Introducing true win shares: estimating team win probability given player stats

Introduction

For years, many claimed Devin Booker puts up “empty stats.” This means his gaudy stats don’t contribute to winning. Instead, he puts up these stats due to his situation. In this case, the Suns’ lack of scoring and ball-handling puts Booker in a position to rack up stats. As soon as he got a competent coach and supporting cast, Booker started to win. With winning, this empty stats narrative faded away. What’s the difference between his stats now and then?

Not much. The main difference between Booker’s stats this year and last is efficiency. His eFG% jumped from 52.1% last year to 57.1% this year (as of December 16). Still, his counting stats stayed consistent. In fact, he’s averaging (marginally) fewer points, rebounds, and assists.

Though Booker improved since last year, his counting stats the same. Yet, he’s winning much more. The Suns sit in playoff contention despite injuries and a suspension to Deandre Ayton. Were Booker’s stats conducive to winning all along? Did he just need a good team around him to win?

Booker presents one example of this problem of how counting stats relate to wins. Naturally, better stats result in more wins because good players make good teams win. But, we have the Devin Bookers and Trae Youngs of the league racking up stats on bad teams. So, it’s hard to know how much they’re helping their team.

To combat this and give a more isolated view of player performance, we created true win shares.

Methods

In a broad sense, true win shares measures how likely a team is to win given a player’s stats.

We’ll do this by creating classification models on game logs. We collected every single box score for every player in every game since the 2014-15 season. This boundary is somewhat arbitrary. 2014-15 was the Warriors’ first championship season, which in some sense marks the start of the modern NBA. Going further back isn’t necessary; there were over 87,000 box scores from 2014-15 to 2017-18.

We collected box scores from Basketball-Reference. Each box score includes a player’s basic counting stats (points, rebounds, assists, etc.) and the result of the game (a win or a loss). We’ll train models that take these basic stats and predict the result of the game.

For the models, we chose the following stats as features.

Offense	Defense	Other
PTS	STL	Location*
AST	BLK	MP
TOV
3PM
FTM

* Location = 1 if the player is at home, -1 if the player is away. We added this because generally, players play better and win more often at home. So, the location may help explain some of the variance.

With these features, we created 5 models:

Logistic classifier (LOG)
Linear discriminant analysis (LDA)
Random forest classifier (RF)
Gradient boosting classifier (GBC)
Deep neural network (DNN)

We trained each model to use the above features to predict a win or a loss. Then, we looked at the prediction probability. The above models are all classifiers, meaning they predict samples to be either (1) a win or (0) a loss. But, each prediction comes with a probability, or likelihood the team will win or lose given the stat line. This probability is what we’ll look at. This gives us our “true win shares.”

The prediction probability will be between 0 and 1. 1 indicates complete certainty that the team will win given the player’s stat line. So, the best possible cumulative true win shares is 82. For this to happen, a player must play all 82 games and the models must be 100% certain he will win each game.

We’ll look at both average and cumulative true win shares for the 2018-19 season. In every game, players from both teams put up awesome stats. So, this means we’ll rarely see high win probability given a stat line. As a result, cumulative true win shares will value durability a lot.

Why true win shares isn’t perfect

Because we’re constructing true win shares based on box score stats, it won’t be perfect. The goal is to make a more accessible holistic metric, so using simple box score stats is better. But, these stats will overvalue some players (like Westbrook) and undervalue others (like good defenders).

Though predicting wins for each player stat line attempts to remove the effect of their teammates, the player’s team still matters. For example, two players can make the exact same passes, but one can rack up more assists if their team hits shots. This will give the player with the better team the better score. Still, other advanced stats suffer from this too; this is unavoidable. For example, offensive win shares considers points produced.

Points produced considers the player’s points scored and the points coming off their assists and offensive rebounds. So, this will also reward players with better teammates. Without using play-by-play lineup data, it’s almost impossible to remove the effect of a player’s team. Even with lineup data, we can’t remove the effect. So, true win shares suffers from a similar problem to most stats: it fails to fully isolate players.

Another issue with basing wins off counting stats is that weird combinations of stats that aren’t “good” often result in wins. This is because external factors affect these stats. For example, we wouldn’t say that the Warriors need Stephen Curry to get a lot of rebounds to win. Yet, in games where Curry recorded at least 9 rebounds, the Warriors are 6-1.

This doesn’t mean that if the Warriors stick Curry under the basket to grab rebounds, they’ll win 85.7% of games. It means that the other team was having a bad shooting night that game. If Curry – who’s not a great rebounder – racked up rebounds, the opponent probably missed a lot of shots. This gives Curry the opportunities to get rebounds.

We can find several other examples of this, but the point stands. Using counting stats will sometimes create weird results.

Model analysis

In the past, we’ve created classification models on imbalanced data sets. This means that most of the data was one class. So, measuring correct predictions wasn’t meaningful. In this case, we have a balanced data set.

We’re predicting a win or loss from a data set of every player’s stats in every game. So, our class proportions are almost equal, as each game has a winner and a loser. This means that accuracy (which measures correct predictions) is an important metric for our model’s performance.

As a preliminary view of performance, we’ll look at each model’s confusion matrix. This measures the number of correct and incorrect predictions of each type. So, for example, a predicted 1 and actual 0 is a false positive; the model predicted a win, but the game was a loss.

The graphs below show each model’s confusion matrix.

We see that all the models are generally accurate; there are more correct predictions than incorrect. This is indicative of good performance here. But, this helps us visualize performance – it’s not a concrete metric.

For metrics of performance, besides accuracy, we’ll use the usual performance estimators. These are recall, precision, F1, log loss, and area under the ROC curve. For our imbalanced data sets, we cared a lot about recall and precision, which measure the ability to accurately find the positive class. With a balanced data set, no single metric is particularly important.

Here’s what all these metrics measure:

Accuracy: total correct predictions
Recall: how many of the positive class samples (1, a win) are returned out of all samples with the positive class
Precision: how many of the samples that we predicted are positive are actually positive
F1: a way to combine recall and precision (lets us compare two models if one has higher recall but lower precision)
Log loss: like accuracy, but for prediction probabilities
Area under the ROC curve (AUCROC): measures how well our models separate between the two classes

For each model, we’ll compare these metrics to the performance of the dummy classifier. The dummy classifier randomly assigns each sample to a class. It bases the assignment on the distribution of the training data. Because our training data has 49.8% 1s (samples where the team won), the dummy classifier will randomly predict 49.8% of the test set to win. Comparing our models to this shows us how much better they are than random.

