• ## The Ultimate PER Guide | Untangling John Hollinger’s Analytics Lovechild

(Image via Bleacher Report)

Player Efficiency Rating (PER) was the turning point for basketball analytics in the public domain; but with time comes controversy. Lots will claim that PER is an outdated metric, that recent efforts of all-in-one metrics have left PER useless. Let’s say this is true, and for good reason. PER has a limited scope compared to lots of modern metrics, which incorporated Plus/Minus and tracking data that seems to map a player’s value to an objectively greater degree than the box score. Let us be reminded that this is a good thing! More advancements means more descriptive power among these all-in-one metrics, so the science of player analysis has undergone significant evolution since Hollinger’s initial effort. So, as a brief summation, PER is NOT one of the absolute best measures of player impact for the modern era. But like any other subject with a rich history, there is value in going back to appreciate tradition. Let us explore the inner workings of PER. What makes it good or bad, and why should or shouldn’t you use it?

How PER Works

PER puts the “E” in “Efficiency” because it was designed as a fairer comparison between high-volume superstars and role players. Like lots of modern impact metrics, PER is a per-possession metric that estimates a player’s effect on his team’s point differential [1]. But instead of using advanced, complex mathematical modeling to accomplish its results, PER is grounded in concept and critical thinking. It works so that each box score statistic (points, assists, etc.) is assigned a weighting, which is personalized to its box score stat such that each weighting reflects the statistic’s point-value. If that sounds a bit confusing, hopefully this example makes things clearer:

LeBron James committed 196 turnovers [2] during the 2022 regular season. Most basketball fans will agree that turnovers are bad! A turnover means the offensive team lost possession of the ball without having scored. Thus, they lost out on the opportunity to score points in that possession; and basketball is often a game that is won in a matter of possessions. Plus, there’s also the drawback from permitting the opposition a transition possession, which tends to yield more points than typical half-court offense. So we can all agree turnovers are bad, right? But how do we know how bad one is? Well, we have to consider what a turnover is taking away from, and the big thing is those aforementioned points the team could have scored if the ball weren’t turned over.

Since a variety of outcomes could’ve followed barring one of James’s turnovers, Hollinger decided to use a single placeholder number to sum up all possible outcomes of a possession. This estimates just how many points the Lakers were missing out on because of the turnover. Let’s think about it this way: on average, NBA offenses scored 1.12 points per possession in the 2022 regular season [3]. Hollinger concludes this was the best estimate of how much an offense is missing out on from turning the ball over, not accounting for how the opponent can gain a transition possession, as stated earlier. But since the turnover is deducting that amount of value, a turnover in 2022 is worth approximately -1.12 points! If we apply that weighting to all of LeBron James’s 196 turnovers this year, we can estimate that he cost the Lakers almost 220 points from his turnovers.

This process is done for all box score statistics (most of which have far more complicated weightings), and the results are summed up to estimate how many points a player is adding (or subtracting) to his team. However, as stated earlier, there is one last adjustment that converts the results to a per-possession basis. Namely, superstars don’t receive any benefits for playing more of the game. This “adjusted” form of PER is what you’ll see on Basketball-Reference or ESPN leaderboards. With that out of the way, let’s discuss the good and the bad of PER, and what its process means for the metric’s ability to evaluate players.

Believe it or not, there is some good stuff about PER. Take this as more of an opinion than a fact, but PER has solid (and interesting) critique behind it. The idea that each statistics has a hypothetical point-value behind it is logic that is used to this day, even with the most revered metrics like Estimated Plus/Minus and BBall-Index’s LEBRON; and PER was the first to do it. Let’s also consider the benefit to translating the results to per-possession rather than per-game or across an entire season. PER can be a reasonable tool for identifying hidden gems slotted at the end of the bench, and can act as an indicator of whether a role player is outperforming one of the better players on the team. Back when PER was the gold standard, there was some value it could provide to teams looking to manage their roster and shuffle their lineups. Not at all a bad result!

However, there are a considerable number of drawbacks to discuss with PER; and unfortunately, these dominate the conversation and are often valid concerns of the metric. Let’s return to the per-possession basis of PER. While there may be benefits, there are also flaws with this approach. There is the matter of fatigue in which players with a heavier load tend to tire out near the end of games, whereas role players can spend more of their time on the court with a fresh set of legs. Superstars also tend to player with better teammates, meaning they have fewer chances to exert their skill; and they often play tougher opponents, whereas role players tend to match up with the opponent’s bench units as well. That is, not all statistics are created equally, and a player’s impact can be reframed and reimaged depending on who else is on the court, which is something PER struggles to account for.

