents of this list. However, one major theme has made itself clear throughout this research: tracking data is the future of impact metrics.

    Despite a “weaker” response variable, RAPTOR performs excellently alongside other major one-number metrics. During Taylor Snarr’s retrodiction testing of some of these metrics, which involved estimating a team’s schedule-adjusted point differential (SRS) with its players’ scores in the metrics from previous seasons (all rookies were assigned -2), RAPTOR was merely outperformed by two metrics, both prior-informed RAPM models. This is a good sign RAPTOR is assigning credit to the right players while also taking advantage of the most descriptive types of data in the modern NBA.

    3. Real Plus/Minus

    Developers: Jeremias Engelmann and Steve Ilardi

    Real Plus/Minus (RPM) is ESPN‘s signature one-number metric, touted for its combination of descriptive and predictive power. According to the co-creator, Steve Ilardi, RPM uses the standard series of RAPM calculations while adding a box prior. This likely means that, instead of regressing all the coefficients towards series as explained in the NPI RAPM segment, Engelmann and Illardi built a long-term RAPM approximation, which then acts as the datapoints the player scores are regressed toward. Value changes and visual instability aside, RPM is among the premier groups of metrics in their ability to divvy the right amounts of credit to players, having finished as the metric with the second-lowest SRS error rate in Snarr’s retrodiction testing.

    2. LEBRON

    Developers: Krishna Narsu and “Tim” (pseudonym?)

    BBall Index‘s shiny new product, as new as the latest NBA offseason, the Luck-adjusted Player Estimate using a Box prior Regularized On-Off (LEBRON) metric makes a tangible case as the best metric on this list. Similar to RPM, it combines the raw power of RAPM with the explanatory power of the box score. LEBRON’s box prior was based on the findings from PIPM, but upgrades the strength of the model through the incorporation of offensive roles, treating different stats differently based on how certain playstyles will or won’t accrue the stats. Three-point and free-throw shooting is also luck-adjusted in a similar fashion to PIPM’s on-off ratings to cancel out noise.

    Part of what makes LEBRON so valuable in a single-season context is its padding techniques, which involve altering a player’s box score profile based on his offensive role. For example, if Andre Drummond shot 45% from three during his first ten games, LEBRON’s box prior will take his offensive role and regress his efficiency downward based on how he is “expected” to stabilize. This makes LEBRON especially useful in evaluating players during shorter stints, and while these adjustments aren’t perfect, the metric’s treatment of box score stats probably uses the best methods of any metric on this list.

    1. Estimated Plus/Minus

    Developer: Taylor Snarr

    I don’t want to say Estimated Plus/Minus (EPM) runs away with the top spot on this list, because it doesn’t, but it’s clear to me that it’s the best widespread impact metric on the market today. Roughly as young as LEBRON, EPM is the product of data scientist, Taylor Snarr. As noted by RPM co-creator Ilardi, EPM is similar to RPM in that it uses RAPM calculations to regress toward the box score, but also includes tracking data. The tracking data, as has been shown with RAPTOR, makes all the difference here. During his retrodiction testings, Snarr constructed linear regression models to estimate the effect of lineup continuity on the metric’s performance.

    To the envy of every other metric, EPM’s reliance on lineup continuity was estimated to be roughly half of the runner-up metric, RPM. It may not sound like a crucial piece of information, but given EPM’s model strength and some of these types of metrics’ largest problems, EPM performs fantastically. It’s also worth mentioning EPM is predictive as well, having led the retrodiction testing in SRS error throughout the examined seasons. I allowed these details to simmer in my head for some time in case I was having some type of knee-jerk reaction to new information, but the points still stand tall and clear: EPM is currently unmatched.

    For the single-year list, I only made two significant changes. Because shooting is much noisier in smaller samples, such as a season or less, I’ll give the edge to Davis’s LA-RAPM over NPI RAPM. Additionally, PIPM’s response issues drop it down a peg for me in the one-year context. I did consider putting LEBRON over EPM due to its padding (EPM doesn’t employ any stabilization methods to my knowledge), but the tracking data leading to greater team independence is too large an advantage for me to overlook.

    Single-Season Rankings

    1. Estimated Plus/Minus
    2. LEBRON
    3. Real Plus/Minus
    4. RAPTOR
    5. Augmented Plus/Minus
    6. Backpicks BPM
    7. Basketball-Reference BPM
    8. Player Impact Plus/Minus
    9. Luck-adjusted RAPM
    10. NPI RAPM

    There was also some noise surrounding DARKO’s Daily Plus/Minus ranking on this list. I did evaluate the metric for this list despite its breaking of the criteria, simply to include it as it stacks up against the other metric in model strength. Based on the statistical model, I would rank it fifth on this list, bumping AuPM down a spot and slotting DPM right behind RAPTOR.

    To my surprise, some people saw DPM as the premier impact metric on the market today. Some questioning led back to DPM’s developer’s, Kostya Medvedovsky, game-level retrodiction testings during the tracking era, which saw DPM lead all metrics. However, DPM is specifically designed to act as a predictive metric, giving it an unjustified advantage in these types of settings. Based on how I “expect” it would perform in descriptive duties based on the construction of its model, I don’t really see an argument for it cracking the inner circle (the Final Four).

    Thanks for reading everyone! Leave your thoughts in the comments on these metrics. Which is your favorite? And which one do you believe is the best?