The table below shows each model’s performance in the above metrics. The best possible value for accuracy, recall, precision, F1, and area under the ROC curve is 1 (and higher is better). Meanwhile, the best possible log loss if 0 (so lower is better).

Model	Accuracy	Recall	Precision	F1	Log loss	AUCROC
LOG	0.596	0.586	0.601	0.594	0.668	0.628
LDA	0.596	0.585	0.602	0.593	0.668	0.628
RF	0.593	0.606	0.595	0.6	0.668	0.627
GBC	0.597	0.603	0.6	0.601	0.666	0.631
DNN	0.597	0.581	0.604	0.592	0.667	0.631
Dummy	0.497	0.491	0.501	0.496	17.373	0.497

Note that the log loss of the dummy classifier is meaningless. Log loss uses prediction probabilities, which the dummy doesn’t use. Instead, the dummy always has prediction probability 1 or 0.

The table below shows each model’s improvement over random.

Model	Accuracy	Recall	Precision	F1	AUCROC
LOG	19.92%	19.35%	19.96%	19.76%	26.36%
LDA	19.92%	19.14%	20.16%	19.56%	26.36%
RF	19.32%	23.42%	18.76%	20.97%	26.16%
GBC	20.12%	22.81%	19.76%	21.17%	26.96%
DNN	20.12%	18.33%	20.56%	19.35%	26.96%

Each model has a large improvement over random of about 20% in each metric. So, the models are predictive of winning games.

As one final check, we’ll discuss overfitting. Overfitting occurs when the models “learn” the given data too well. So, they’ll have high performance on the specific data, but won’t predict new data well.

One way we avoid overfitting is by grid search. Each model has hyperparameters – things that determine how the model fits the data (like a slope in linear regression). We created a grid of possible hyperparameters for each model to search. We created a model with each possible combination of elements in the grid. Then, we chose the hyperparameters that resulted in the best accuracy when tested across different splits of the data. We performed grid search on a random 10% subset of our data. Grid search on our full data set would be slow because of its size.

Along with grid search, we’ll look at the cross-validated scores for accuracy and recall. We did k-fold cross-validation with k = 3, meaning we split the data into 3 bins. With these 3 bins, we used 1 as the testing set and the other 2 as training sets. Then, we did this cycle for every possible combination of the bins. The cross-validated scores are the average scores across each split of the bins.

As long as our cross-validated scores are close to our real scores, we’re likely not overfitting. The table below shows the cross-validated scores and confidence intervals.

Model	CV Accuracy	95% CI	CV Recall	95% CI
LOG	0.596	+/- 0.008	0.602	+/- 0.002
LDA	0.597	+/- 0.007	0.602	+/- 0.003
RF	0.591	+/- 0.009	0.628	+/- 0.003
GBC	0.594	+/- 0.008	0.625	+/- 0.006
DNN	0.595	+/- 0.004	0.603	+/- 0.006

Each model’s CV scores are either barely lower or higher than their actual scores. So, we can say with confidence that our models are likely not overfitting.

Altogether, these performance metrics indicate our models are strong. Now that we’re done analyzing the models, let’s see what they say.

Results

To calculate true win shares for the 2018-19 season, we collected game logs for every player. We limited our data set to those who played at least half the season (41 games). We gave our models this data to predict the win probability. True win shares is the average of the prediction probabilities from the 5 models.

We’ll look at true win shares in two ways. First, we’ll look at cumulative true win shares. Durability plays a big role in cumulative true win shares, as most top players earn a similar number of true win shares per game. So, the cumulative leaders will consist of good players who also played lots of games.

Along with cumulative leaders, we’ll look at the average leaders. This is the average of the player’s true win shares in all their games. So, durability won’t play a role here.

We can think of both types of true win shares as calculating wins in a basketball vacuum. The models predict wins using individual stat lines. So, they’re saying “ignoring teammates and opponents, this player should win this many games.” Cumulative true win shares estimates how many games you’d expect to win given that player’s season in a vacuum. Average true win shares estimates the win percentage you’d expect given that player’s stats.

The table below shows each player’s average true win shares. The true win shares is in the “avg” (average) column. You can sort the table and search for any player.