The other glaring issue with PER is that it lacks a benchmark, or some type of measurement to fall back on to confirm the metric is grounded in reliability. If you’re familiar with other popular impact metrics, you may remember that they are often backed by RAPM, which is arguably the strongest all-in-one metric basketball has to offer. If not, I have written in-depth about RAPM before [4] if you’re interested in learning more about it. (TW: Math.) PER has been around for nearly twenty years, so it’s no surprise that it has been one-upped by more recent metrics, but the larger issue is that John Hollinger has refused to update the metric. PER has been more or less the same since 2005, which excludes the metric from the comprehensive analytical techniques of today. This, paired with the inconclusive nature of the metric’s logic, makes PER one of the less viable options to analyze players.

Should You Use It?

The biggest argument against using PER is that there are many better alternatives, which is true. Estimated Plus/Minus, LEBRON, RAPTOR, and BPM, among others, all have more solid bases in accomplishing their goals. We’ve discussed the positives and the negatives of the metric, and are hopefully all able to recognize that both exist. But, again, PER is simply outdated. Hollinger’s refusal to refine his metric has left it in the dust. You’re much better off using the Backpicks (proprietary) or Basketball-Reference models of BPM if you’re looking to view a player’s impact from the perspective of the box score. But does this mean PER is bad?

I wouldn’t say so. PER has a very intriguing basis, and the logic Hollinger incorporated into the metric shows a considerable understanding of how basketball is played and won. Therefore, PER is still going to be quite a hit-or-miss metric, as lots of them are. But it’s not “bad” to the point that it measures every player off the mark. Heck, there’s the off-chance that PER pins a player down just right! However, it’s not great either, especially considering its peers. So the next time someone tells you PER is the worst thing to grace the Earth, tell them it could be worse. If it helps, tell them to look into Wins Produced from the Wages of Wins Journal. But that’s all from me, folks. I hope this was a somewhat insightful look into PER, and that you’re next perusing of a leaderboard is that much more confident.

[4] http://www.cryptbeam.com/2021/03/08/how-do-nba-impact-metrics-work/

• ## My Top-10 NBA MVP Candidates (2/27/22)

(📸 The Ringer)

The conflict between performing and storytelling on the basketball court has clouded the MVP race for decades; and like other highly-divisive topics in sports, both sides are represented by two camps:

### Criteria

Traditionally, the MVP has a very loose criterion that hinges on the voter’s ability to tell a story with their vote. For example, take 2011 Derrick Rose’s MVP. He was clearly not the best regular-season player that year, but the Chicago Bulls sneaked up behind the newly-formed Heatles and snagged the first seed in the East. Sure, the Bulls were successful because of their defense and not their offense, but Rose’s floor-raising efforts and acrobatic, engaging playstyle drew fans to the screens and promoted the league’s popularity. Was Derrick Rose the “Most Valuable Player” in 2011? No; but nominating him as the MVP was good for the NBA.

Perhaps more recently, there are those who strictly adhere to how “good” a player is when selecting their MVP ballot. This is a basketball-only approach that looks to recognize players based on their ability to affect a team’s chances of winnings: win-loss record, seeding, home-court advantage, all of that. There’s an obvious appeal here: it’s less biased than narrative-based voting when done right; it provides a sturdier baseline to evaluate candidates (not everyone cares who the best player on the best team is when using storylines); and it forces us to look closer at what’s happening on the court and overcome the deficiencies in our thought-processes.

I flesh out these two approaches to not advocate for one or the other, but to establish my priorities as I assemble this list. Typically, my content has been based around the second approach: trying to use observations and material evidence to support arguments for one player or another. While such an approach is fully appropriate for, say, a player rankings list, I’m not sure the same applies to the MVP Award. Perhaps the “Most Valuable Player” isn’t necessarily providing the most value toward winning, but toward the welfare of the Association. With this in mind, I’ll still reference a player’s actual skill and heavily weigh it in my final ranking, but another priority is how a player has been drawing fan interest and promoting league viewership to provide a more holistic view of who has been the NBA’s Most Valuable Player in 2022.

—-

10. Kevin Durant

The Slim Reaper has missed some time with injury troubles, but has still been playing around MVP levels when he’s on the court. Durant has assembled a masterful offensive skill set throughout his career, pairing his length in driving lanes with all-time shooting ability, which are exactly the types of characteristics you’d wish to see in a player who moves the needle for championship offenses.

9. Luka Doncic

The greatest basketball prodigy since LeBron James started off the season in a bit of a slump, but picked himself up in recent weeks, re-evolving into the dangerous offensive centerpiece we’ve seen him be for the third consecutive season. Doncic can hit defenses quickly with unexpected attacks and passes out of traps extremely well. He’s a similar build to James in that he can quarterback an elite offense surrounded by shooters who leverages his drive-and-kick game to their advantage. Dallas has also made a surprise entrance as a top-five team in the West by SRS. [1]

8. Chris Paul

The Phoenix Suns have been the best team in basketball so far, and it would be narratively unjust to go without recognizing one of their players. Among the league leaders in my hand-tracking of shot creation, Paul is a masterful pick-and-roll ball-handler, splitting defenses at will and punishing drop with his lethal mid-range shooting. He drives Phoenix’s offense and manages to play at All-NBA levels while fighting against Father Time’s inescapable aging curve. CP3 is a talent for the ages.