rank	player	avg	log	lda	rf	gbc	dnn
1	James Harden	0.679826385	0.691017985	0.686499413	0.654407519	0.663205882	0.704001125
2	Russell Westbrook	0.666086084	0.667353488	0.663517322	0.631043229	0.657418274	0.711098105
3	Giannis Antetokounmpo	0.647005908	0.64227022	0.639273655	0.630830061	0.662500583	0.66015502
4	Stephen Curry	0.64474664	0.655399959	0.651717657	0.623821612	0.629389893	0.66340408
5	LeBron James	0.640480361	0.644883246	0.641439919	0.610836413	0.631442769	0.67379946
6	Anthony Davis	0.63634784	0.664788276	0.661937886	0.585550581	0.606618834	0.662843623
7	Nikola Jokic	0.632492455	0.628631695	0.62578115	0.619823634	0.636337875	0.651887924
8	Kyrie Irving	0.625498372	0.629404877	0.626317133	0.611210241	0.6182138	0.642345809
9	Joel Embiid	0.620202791	0.62542593	0.622975882	0.607913992	0.614587866	0.630110287
10	Paul George	0.608643378	0.631556006	0.628318345	0.572540071	0.585975788	0.624826679
11	Damian Lillard	0.606848355	0.608341881	0.605065554	0.599765076	0.600646473	0.620422792
12	D'Angelo Russell	0.606730822	0.60624881	0.603423125	0.595751886	0.606294913	0.621935374
13	Nikola Vucevic	0.603435992	0.61466652	0.612581795	0.581205298	0.593924535	0.614801813
14	Karl-Anthony Towns	0.600303025	0.612091893	0.609737117	0.579366078	0.586202667	0.61411737
15	Kevin Durant	0.598248177	0.593029077	0.590568918	0.599597779	0.595232596	0.612812515
16	Kemba Walker	0.595631303	0.601763364	0.598853817	0.585686396	0.581306434	0.610546502
17	Kawhi Leonard	0.595544755	0.592791088	0.590804765	0.597738825	0.595410343	0.600978754
18	Chris Paul	0.591138372	0.599611842	0.596494349	0.575265077	0.591419407	0.592901184
19	Luka Doncic	0.589307472	0.586444978	0.583678533	0.589231054	0.596224047	0.590958749
20	Mike Conley	0.588203378	0.588745717	0.586201842	0.582670477	0.590547572	0.59285128
21	Kyle Lowry	0.58098607	0.593686509	0.590799701	0.560290523	0.574746993	0.585406624
22	Eric Bledsoe	0.568951983	0.567665369	0.565785477	0.565295458	0.575431956	0.570581658
23	Jrue Holiday	0.567495609	0.577482472	0.574723042	0.550460845	0.553439609	0.581372075
24	Blake Griffin	0.566681591	0.568836355	0.566393072	0.562099801	0.559645966	0.576432762
25	Bradley Beal	0.562816439	0.575458896	0.572997844	0.541327058	0.543841759	0.580456637
26	Jusuf Nurkic	0.562541487	0.562763147	0.561464195	0.551696881	0.56549023	0.571292984
27	Ben Simmons	0.56027027	0.551905945	0.550027179	0.565846066	0.563853966	0.569718192
28	De'Aaron Fox	0.560143146	0.561129557	0.558984384	0.565105269	0.557922954	0.557573567
29	Lou Williams	0.559909746	0.555514457	0.553508209	0.555929864	0.568037378	0.56655882
30	Trae Young	0.559865566	0.560209062	0.557665346	0.558134285	0.561002306	0.562316829
31	Danilo Gallinari	0.558485935	0.556897673	0.555128311	0.558910569	0.565840968	0.555652151
32	Al Horford	0.558480692	0.562843519	0.561353979	0.544839254	0.559376961	0.563989749
33	Rudy Gobert	0.558368642	0.566103301	0.564905514	0.547346778	0.553438829	0.560048785
34	Hassan Whiteside	0.557415602	0.571881899	0.571158247	0.538477216	0.55265469	0.552905958
35	Myles Turner	0.55213184	0.559272608	0.558342378	0.542063024	0.54588425	0.555096938
36	Marc Gasol	0.551536842	0.556905003	0.555246366	0.538313728	0.543925118	0.563293996
37	Khris Middleton	0.550299349	0.552467115	0.550625683	0.543553802	0.555354569	0.549495574
38	Buddy Hield	0.549980567	0.55105106	0.549285303	0.551013076	0.548862989	0.549690408
39	Jeff Teague	0.546982589	0.554639853	0.553023252	0.547051898	0.546681307	0.533516637
40	Draymond Green	0.546643833	0.543201263	0.541574403	0.533610944	0.552322713	0.56250984
41	Devin Booker	0.545164383	0.537821817	0.535366041	0.560529666	0.53844885	0.55365554
42	Nikola Mirotic	0.544242008	0.547458814	0.545617828	0.542764638	0.544294472	0.541074288
43	Mitchell Robinson	0.544015545	0.553124723	0.552762396	0.534974526	0.532611218	0.546604861
44	Elfrid Payton	0.54341304	0.546514742	0.544932419	0.535540386	0.539723221	0.550354432
45	Andre Drummond	0.542702709	0.562016078	0.560959739	0.521492515	0.525887859	0.543157353
46	Brook Lopez	0.542131787	0.54586377	0.544666625	0.534123214	0.542540893	0.543464432
47	Donovan Mitchell	0.54067103	0.538036206	0.53618768	0.54959611	0.537888975	0.541646177
48	Jonas Valanciunas	0.539173688	0.54713338	0.546314216	0.532433972	0.530916352	0.539070518
49	Terrence Ross	0.538493972	0.534997503	0.533791736	0.545321246	0.542522623	0.535836753
50	Larry Nance	0.538358776	0.544222362	0.5435003	0.523631169	0.536199081	0.544240968
51	Klay Thompson	0.537837197	0.536797254	0.535481047	0.540793442	0.534494445	0.541619798
52	Shabazz Napier	0.537700539	0.542784703	0.541808315	0.528309068	0.538814968	0.536785639
53	Kyle O'Quinn	0.537006446	0.541635047	0.541364568	0.521510265	0.533285787	0.547236563
54	Dewayne Dedmon	0.534799129	0.542098234	0.54120745	0.523734464	0.532753179	0.534202317
55	Joakim Noah	0.534706273	0.545967184	0.545543951	0.513210846	0.523254474	0.545554909
56	Julius Randle	0.533251632	0.529766893	0.528508975	0.537109562	0.533487369	0.537385361
57	Ekpe Udoh	0.532972763	0.536830159	0.536567465	0.518543256	0.530474411	0.542448521
58	DeMar DeRozan	0.532887728	0.520171936	0.518848522	0.551937417	0.539130773	0.534349994
59	Jimmy Butler	0.532274905	0.531411429	0.529802853	0.534298292	0.53060098	0.535260973
60	Derrick Rose	0.531992561	0.532874926	0.531768211	0.526010012	0.530953779	0.538355877
61	Jamal Murray	0.531872321	0.535081859	0.533557407	0.527833379	0.526270069	0.536618888
62	Luke Kornet	0.531285963	0.542245544	0.541254029	0.510213903	0.520564986	0.54215135
63	Darren Collison	0.530587789	0.534632735	0.533046192	0.528786468	0.530676187	0.525797363
64	Derrick Favors	0.530561877	0.535253184	0.534743564	0.522395277	0.531653975	0.528763384
65	Terry Rozier	0.530543106	0.531149877	0.530008272	0.52314171	0.537573204	0.530842467
66	John Collins	0.529780005	0.534571109	0.533888653	0.524919483	0.523459958	0.532060819
67	Tony Parker	0.52967663	0.530197726	0.530045791	0.520429315	0.534551169	0.533159148
68	Nemanja Bjelica	0.528990608	0.534832807	0.534037055	0.517069158	0.525836309	0.533177714
69	Rajon Rondo	0.528324216	0.537253456	0.535329144	0.504370628	0.519626713	0.545041138