7. Ja Morant

My favorite player to watch in 2022 and the sport’s next great athletic freak. Morant has been the figurehead of an exciting Memphis Grizzlies squad while being one of the more improved players in the league, playing around All-NBA basketball this year. At his best, Morant creates easy offense like the game’s very best. His incredibly dynamic scoring and uncanny passing vision formulates one of the most unique offense skill sets in the sport. Morant will do all this and also steal defensive rebounds from your favorite big man.

6. DeMar DeRozan

DeRozan is one of very few players who have proved they can still be one of the game’s very best scorers without three-point shooting. He’s been breaking basketball with his mid-range shooting, making 51% of a mind-shattering 14.5 attempts per 75 possessions! [2] DeRozan’s storyline would arguably make him a finalist if I were more partial to narratives, but there’s too weak of a stance based on performance alone. Playoff concerns aside, this player has been a unit on the basketball court, revitalizing a stunted career and shedding loads of doubt from critics.

5. LeBron James

The King is still really good at basketball. He’s been having one of his best regular season in years, punishing defenses with the scoring that vaulted his name into the GOAT conversation many years ago. Also one of the best passers in the sport and an adequate floor-spacer whose timeless athletic prowess makes him a strong defensive player even in his nineteenth season. The regular season could be hinting toward the reemergence of Playoff LeBron in a few month’s time.

4. Giannis Antetokounmpo

Ah, the wonders of voter fatigue. The Greek Freak was the third finalist on my ballot from last year, and while he’s done an outstanding job of raising the ceiling for a smaller-market team, the league might do better spicing things up a bit. Regardless, Antetokounmpo is arguably the first or second-best player in basketball right now, making the fourth spot my absolute floor for him.

3. Stephen Curry

Probably the face of the NBA. Curry is among the league-leaders in merchandise sales [3] and promotes the best TV ratings [4] in the league. His scoring has taken a massive hit from its glorious past, but his ability to bend and break defenses remains. Curry is loved by impact metrics and is having one of the best defensive and passing seasons of his career. Given he had maintained his early-season hot streak, he would be the top player on this list. But for now, he slides back to third.

2. Joel Embiid

Embiid is a masterful scorer who pairs punishing brute force in the paint with grateful skill on the block that garnered (self-anointed) comparisons to the likes of Kobe Bryant and Hakeem Olajuwon. He’s still one of the strongest defenders in the league and an improving playmaker. The fans seem to want to see Embiid as a finalist for a second straight season, and such recognition is warranted.

1. Nikola Jokic

The claim for the best player in the league in 2022 seems particularly exclusive this season because of the Joker. We’re talking about a player who has legitimate arguments as both the best scorer and playmaker in the sport right now, blending three-level scoring with an unheralded array of passes that stretch defenses to their absolute limits. Jokic has also been a clear positive on defense this season. By the way, Denver outscoring teams by +9.7 points per 100 with him on the floor and have been 19.2 points worse with him off. [5]

[2] https://backpicks.com/2022-players/

[3] https://www.nba.com/news/nba-top-selling-jerseys

[4] https://sbi.co.in/web/sbi-in-the-news/research-desk

• ## Park-Adjusted Statistics for the MLB

(📸 MLB.com)

The development of sabermetrics in Major League Baseball has coincided with an increased awareness of confounders, one of which is the effect of ballparks and their playing environments. The ubiquitous example is Coors Field in Denver, whose abnormal elevation is known to cause baseballs to travel 5 to 10% farther than at typical sea level. [1] While comprehensive statistics like On-Base Plus Slugging (OPS) and weighted Runs Created (wRC) have spawned improvements that account for such prior knowledge, these principles have yet to be widely applied to traditional box scores. Thus, I set out to develop a subset of “park factors” that can be used to manipulate statistics like batting average and home runs to provide a more level playing field when comparing these measurements between players of varying ballpark conditions.

## The Example

Colorado Rockies players often have more scrutinized slash lines and power statistics because of the aforementioned data on the elevation effect. Let’s use home runs in the 2021 regular season as the example of park-adjusted statistics to observe the supposed bottom-line effect in home-run frequency between stadiums. To estimate a ballpark’s effect on home runs among all thirty teams, their home-run frequency (measured as home runs per plate appearance) is compared between home and away games. To include a larger breadth of information, a five-year data set was used. (For 2021, seasons 2017 through 2021 were used to calculate park factors.)

Because the entire league is usually more prone to hit home runs at home than on the road (likely stemming from the home-field advantage), a small adjustment is made to reflect this. Additionally, only half of the measured effect is added to the rating because teams split roughly half of their schedule between home and away games. Therefore, the final measurement we’re left with is the percent increment of a team’s home-run frequency on the road versus at home relative to the league. This park factor can be used on the player level, too. Let’s see how the power-hitting landscape changes when these listed adjustments are applied to MLB batters.

## The Results

NB: Traded players occupy multiple rows for each team played for.

Marcus SemienTOR43452
Fernando Tatis Jr.SDP4342-1
Shohei OhtaniLAA43463
Brandon LoweTBR4339-4
Matt OlsonOAK4139-2
Mitch HanigerSEA4139-2
Rafael DeversBOS4038-2
Tyler O’NeillSTL3934-5
Pete AlonsoNYM3837-1
Jose RamirezCLE3736-1
Kyle SeagerSEA3735-2
Aaron JudgeNYY36393
Mike ZuninoTBR3633-3
Paul GoldschmidtSTL3631-5
Brandon BeltSFG3429-5
Jorge PolancoMIN3433-1
Austin RileyATL3433-1
Yordan AlvarezHOU3433-1
Hunter RenfroeBOS3331-2
Giancarlo StantonNYY33352
Joey VottoCIN32364
Bryce HarperPHI32353
Freddie FreemanATL3231-1
Jose AltuveHOU31310
Franmil ReyesCLE3130-1
Miguel SanoMIN3130-1
Nick CastellanosCIN31343
Teoscar HernandezTOR31321
Ozzie AlbiesATL3130-1
Kyle TuckerHOU30300
J.D. MartinezBOS2928-1
Ryan MountcastleBAL29334
Mike YastrzemskiSFG2925-4
Matt ChapmanOAK2927-2
Jose AbreuCHW29301
Patrick WisdomCHC28280
Juan SotoWSN28291
Avisail GarciaMIL28291
Brandon CrawfordSFG2824-4
Eugenio SuarezCIN28313
Bo BichetteTOR28291
Dansby SwansonATL27270
Jared WalshLAA27292
Bryan ReynoldsPIT2724-3
Cedric Mullins IIBAL27303
Josh DonaldsonMIN2726-1
Carlos CorreaHOU26260
Bobby DalbecBOS2625-1
Josh BellWSN26271
Ian HappCHC25250
C.J. CronCOL25283
Rhys HoskinsPHI24273
Andrew McCutchenPHI24273
Ronald Acuna Jr.ATL24240
Kyle SchwarberWSN24251
Xander BogaertsBOS2423-1
Jesus AguilarMIA2422-2
Joey GalloTEX24251
Robbie GrossmanDET2423-1
Eduardo EscobarARI2322-1
Jonathan SchoopDET2322-1
Eric HaaseDET2322-1
Luis UriasMIL22231
Javier BaezCHC22220
Yasmani GrandalCHW22231
Randy ArozarenaTBR2220-2
Paul DeJongSTL2219-3
Carlos SantanaKCR2219-3
Jesse WinkerCIN22242
Jake CronenworthSDP21210
Gary SanchezNYY21232
Trevor StoryCOL21243
Seth BrownOAK2120-1
Willson ContrerasCHC21210
Enrique HernandezBOS2120-1
Randal GrichukTOR21221
George SpringerTOR21221
Buster PoseySFG2118-3
Wilmer FloresSFG2118-3
Francisco LindorNYM2120-1
Dylan CarlsonSTL2118-3
Ryan McMahonCOL20233
Lourdes Gurriel Jr.TOR20211
Jazz Chisholm Jr.MIA2018-2
Austin HaysBAL20222
Byron BuxtonMIN19190
Nelson CruzMIN19190
Max KeplerMIN19190
Andrew BenintendiKCR1917-2
Jonathan IndiaCIN19212
Ty FranceSEA1918-1
Jonathan VillarNYM1918-1
Trey ManciniBAL19212
Darin RufSFG1916-3
Cesar HernandezCLE1918-1
Hunter DozierKCR1816-2
Kris BryantCHC18180
Mark CanhaOAK1817-1
Sean MurphyOAK1817-1
Trea TurnerWSN17181
Nathaniel LoweTEX17181
Tyler NaquinCIN17192
Jeimer CandelarioDET1716-1
Tim AndersonCHW16171
Anthony SantanderBAL16182
Elias DiazCOL16182
Justin UptonLAA16171
Luis TorrensSEA1615-1
Kevin PillarNYM1615-1
J.T. RealmutoPHI15172
Jesus SanchezMIA1514-1
Trent GrishamSDP15150
Tommy PhamSDP15150
Yuli GurrielHOU15150
Evan LongoriaSFG1513-2
Alex DickersonSFG1513-2
Jed LowrieOAK1514-1
Ramon LaureanoOAK1514-1
Jorge SolerKCR1513-2
Jarred KelenicSEA1514-1
Michael ConfortoNYM1514-1
Ketel MarteARI1514-1
Kyle FarmerCIN14162
Ryan JeffersMIN14140
Andrew VaughnCHW14151
Jorge SolerATL14140
Chas McCormickHOU14140
Nelson CruzTBR1413-1
Yandy DiazTBR1413-1
Brett PhillipsTBR1413-1
Anthony RizzoCHC14140