70	JaVale McGee	0.528099387	0.534795019	0.534479341	0.523176266	0.520635949	0.527410358
71	Montrezl Harrell	0.527170074	0.52525	0.524652809	0.528956528	0.531235808	0.525755224
72	Bogdan Bogdanovic	0.526685959	0.529529563	0.528234735	0.523173931	0.528898649	0.523592916
73	Mo Bamba	0.526398149	0.536227205	0.535977689	0.511498184	0.517617496	0.530670173
74	Lonzo Ball	0.525307002	0.530682367	0.529272756	0.507977919	0.52571297	0.532889001
75	Lauri Markkanen	0.524633399	0.532137934	0.530751641	0.516656659	0.52107601	0.52254475
76	Dwyane Wade	0.524601405	0.525275031	0.52396219	0.521672011	0.52920468	0.522893113
77	LaMarcus Aldridge	0.52444146	0.520779582	0.520087342	0.528559985	0.526092075	0.526688314
78	Jeremy Lamb	0.524239395	0.525812631	0.524862166	0.521886272	0.52521854	0.523417366
79	Fred VanVleet	0.523508677	0.525894458	0.524335115	0.522735261	0.525406229	0.519172322
80	Joe Ingles	0.523020236	0.528235789	0.526488675	0.515273547	0.520677745	0.524425423
81	Boban Marjanovic	0.522813768	0.534325072	0.533901235	0.49886558	0.510263774	0.53671318
82	Kyle Korver	0.522600454	0.518020384	0.517552384	0.524506148	0.532143681	0.520779674
83	Reggie Jackson	0.522544363	0.524054287	0.522597072	0.522622921	0.524870547	0.518576989
84	Bobby Portis	0.521861085	0.524685397	0.523638344	0.517931619	0.522084415	0.520965649
85	Vince Carter	0.521621315	0.52452335	0.5238229	0.514564597	0.520394051	0.524801678
86	Georges Niang	0.521454438	0.530115597	0.530008596	0.503633019	0.512528134	0.530986843
87	Paul Millsap	0.521232655	0.523070238	0.522362584	0.517342213	0.523850886	0.519537356
88	Domantas Sabonis	0.520981525	0.527099267	0.526225555	0.503557706	0.518108912	0.529916188
89	Mason Plumlee	0.520898132	0.527831232	0.527115825	0.505396892	0.517907991	0.526238717
90	Alex Len	0.520621687	0.527436977	0.526773484	0.508826831	0.517708699	0.522362442
91	Ricky Rubio	0.520605357	0.524683946	0.523012994	0.515953438	0.521498767	0.51787764
92	Patrick Beverley	0.520073505	0.518211443	0.517137967	0.515913227	0.525603362	0.523501527
93	Gordon Hayward	0.520064522	0.518338264	0.517613565	0.520209614	0.526712872	0.517448292
94	Monte Morris	0.519991091	0.522714911	0.521809063	0.516618525	0.519987189	0.518825766
95	Thomas Bryant	0.519978028	0.530711768	0.530170177	0.504369406	0.509834238	0.52480455
96	Pat Connaughton	0.519819205	0.520927299	0.520326887	0.511870741	0.525031984	0.520939112
97	Otto Porter	0.519376252	0.524287086	0.523309679	0.511795142	0.513971212	0.52351814
98	Justin Anderson	0.518954746	0.523029331	0.523010297	0.508498157	0.517174242	0.523061704
99	Trey Burke	0.51893088	0.521323627	0.520446432	0.512770588	0.518957093	0.521156659
100	Rudy Gay	0.518502954	0.525244846	0.524355989	0.504421167	0.51751044	0.520982331
101	Clint Capela	0.518407114	0.519398775	0.518937985	0.517349483	0.523026736	0.51332259
102	Quinn Cook	0.518338094	0.521991484	0.521402043	0.506498545	0.515182358	0.526616038
103	Davis Bertans	0.518279835	0.516679754	0.515953875	0.517994607	0.520492296	0.520278645
104	Nerlens Noel	0.518022123	0.536951787	0.536661539	0.492226866	0.496357207	0.527913217
105	CJ McCollum	0.517583653	0.514758272	0.513577461	0.525114157	0.517088431	0.517379942
106	Jonas Jerebko	0.51735366	0.523638487	0.523254493	0.503042733	0.51446879	0.522363798
107	Omari Spellman	0.517350372	0.522686777	0.522499134	0.504321464	0.513848785	0.523395699
108	Aaron Holiday	0.517293113	0.523738742	0.52312233	0.504350894	0.516153005	0.519100592
109	Serge Ibaka	0.517287686	0.520742076	0.52016276	0.513500079	0.5177172	0.514316316
110	Daniel Theis	0.517011667	0.525421344	0.525067952	0.500921237	0.509364904	0.524282898
111	Patty Mills	0.516518239	0.51478434	0.51373881	0.514713137	0.529252297	0.510102608
112	Spencer Dinwiddie	0.516516242	0.515348564	0.513783271	0.517719349	0.521973913	0.513756114
113	Kent Bazemore	0.516333061	0.518403657	0.517716278	0.511285675	0.51751286	0.516746836
114	J.J. Redick	0.516018018	0.514555452	0.513184692	0.526575582	0.517417277	0.508357084
115	Frank Kaminsky	0.515975089	0.524173853	0.523436281	0.499180878	0.511054777	0.522029654
116	Malcolm Brogdon	0.515786453	0.5186002	0.517508823	0.51081733	0.515662654	0.516343258
117	Matthew Dellavedova	0.515619791	0.521027192	0.520386103	0.505153255	0.5229221	0.508610305
118	Maxi Kleber	0.51533212	0.517768143	0.517571638	0.509279285	0.515582054	0.516459482
119	Gorgui Dieng	0.515147899	0.532181295	0.531800861	0.487786522	0.496718414	0.527252401
120	T.J. Leaf	0.514711505	0.523319588	0.523354037	0.500528051	0.504460243	0.521895607
121	Jae Crowder	0.514341202	0.511048716	0.510161032	0.52012548	0.517619785	0.512750998
122	Lance Stephenson	0.514290038	0.519070753	0.518380157	0.503899288	0.513182836	0.516917158
123	Willie Cauley-Stein	0.514219487	0.520584238	0.520080605	0.503266659	0.512314897	0.514851036
124	Tobias Harris	0.514179816	0.516386751	0.515141348	0.514994908	0.509594707	0.514781365
125	Richaun Holmes	0.513769003	0.523427935	0.523059701	0.5011065	0.504283578	0.516967302
126	Sindarius Thornwell	0.513722149	0.508254172	0.508342457	0.513125369	0.516642245	0.522246504
127	Meyers Leonard	0.513354624	0.523394429	0.523023635	0.494715191	0.504978152	0.520661715
128	Marcus Smart	0.513303031	0.514016751	0.512985375	0.508378138	0.521689227	0.509445664
129	De'Anthony Melton	0.513244505	0.515774911	0.515428464	0.50490524	0.517103688	0.513010222
130	Tyus Jones	0.513198271	0.52147453	0.520417996	0.506111266	0.513447732	0.50453983
131	Andre Iguodala	0.513158486	0.512153535	0.511528137	0.508147954	0.520776622	0.51318618
132	Thon Maker	0.513040379	0.520014113	0.519826352	0.502605357	0.506400947	0.516355123
133	Delon Wright	0.512958421	0.520906675	0.520070721	0.498243934	0.507817293	0.517753482
134	Tim Frazier	0.512881437	0.519157972	0.518413579	0.499981288	0.513206299	0.513648044
135	Kenrich Williams	0.512784026	0.506384072	0.506289383	0.512879885	0.52004989	0.518316903
136	Marvin Williams	0.512747528	0.508572143	0.508073784	0.516794116	0.5142087	0.516088899
137	Dirk Nowitzki	0.512475858	0.523208935	0.522650739	0.493467609	0.501278345	0.521773661
138	Aaron Gordon	0.512158098	0.513711472	0.512638233	0.512585693	0.505663401	0.516191689