Austin SlaterSFG1412-2
Rougned OdorNYY14151
Alex VerdugoBOS1413-1
Michael A. TaylorKCR1412-2
Ryan ZimmermanWSN14140
Kolten WongMIL14140
Carson KellyARI13130
Mitch GarverMIN13130
Brendan RodgersCOL13152
Frank SchwindelCHC13130
Gio UrshelaNYY13141
Jean SeguraPHI13141
Tommy EdmanSTL1311-2
Manny PinaMIL13130
Dylan MooreSEA1312-1
Luis RobertCHW12131
Sam HilliardCOL12142
Gregory PolancoPIT1211-1
Eric HosmerSDP12120
Alex BregmanHOU12120
Joey GalloNYY12131
Max StassiLAA12131
Joey WendleTBR1211-1
Ji-Man ChoiTBR1211-1
Odubel HerreraPHI12131
Didi GregoriusPHI12131
Tyrone TaylorMIL12120
DJ PetersTEX12120
Tom MurphySEA1211-1
Charlie BlackmonCOL11132
Dominic SmithNYM11110
Josh RojasARI11110
Daulton VarshoARI11110
Pavin SmithARI11110
Whit MerrifieldKCR1110-1
Amed RosarioCLE11110
Colin MoranPIT1110-1
Rafael OrtegaCHC11110
Joc PedersonCHC11110
Manuel MargotTBR1110-1
D.J. StewartBAL11121
Omar NarvaezMIL11110
Mitch MorelandOAK1110-1
Nick SolakTEX11110
Danny JansenTOR11110
Gavin SheetsCHW10111
James McCannNYM10100
Christian WalkerARI10100
Austin HedgesCLE10100
Ryan O’HearnKCR109-1
Luke VoitNYY10111
Lewis BrinsonMIA109-1
Garrett CooperMIA109-1
Miguel RojasMIA109-1
Pedro SeverinoBAL10111
Maikel FrancoBAL10111
Garrett HampsonCOL10111
Jonah HeimTEX10100
Eloy JimenezCHW10100
Jake FraleySEA990
J.P. CrawfordSEA990
Javier BaezNYM990
Steven DuggarSFG98-1
Willi CastroDET990
Niko GoodrumDET990
DJ LeMahieuNYY9101
Brett GardnerNYY9101
Kyle HigashiokaNYY9101
Yu ChangCLE990
Jack MayfieldLAA9101
Brent RookerMIN990
Tyler StephensonCIN9101
Aristides AquinoCIN9101
Yoshi TsutsugoPIT98-1
Ben GamelPIT98-1
Jacob StallingsPIT98-1
Dom NunezCOL9101
Lewin DiazMIA98-1
Yan GomesWSN990
Christian YelichMIL990
Daniel VogelbachMIL990
Tony KempOAK880
Taylor TrammellSEA880
Gleyber TorresNYY891
Brandon NimmoNYM880
David PeraltaARI880
Alex KirilloffMIN880
Ha-seong KimSDP880
Tommy La StellaSFG87-1
Donovan SolanoSFG87-1
Kris BryantSFG87-1
William ContrerasATL880
Michael BrantleyHOU880
Aledmys DiazHOU880
Jason CastroHOU880
Jason HeywardCHC880
David BoteCHC880
Freddy GalvisBAL891
Michael PerezPIT87-1
Lorenzo CainMIL880
Isiah Kiner-FalefaTEX880
Starling MarteMIA87-1
Brian AndersonMIA87-1
Wander FrancoTBR87-1
Alejandro KirkTOR880
Brian GoodwinCHW880
Anthony RizzoNYY781
Jose IglesiasLAA781
Mike TroutLAA781
Taylor WardLAA781
Kyle SchwarberBOS770
Jeff McNeilNYM770
Asdrubal CabreraARI770
Eddie RosarioCLE770
Josh NaylorCLE770
Jordan LuplowCLE770
Roberto PerezCLE770
Harold RamirezCLE770
Willians AstudilloMIN770
Trevor LarnachMIN770
Victor CaratiniSDP770
Marcell OzunaATL770
Eddie RosarioATL770
Travis d’ArnaudATL770
Joc PedersonATL770
Connor JoeCOL781
Edmundo SosaSTL76-1
Lane ThomasWSN770
Rowdy TellezMIL770
Andy IbanezTEX770
Cavan BiggioTOR770
Ke’Bryan HayesPIT76-1
Yermin MercedesCHW770
Francisco MejiaTBR76-1
Phil GosselinLAA671
Ronald TorreyesPHI671
Alec BohmPHI671
Christian VazquezBOS660
Christian ArroyoBOS660
Tucker BarnhartCIN671
Jose PerazaNYM660
Ramon UriasBAL671
Josh VanMeterARI660
Andy YoungARI660
Dustin GarneauDET660