139	Gary Clark	0.512143132	0.514422383	0.514288662	0.50109242	0.511799856	0.519112338
140	Derrick White	0.511728037	0.515751248	0.515034627	0.503915257	0.513764859	0.510174194
141	Zach LaVine	0.511589061	0.506048994	0.504507938	0.524889447	0.512490344	0.510008584
142	D.J. Augustin	0.511571872	0.515935386	0.514547505	0.50720835	0.513869481	0.50629864
143	Quincy Pondexter	0.511544783	0.508657537	0.508499776	0.509179706	0.511490392	0.519896504
144	Danny Green	0.510965758	0.505528494	0.504718903	0.516483237	0.513159428	0.514938729
145	Taurean Waller-Prince	0.510864777	0.509607889	0.509189185	0.519684813	0.512160269	0.503681728
146	Timothe Luwawu-Cabbarot	0.510753894	0.505294126	0.505525876	0.515389384	0.514865011	0.512695075
147	Troy Brown	0.51053148	0.517521972	0.517473221	0.496694933	0.503192397	0.517774879
148	Cheick Diallo	0.510477767	0.51756698	0.517543652	0.497072212	0.502950418	0.517255573
149	Justise Winslow	0.509889635	0.510141181	0.509025057	0.507103043	0.514298222	0.508880674
150	Dion Waiters	0.509791653	0.509625254	0.508492978	0.510499442	0.511606334	0.508734257
151	Jamal Crawford	0.509762184	0.514540677	0.513840355	0.503916684	0.513255355	0.50325785
152	Gerald Green	0.509622104	0.50790651	0.507402684	0.510038852	0.51080762	0.511954854
153	Furkan Korkmaz	0.509572431	0.517813059	0.5174036	0.494165864	0.5012725	0.517207134
154	Dwight Powell	0.508992466	0.51327651	0.512774149	0.501419557	0.506514435	0.510977678
155	Ish Smith	0.507905675	0.511540029	0.511016294	0.500873961	0.507809483	0.508288606
156	Josh Richardson	0.507886326	0.515940581	0.514728051	0.502647743	0.499639343	0.506475912
157	Jayson Tatum	0.507478706	0.506386317	0.505649159	0.512194522	0.512156006	0.501007528
158	Pascal Siakam	0.507272091	0.508091854	0.507313292	0.508892157	0.506042456	0.506020697
159	Amir Johnson	0.507263712	0.517954788	0.51773138	0.486696454	0.494104421	0.519831518
160	C.J. Miles	0.507079871	0.506496829	0.50639088	0.503810129	0.508826483	0.509875034
161	Ivica Zubac	0.506903363	0.51430365	0.514019951	0.49480218	0.498614327	0.512776706
162	Iman Shumpert	0.506746292	0.501537811	0.501405272	0.508782437	0.514048958	0.507956984
163	Wayne Ellington	0.506733956	0.501147057	0.500250992	0.512678868	0.509906914	0.509685948
164	Yogi Ferrell	0.506574838	0.514909391	0.514487191	0.491096466	0.49985633	0.512524812
165	DeAndre Jordan	0.506542421	0.509549797	0.509095596	0.498935542	0.504348253	0.510782915
166	Jordan Clarkson	0.506350396	0.504662588	0.503874275	0.511452969	0.50684013	0.504922021
167	Jakob Poeltl	0.506127071	0.51807166	0.517835309	0.488697488	0.493418928	0.512611972
168	Jarrett Allen	0.505943854	0.508309319	0.508002637	0.505889103	0.506006324	0.501511889
169	Jordan Bell	0.505818437	0.512685926	0.512558483	0.490293275	0.496710752	0.516843747
170	Cody Zeller	0.505817735	0.507997118	0.507980755	0.498654972	0.505927077	0.508528755
171	Marcus Morris	0.505788861	0.506285263	0.505487155	0.50817697	0.507144051	0.501850864
172	Sam Dekker	0.50558472	0.511281411	0.511681102	0.496292079	0.49724728	0.51142173
173	Willy Hernangomez	0.505498587	0.519755521	0.519169267	0.478406071	0.496065513	0.514096561
174	Malik Monk	0.504762412	0.509468695	0.50870234	0.495390468	0.50311481	0.507135747
175	Malik Beasley	0.50467626	0.503334628	0.50276683	0.50660595	0.503356243	0.507317648
176	D.J. Wilson	0.504669527	0.50631353	0.505994072	0.495545465	0.508299089	0.507195481
177	Jahlil Okafor	0.504345648	0.50604709	0.506015471	0.499393775	0.500469807	0.509802099
178	Kris Dunn	0.504234636	0.506615953	0.505279061	0.501620113	0.509252314	0.498405741
179	JaMychal Green	0.504227063	0.507588844	0.507144559	0.499590628	0.50898115	0.497830135
180	Kelly Olynyk	0.504131043	0.505315872	0.50460305	0.497317184	0.510222527	0.503196582
181	Stanley Johnson	0.504110426	0.504468601	0.504478266	0.502653952	0.502790826	0.506160483
182	Deandre Ayton	0.503867932	0.503991611	0.503776401	0.503739358	0.505547093	0.502285198
183	Sterling Brown	0.50369529	0.504613659	0.504607031	0.498674789	0.502400469	0.508180503
184	Aron Baynes	0.503616373	0.510929924	0.51069185	0.490007246	0.499574452	0.506878393
185	Bam Adebayo	0.503608957	0.507952176	0.507527127	0.494223267	0.500207458	0.508134756
186	Dennis Schroeder	0.503107987	0.500937857	0.499949229	0.513149846	0.507981065	0.493521937
187	Kevon Looney	0.502973566	0.510175863	0.510002128	0.489999909	0.496535273	0.508154656
188	Landry Shamet	0.502613769	0.496854565	0.496415937	0.512153927	0.50655737	0.501087049
189	Trey Lyles	0.502363197	0.509868091	0.509362348	0.491230114	0.494603863	0.50675157
190	Devin Harris	0.502199228	0.510122225	0.509710862	0.486912485	0.500160299	0.504090266
191	Eric Gordon	0.502126997	0.494403719	0.493555514	0.520958394	0.503322251	0.498395107
192	Norman Powell	0.502047861	0.503303771	0.50308924	0.501073652	0.503284996	0.499487646
193	Abdel Nader	0.501473435	0.502577384	0.502739224	0.495083222	0.498038865	0.508928481
194	Marvin Bagley	0.501431019	0.505139089	0.504710415	0.499179285	0.501654117	0.496472188
195	Tyler Johnson	0.501104239	0.500110828	0.499371543	0.505574201	0.505444659	0.495019963
196	Harry Giles	0.500994081	0.509159955	0.508983642	0.485444748	0.490369298	0.511012759
197	Marquese Chriss	0.500914987	0.509542403	0.50962225	0.487377785	0.48909668	0.508935817
198	Ian Clark	0.500861516	0.501146869	0.501001969	0.498987131	0.501465768	0.501705841
199	Ed Davis	0.500624056	0.51646627	0.516270115	0.478892635	0.490978932	0.500512329
200	Jonathan Isaac	0.500580918	0.498043762	0.497760184	0.506554736	0.504306506	0.496239404
201	Jonah Bolden	0.500478918	0.505694014	0.50487488	0.48651526	0.496525466	0.508784969
202	Jerian Grant	0.500447519	0.505355094	0.50469896	0.486433339	0.504258427	0.501491774
203	Markieff Morris	0.500156451	0.502786802	0.502285256	0.495941831	0.498625026	0.501143341
204	Mike Scott	0.499348583	0.502041626	0.501880398	0.493126043	0.496626313	0.503068534
205	Rondae Hollis-Jefferson	0.499301516	0.504748497	0.504800219	0.490517678	0.494671769	0.501769418
206	Chasson Randle	0.499089149	0.507369573	0.507068701	0.489891763	0.493829348	0.497286358
207	Tyreke Evans	0.499065244	0.5052277	0.504555737	0.489058782	0.497255603	0.499228397