Jake RogersDET660
Wilson RamosDET660
Zack ShortDET660
Joshua FuentesCOL671
Jake MeyersHOU660
Abraham ToroHOU660
Mauricio DubonSFG65-1
Curt CasaliSFG65-1
Josh HarrisonWSN660
Luis GarciaWSN660
Carter KieboomWSN660
Jace PetersonMIL660
Eduardo EscobarMIL660
Travis ShawMIL660
Willie CalhounTEX660
Jason MartinTEX660
Eli WhiteTEX660
Lars NootbaarSTL65-1
Jake LambCHW660
Edward OlivaresKCR65-1
Anthony AlfordPIT65-1
Phillip EvansPIT65-1
Kevin NewmanPIT65-1
Rodolfo CastroPIT65-1
Miguel AndujarNYY660
Anthony RendonLAA660
Juan LagaresLAA660
Kurt SuzukiLAA660
Jose RojasLAA660
Luis RengifoLAA660
Bryan De La CruzMIA550
Mike BrosseauTBR550
Mike MoustakasCIN561
Raimel TapiaCOL561
Stephen PiscottyOAK550
Starling MarteOAK550
Yan GomesOAK550
Danny SantanaBOS550
Abraham ToroSEA550
Kyle LewisSEA550
J.D. DavisNYM550
Billy McKinneyNYM550
Stephen VogtARI550
Kole CalhounARI550
Nick AhmedARI550
Victor ReyesDET550
Andres GimenezCLE550
Kyle GarlickMIN550
Abraham AlmonteATL550
Guillermo HerediaATL550
Robinson ChirinosCHC550
Jake MarisnickCHC550
Sergio AlcantaraCHC550
Matt DuffyCHC550
Andrew StevensonWSN550
Charlie CulbersonTEX550
Jose TrevinoTEX550
Seby ZavalaCHW550
Leury GarciaCHW550
Mike TauchmanSFG54-1
Clint FrazierNYY550
Albert PujolsLAA550
Justin WilliamsSTL54-1
Freddy GalvisPHI550
Wilmer DifoPIT440
Pat ValaikaBAL451
Nick FortesMIA440
Jorge AlfaroMIA440
Jon BertiMIA440
Isan DiazMIA440
Sandy LeonMIA440
Kevin KiermaierTBR440
Jordan LuplowTBR440
Shed Long Jr.SEA440
Jose MarmolejosSEA440
Brandon DruryNYM440
Daz CameronDET440
Renato NunezDET440
Daniel JohnsonCLE440
Owen MillerCLE440
Nick GordonMIN440
Jurickson ProfarSDP440
Pablo SandovalATL440
Jose SiriHOU440
Trayce ThompsonCHC440
Alcides EscobarWSN440
Keston HiuraMIL440
John HicksTEX440
David DahlTEX440
Corey DickersonTOR440
Rowdy TellezTOR440
Zack CollinsCHW440
Aaron HicksNYY440
Austin WynnsBAL440
Jason VoslerSFG330
Jose RondonSTL330
Matt CarpenterSTL330
Hoy ParkPIT330
Alex JacksonMIA330
Elvis AndrusOAK330
Aramis GarciaOAK330
Kevin PlaweckiBOS330
Travis ShawBOS330
Jonathan ArauzBOS330
Tomas NidoNYM330
Harold CastroDET330
Derek HillDET330
Ernie ClementCLE330
Andrelton SimmonsMIN330
Jake CaveMIN330
Ben RortvedtMIN330
Marwin GonzalezHOU330
Michael HermosilloCHC330
Starlin CastroWSN330
Billy McKinneyMIL330
Leody TaverasTEX330
Cesar HernandezCHW330
Mike FordNYY330
Max SchrockCIN330
Rio RuizBAL330
Nicky LopezKCR220
Hanser AlbertoKCR220
Ka’ai TomPIT220
Cole TuckerPIT220
Erik GonzalezPIT220
Corey DickersonMIA220
Josh HarrisonOAK220
Jarren DuranBOS220
Marwin GonzalezBOS220
Michael ChavisBOS220
Donovan WaltonSEA220
Sam HaggertySEA220
Cal RaleighSEA220
Evan WhiteSEA220
Josh ReddickARI220
Jake McCarthyARI220
JaCoby JonesDET220
Myles StrawCLE220
Rene RiveraCLE220
Wilson RamosCLE220
Jake BauersCLE220
Rob RefsnyderMIN220
Gilberto CelestinoMIN220
Luis ArraezMIN220
Webster RivasSDP220
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Alexander WellsBAL000
Darwinzon HernandezBOS000
Michael KingNYY000
Charlie BarnesMIN000
Brandon BielakHOU000