208	Cory Joseph	0.498887927	0.495523732	0.494970379	0.498470806	0.509674435	0.495800281
209	T.J. Warren	0.498748272	0.496354663	0.495747583	0.501746085	0.505366597	0.494526433
210	Trevor Ariza	0.498451145	0.500167898	0.49911806	0.496856648	0.49273115	0.503381968
211	Troy Daniels	0.498339385	0.500345404	0.499994493	0.488947005	0.496139995	0.506270028
212	T.J. McConnell	0.497847462	0.503209497	0.502847929	0.489104963	0.495815912	0.498259011
213	Dennis Smith	0.497552282	0.496712645	0.495876715	0.506833398	0.50021321	0.488125445
214	Mike Muscala	0.497521025	0.499027949	0.49845907	0.491181048	0.498711673	0.500225384
215	Miles Bridges	0.49736364	0.499918713	0.499810936	0.491643354	0.496424482	0.499020714
216	Kentavious Caldwell-Pope	0.497243416	0.495097364	0.494620294	0.501660446	0.498864058	0.495974918
217	Will Barton	0.497178354	0.495344488	0.494682921	0.497153951	0.504799268	0.493911141
218	Ersan İlyasova	0.497078073	0.499397364	0.499260856	0.490187392	0.498128606	0.49841615
219	Wendell Carter	0.496821898	0.495081783	0.494788493	0.499080528	0.50174113	0.493417557
220	Anthony Tolliver	0.496720982	0.495026989	0.494833951	0.495463446	0.501509087	0.496771436
221	Zach Collins	0.496072899	0.501213952	0.501145485	0.485844746	0.49377986	0.498380452
222	Tomas Satoransky	0.496062561	0.504336537	0.503442711	0.487801616	0.490379671	0.49435227
223	Kelly Oubre	0.495854751	0.495982307	0.495182938	0.499868289	0.49795501	0.49028521
224	Jaren Jackson	0.495210655	0.495695172	0.495401001	0.498765688	0.49558307	0.490608342
225	Luke Kennard	0.495019623	0.493176457	0.492632392	0.497603511	0.497994764	0.493690991
226	Greg Monroe	0.494713334	0.502859972	0.502622245	0.48310817	0.482125854	0.502850427
227	Evan Turner	0.494633251	0.493732164	0.493414011	0.491252338	0.497643736	0.497124008
228	Dario Saric	0.494629898	0.49504195	0.494641726	0.494514569	0.497887859	0.491063384
229	Marco Belinelli	0.494550909	0.493638395	0.493066622	0.498297061	0.498094999	0.48965747
230	Noah Vonleh	0.493785965	0.494988787	0.494388581	0.490238122	0.493010005	0.496304329
231	Jaylen Brown	0.493450794	0.490922083	0.490680099	0.501102396	0.495699584	0.48884981
232	Zaza Pachulia	0.493447475	0.504078972	0.503937	0.474294851	0.484606236	0.500320315
233	Nik Stauskas	0.49330791	0.499160747	0.499012371	0.481506266	0.489187941	0.497672226
234	Khem Birch	0.493249318	0.50652267	0.506088112	0.476539705	0.477385772	0.499710332
235	Tim Hardaway	0.492833601	0.49022855	0.489041501	0.505224591	0.496675003	0.482998358
236	Shaquille Harrison	0.492769013	0.496597743	0.496376441	0.486307273	0.48854281	0.496020798
237	Langston Galloway	0.492691515	0.490093097	0.489805318	0.499183196	0.493075433	0.491300529
238	Seth Curry	0.492537207	0.488428681	0.488365175	0.498463366	0.49594409	0.491484723
239	Alfonzo McKinnie	0.492391204	0.500373981	0.500415835	0.478634795	0.483843347	0.498688061
240	Jose Calderon	0.492380932	0.494440301	0.494294755	0.489089762	0.499409828	0.484670016
241	Kosta Koufos	0.49194652	0.506669759	0.506416293	0.467815071	0.475752853	0.503078624
242	DeMarre Carroll	0.491829314	0.488192734	0.487838953	0.496961146	0.500760073	0.485393662
243	Antonio Blakeney	0.491784303	0.493411646	0.493424596	0.488137526	0.490048668	0.49389908
244	George Hill	0.491428334	0.488493608	0.488396401	0.496048445	0.498000021	0.486203194
245	Nene Hilario	0.491292393	0.504482402	0.504827424	0.473883317	0.474574822	0.498694001
246	Ryan Arcidiacono	0.491270923	0.489604332	0.489132055	0.494625961	0.497315911	0.485676359
247	Thabo Sefolosha	0.491183919	0.501339064	0.500939847	0.475469897	0.4776017	0.500569088
248	Justin Jackson	0.491022995	0.490650533	0.49058624	0.491929985	0.491330711	0.490617504
249	Jonathon Simmons	0.490460612	0.490096968	0.490268024	0.495259101	0.493276443	0.483402525
250	Jeremy Lin	0.490322317	0.497640486	0.496783629	0.477846288	0.487819526	0.491521655
251	Torrey Craig	0.490083144	0.487791528	0.487899973	0.490502336	0.493375307	0.490846578
252	Emmanuel Mudiay	0.489815649	0.489433717	0.488511883	0.49596723	0.49177273	0.483392684
253	Tony Snell	0.489801781	0.489595791	0.489459025	0.488570106	0.492501771	0.488882214
254	Allen Crabbe	0.489535391	0.478832533	0.478671437	0.503952509	0.498040784	0.488179691
255	Enes Kanter	0.489506013	0.499294715	0.498449094	0.473632741	0.481357223	0.494796292
256	Tyrone Wallace	0.489437593	0.492359348	0.492576699	0.479606064	0.484453402	0.498192451
257	Derrick Jones	0.489319553	0.488336652	0.488324585	0.489761221	0.489843762	0.490331546
258	Marcin Gortat	0.488945241	0.494521678	0.494417262	0.479401376	0.480640807	0.495745081
259	Jabari Parker	0.48881123	0.490671272	0.490080298	0.487500161	0.490126598	0.485677823
260	Al-Farouq Aminu	0.488538173	0.483905011	0.48359166	0.491423673	0.492877406	0.490893115
261	Ivan Rabb	0.48799673	0.494618864	0.494387473	0.473831841	0.480937131	0.49620834
262	Maurice Harkless	0.487975397	0.487709591	0.487630611	0.484285408	0.490188119	0.490063254
263	Patrick Patterson	0.487866492	0.488793765	0.488868766	0.482114513	0.487393532	0.492161885
264	Thaddeus Young	0.487866037	0.483746415	0.483572122	0.493204613	0.490934356	0.48787268
265	Kevin Huerter	0.487761964	0.48604767	0.485438524	0.492427517	0.488465387	0.486430721
266	David Nwaba	0.487701252	0.489566791	0.489858712	0.485527336	0.484126662	0.48942676
267	Moritz Wagner	0.487651363	0.491584913	0.491175462	0.480573182	0.483551111	0.491372146
268	Alec Burks	0.487382611	0.49377409	0.493198078	0.477607332	0.481605274	0.490728277
269	Jake Layman	0.48698223	0.487673639	0.48767548	0.485792466	0.484900645	0.488868917
270	Dante Cunningham	0.486878378	0.486230773	0.48626683	0.482575304	0.488555418	0.490763567
271	Wilson Chandler	0.486725781	0.483706667	0.483821704	0.488811891	0.48664752	0.490641123
272	Elie Okobo	0.486361362	0.486939904	0.486865704	0.487067495	0.490345033	0.480588674
273	Bryn Forbes	0.486054581	0.480449221	0.479981845	0.498684167	0.49105697	0.480100701
274	Evan Fournier	0.485746844	0.484619023	0.483854965	0.495141178	0.486964593	0.478154461
275	DeAndre' Bembry	0.48532131	0.486415775	0.486163333	0.482134009	0.486962453	0.48493098
276	Taj Gibson	0.484755749	0.48563822	0.485598165	0.484749212	0.485370945	0.482422204