Griffin CanningLAA000
Drew CarltonDET000
Tucker DavidsonATL000
Kevin GinkelARI000
Tanner HouckBOS000
Gabe KlobositsWSN000
Alex LangeDET000
Clarke SchmidtNYY000
Jose SuarezLAA000
Trevor StephanCLE000
Jhon RomeroWSN000
Ljay NewsomeSEA000
Jesus LuzardoOAK000
Jesus LuzardoMIA000
Zach PlesacCLE000
Bryse WilsonPIT000
Dylan LeeATL000
Tyler WellsBAL000
Wyatt MillsSEA000
John SchreiberBOS000
Hunter OwenPIT000
Darren McCaughanSEA000
Ronald BolanosKCR000
Sean GuentherMIA000
Kaleb OrtBOS000
Bailey FalterPHI000
Miguel SanchezMIL000
Mauricio LloveraPHI000
James KarinchakCLE000
Nick NelsonNYY000
Nate PearsonTOR000
Ty TiceTOR000
Ty TiceATL000
Zach PopMIA000
Ben BowdenCOL000
Eli MorganCLE000
Jeremy BeasleyTOR000
Mike BaumannBAL000
Yennsy DiazNYM000
Tyler IveyHOU000
Zac LowtherBAL000
Griffin JaxMIN000
Mario FelicianoMIL000
Deivi GarciaNYY000
Jhonathan DiazLAA000
Alec BettingerMIL000
Andre ScrubbHOU000
Kyle DohyPHI000
Riley O’BrienCIN000
Ramon RossoPHI000
Matt ManningDET000
Bruce ZimmermannBAL000
Andres MunozSEA000
Tyler ZuberKCR000
Antonio SantosCOL000
Isaac MattsonBAL000
Anthony KayTOR000
Nick MargeviciusSEA000
Josh FlemingTBR000
Jovani MoranMIN000
Enoli ParedesHOU000
Peter SolomonHOU000
J.B. BukauskasARI000
Casey MizeDET000
Scott HurstSTL000
Kyle NelsonCLE000
Nick SandlinCLE000
Kutter CrawfordBOS000
JC MejiaCLE000
Yusei KikuchiSEA000
Cristopher SanchezPHI000
Manuel RodriguezCHC000
Eduard BazardoBOS000
Francisco PerezCLE000
Oliver OrtegaLAA000
Emmanuel ClaseCLE000
Seth MartinezHOU000
Luis GilNYY000
Thomas SzapuckiNYM000
Demarcus EvansTEX000
Dauri MoretaCIN000
Miguel YajurePIT000
Tyler PayneCHC000
Brooks KriskeBAL000
Brooks KriskeNYY000
Connor BrogdonPHI000
Lucas GilbreathCOL000
Jake LatzTEX000
Glenn OttoTEX000
Joe RyanMIN000
Ryan FeltnerCOL000
Kris BubicKCR000
Shane McClanahanTBR000
Daniel LynchKCR000
Reiss KnehrSDP000
Jackson KowarKCR000
Jake CousinsMIL000
Elvis PegueroLAA000
Kervin CastroSFG000
Luis OviedoPIT000
Jose MarteLAA000
Mason ThompsonWSN000
Mason ThompsonSDP000
Gregory SantosSFG000
Camilo DovalSFG000
Luis FriasARI000
Angel RondonSTL000
John KingTEX000
Aaron FletcherSEA000
Kyle TylerLAA000
Max KranickPIT000
Hans CrousePHI000
Mac ScerolerBAL000
Jon HeasleyKCR000
Paul CampbellMIA000
Logan GilbertSEA000
Shane BazTBR000
Tarik SkubalDET000
Dylan ColemanKCR000
Joe BarlowTEX000
Chris RodriguezLAA000
A.J. AlexyTEX000
Stephen RidingsNYY000
Nivaldo RodriguezHOU000
Carlos HernandezKCR000
Angel ZerpaKCR000
Roansy ContrerasPIT000
Luis PatinoTBR000
Spencer HowardTEX000
Packy NaughtonLAA000
Codi HeuerCHW000
Codi HeuerCHC000
Janson JunkLAA000
Damon JonesPHI000
Nick SnyderTEX000
Aaron AshbyMIL000
Ryan DorowTEX000
Brett de GeusTEX000
Brett de GeusARI000
Luis GarciaHOU000
Randy DobnakMIN000
Nick AllgeyerTOR000
Jonathan StieverCHW000
Cody WilsonWSN000
Andrew WantzLAA000
Austin WarrenLAA000
Cooper CriswellLAA000
Nick MearsPIT000
Drew RasmussenMIL000
Alek ManoahTOR000
Garrett CrochetCHW000
Reid DetmersLAA000
Spencer StriderATL000
Kohei AriharaTEX000
Hyeon-jong YangTEX000
Hirokazu SawamuraBOS000