277	Devonte' Graham	0.484728503	0.492429251	0.491238911	0.470374238	0.483806421	0.485793691
278	Josh Hart	0.484601115	0.478927005	0.478828643	0.491299125	0.487066212	0.48688459
279	Cristiano Felício	0.48445398	0.490301547	0.49052112	0.474060826	0.475692554	0.491693852
280	Hamidou Diallo	0.484288253	0.4864743	0.48657061	0.481534612	0.478953445	0.487908299
281	Kyle Kuzma	0.484146904	0.48322611	0.48242651	0.49002067	0.481563488	0.483497742
282	Shelvin Mack	0.483860065	0.48432042	0.483908797	0.484635586	0.487653162	0.478782362
283	Bismack Biyombo	0.483815078	0.491739804	0.491605929	0.468821394	0.474504924	0.492403341
284	Nicolas Batum	0.483745579	0.481125268	0.480661994	0.484714781	0.483494186	0.488731665
285	Mario Hezonja	0.483028291	0.484794375	0.484728162	0.479153033	0.479031333	0.487434554
286	Joe Harris	0.482790997	0.480203618	0.479468605	0.492514806	0.484658342	0.477109613
287	Michael Kidd-Gilchrist	0.482739039	0.488531165	0.488611696	0.477268094	0.474942422	0.484341818
288	Darius Miller	0.482604744	0.475748688	0.475352954	0.498205117	0.487442928	0.476274031
289	Tyler Dorsey	0.48238234	0.489762056	0.488990864	0.467349903	0.476683205	0.489125669
290	Tristan Thompson	0.482106151	0.489021315	0.488834697	0.473183082	0.47437442	0.485117243
291	OG Anunoby	0.481648519	0.476739179	0.47695313	0.484728836	0.485800441	0.484021007
292	Jalen Brunson	0.481211109	0.485101033	0.484450569	0.47476676	0.481197001	0.480540184
293	Juan Hernangomez	0.481191292	0.481140985	0.481091803	0.480227367	0.480732026	0.482764279
294	Bojan Bogdanovic	0.480927278	0.4761017	0.475585612	0.493565644	0.488018817	0.471364616
295	Shaun Livingston	0.48023408	0.486604557	0.486642639	0.471497548	0.476484189	0.479941466
296	Shai Gilgeous-Alexander	0.480114587	0.478448312	0.478132649	0.489008344	0.483629282	0.47135435
297	Josh Jackson	0.480019953	0.483571945	0.483265565	0.476250865	0.47730958	0.479701808
298	Jeff Green	0.480013255	0.478648619	0.478348712	0.486464764	0.482693827	0.473910353
299	Royce O'Neale	0.480005153	0.476918395	0.47695441	0.479725696	0.483026646	0.48340062
300	Rodney McGruder	0.479655646	0.473631926	0.473642632	0.488413879	0.482390427	0.480199364
301	Jerami Grant	0.479337007	0.47398614	0.47391289	0.487428838	0.483577259	0.477779908
302	Dwayne Bacon	0.478903531	0.47923695	0.478989862	0.47931989	0.474585082	0.48238587
303	Damyean Dotson	0.478650676	0.477052537	0.476786666	0.481125474	0.481372854	0.476915851
304	James Johnson	0.478508945	0.483546206	0.482818861	0.46815981	0.478234271	0.479785576
305	Semi Ojeleye	0.478093712	0.482079046	0.48196091	0.469456349	0.473240776	0.483731479
306	Gary Harris	0.477829836	0.474209715	0.473941414	0.486826145	0.480290805	0.473881099
307	Dragan Bender	0.477827488	0.475636676	0.47544437	0.477444595	0.478607515	0.482004287
308	Rodions Kurucs	0.477016305	0.478132786	0.478131659	0.474998733	0.476940265	0.476878082
309	Solomon Hill	0.476136316	0.469905903	0.470361693	0.482162866	0.480631404	0.477619713
310	Dorian Finney-Smith	0.475942398	0.471367322	0.471396064	0.479400282	0.479025226	0.478523099
311	Lance Thomas	0.475707014	0.475581625	0.476356935	0.475992247	0.473397927	0.477206333
312	Glenn Robinson	0.475298989	0.478810473	0.47899516	0.469254525	0.470909034	0.478525751
313	Tyson Chandler	0.475232511	0.477098296	0.477205358	0.470179406	0.473977893	0.477701601
314	Doug McDermott	0.474889756	0.476035362	0.476072663	0.47661451	0.472975674	0.472750569
315	Harrison Barnes	0.474834368	0.466827972	0.466288043	0.492576378	0.481212757	0.467266691
316	Steven Adams	0.474634203	0.469407587	0.469602351	0.480783782	0.483537974	0.469839322
317	Mikal Bridges	0.474195277	0.465334451	0.465232825	0.484851149	0.479573009	0.475984949
318	Wesley Matthews	0.473973826	0.468792411	0.468425662	0.489224019	0.477176639	0.466250399
319	Ante Zizic	0.47385263	0.474359563	0.474415318	0.473880157	0.473788112	0.472819999
320	Robin Lopez	0.472710612	0.4672528	0.467635902	0.484153338	0.479031693	0.465479329
321	Andrew Wiggins	0.472112248	0.469699104	0.469146552	0.484857682	0.47222811	0.464629795
322	Frank Jackson	0.471115402	0.468223895	0.468275384	0.479820742	0.470920708	0.468336282
323	Josh Okogie	0.470904423	0.464000874	0.464089196	0.480033092	0.477060662	0.46933829
324	Kyle Anderson	0.470776361	0.462614792	0.462531055	0.482543615	0.479775192	0.466417152
325	Justin Holiday	0.469956281	0.461168328	0.460968388	0.483778416	0.470355062	0.47351121
326	Wayne Selden	0.469344152	0.469638012	0.469811619	0.470656823	0.469902238	0.466712066
327	Reggie Bullock	0.469281236	0.463814056	0.463322473	0.48255392	0.471610928	0.465104803
328	Jared Dudley	0.469066767	0.464829982	0.464968738	0.472923902	0.475190061	0.467421152
329	Cedi Osman	0.468708092	0.462240931	0.461921861	0.481999843	0.472645503	0.464732322
330	Frank Ntilikina	0.467936428	0.466559056	0.466188227	0.469516976	0.473562623	0.463855259
331	P.J. Tucker	0.464386913	0.442582939	0.442791757	0.488058226	0.474850742	0.473650903
332	Wesley Iwundu	0.463303936	0.46218866	0.462357298	0.464963673	0.467509482	0.459500565
333	Bruce Brown	0.462881381	0.458201974	0.458666818	0.470441642	0.466595335	0.460501133
334	Austin Rivers	0.460970786	0.452597103	0.45261116	0.476498812	0.468841387	0.454305468
335	James Ennis	0.460326364	0.456484829	0.456356264	0.467599874	0.463406683	0.45778417
336	Rodney Hood	0.459371181	0.456224864	0.456035204	0.469360096	0.459466717	0.455769026
337	E'Twaun Moore	0.458219049	0.451955331	0.45182516	0.47534784	0.457749922	0.454216992
338	Kevin Knox	0.457878208	0.454989167	0.455007077	0.46953761	0.458392603	0.451464585
339	Chandler Hutchison	0.457310691	0.452160226	0.452690825	0.463964829	0.460464275	0.457273299
340	Garrett Temple	0.456853375	0.445634096	0.445955673	0.477015942	0.462739711	0.452921452
341	Allonzo Trier	0.455134207	0.452924948	0.452813291	0.461843607	0.458757897	0.44933129
342	Brandon Ingram	0.452004126	0.447622542	0.447791408	0.462448343	0.458670272	0.443488067
343	Collin Sexton	0.445381985	0.440583737	0.440477978	0.462107269	0.45049615	0.433244791
344	Avery Bradley	0.445007567	0.431412916	0.431645143	0.472289794	0.455970814	0.433719166