The above table represents five properties: 1) the player’s name; 2) the team for which the player accrued his statistics; 3) his “adjusted” home run total, which uses his team’s park factor; 4) his raw home run total, which does not use his team’s park factor; and 5) “luck,” which measures the difference between his actual home run total and his adjusted home run total. If we sort the table to reflect the luckiest and unluckiest batters, their listed teams will start to reflect which ballparks have the greatest promotion for home runs and which ones do not. It’s no surprise that there are numerous Rockies players near the top of this list:

• C.J. Cron +3 (7th)
• Trevor Story +3 (10th)
• Ryan McMahon +3 (12th)
• Elias Diaz +2 (23rd)
• Brendan Rodgers +2 (30th)
• Sam Hilliard +2 (34th)
• Charlie Blackmon +2 (37th)

Interestingly enough, Colorado has the lowest home-run park factor in 2021, which means the Coors Field environment has the most positive effect on homers compared to other ballparks! Conversely, we can sort to find the “unluckiest” batsmen in the league. Here, we (expectantly) see a whole new crop of players and teams:

2. Tyler O’Neill -5 (STL)
4. Brandon Belt -5 (SFG)
5. Paul Goldschmidt -5 (STL)
6. Mike Yastrzemski -4 (SFG)
7. Brandon Crawford -4 (SFG)
8. Brandon Lowe -4 (TBR)
9. Mike Zunino -3 (TBR)
10. Buster Posey -3 (SFG)

The analytical approach does seem to corroborate the traditional ideas about Coors Field while also revealing insights into which ballparks don’t induce more home runs than usual. Here are the top-5 and bottom-5 teams in this 2021 version of the home-run park factor (higher meaning worse home-run environment, lower meaning better):

• San Francisco Giants (1st)
• St. Louis Cardinals (2nd)
• Kansas City Royals (3rd)
• Pittsburgh Pirates (4th)
• Miami Marlins (5th)
• Los Angeles Dodgers (26th)
• Cincinnati Reds (28th)
• Baltimore Orioles (29th)

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

(📸 ClevelandSports.org)

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.

Absolutely

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.

Probably

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.

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.

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.

Maybe

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

Starters:

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

Reserves:

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

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

Starters:

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

Reserves:

• 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:

• Backpicks.com
• PBPStats.com

• ## 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]

Overview

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.

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.

PlayerTmGMPO CrPMD CrPMCrPM
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 TurnerIND30887-0.64.64.1
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 DrummondPHI29571-2.86.03.2
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 ŞengünHOU29538-0.12.62.5
Jarred VanderbiltMIN28682-1.64.02.4
Daniel GaffordWAS28601-1.13.42.3
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 MobleyCLE25840-0.92.92.0
Mike ConleyUTA267273.2-1.21.9
Deandre AytonPHO206250.51.51.9
Malcolm BrogdonIND258832.7-0.81.9
Devin BookerPHO216763.1-1.21.9
Robert WilliamsBOS23638-0.42.31.9
Derrick RoseNYK266362.2-0.41.8
Paul GeorgeLAC248610.61.21.8
Darius GarlandCLE299913.0-1.31.8
Draymond GreenGSW28849-0.92.61.7
Jakob PoeltlSAS216060.51.11.6
Nikola VučevićCHI20663-0.92.51.6
De’Anthony MeltonMEM27654-0.62.21.6
Ricky RubioCLE318801.20.31.5
Brandon IngramNOP248552.3-0.81.5
Cole AnthonyORL237851.9-0.51.4
Alex CarusoCHI24685-0.11.51.4
Mo BambaORL27774-2.43.81.4
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 RobinsonNYK27653-1.52.61.1
Aaron GordonDEN299451.2-0.21.1
Devin VassellSAS235590.11.01.1
Tyus JonesMEM306341.8-0.71.1
Cedi OsmanCLE255521.3-0.21.1
Kevon LooneyGSW30564-1.02.01.0
Deni AvdijaWAS31672-1.32.31.0
Christian WoodHOU28888-1.02.01.0
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 ZubacLAC30742-1.21.90.7
Kyle AndersonMEM26565-1.31.90.6
Alec BurksNYK297740.40.30.6
Caris LeVertIND236681.3-0.70.6
Cody MartinCHO297990.10.40.6
Tyrese HaliburtonSAC289300.10.40.5
Larry Nance Jr.POR30650-0.91.40.5
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 BallCHI27958-0.91.20.3
Jordan ClarksonUTA297301.3-1.00.2
OG AnunobyTOR165880.5-0.30.2
Marcus SmartBOS29991-0.30.40.2
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
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
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
Evan FournierNYK30857-1.6-1.8-3.4
Malik BeasleyMIN29750-1.7-1.8-3.4
R.J. HamptonORL29536-2.4-1.1-3.5
Garrett TempleNOP29532-4.20.5-3.6
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)

(📸 ClevelandSports.org)

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.

“Absolutely”

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.

“Probably”

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.

• 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.

“Maybe”

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)
• 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.

East

Starters

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

Reserves

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

Wildcards

• 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.

West

Starters

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

Reserves

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

Wildcards

• 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)

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:

Criteria

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)

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:

Criteria

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)

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:

Criteria

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.

PBPStats

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

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.)