The table below shows each player’s cumulative true win shares.

rank	player	avg	log	lda	rf	gbc	dnn
1	James Harden	53.02645802	53.8994028	53.54695425	51.04378649	51.73005883	54.91208775
2	Nikola Jokic	50.59939643	50.29053557	50.06249199	49.58589072	50.90702997	52.15103391
3	D'Angelo Russell	49.14519655	49.10615364	48.87727315	48.25590274	49.10988796	50.37676529
4	Kemba Walker	48.84176681	49.34459588	49.10601296	48.02628448	47.66712759	50.06481312
5	Russell Westbrook	48.6242841	48.71680459	48.43676451	46.06615571	47.99153399	51.91016167
6	Damian Lillard	48.54786842	48.66735051	48.40524434	47.98120607	48.05171786	49.63382334
7	Nikola Vucevic	48.27487937	49.17332164	49.0065436	46.49642384	47.51396276	49.18414501
8	Paul George	46.8655401	48.62981243	48.38051258	44.08558546	45.12013569	48.11165432
9	Kevin Durant	46.66335781	46.25626802	46.06437557	46.76862678	46.42814248	47.7993762
10	Giannis Antetokounmpo	46.58442536	46.24345587	46.02770314	45.41976441	47.70004195	47.53116144
11	Karl-Anthony Towns	46.22333292	47.13107578	46.94975797	44.61118797	45.13760537	47.28703752
12	Bradley Beal	46.15094798	47.18762945	46.98582323	44.38881873	44.59502425	47.59744426
13	De'Aaron Fox	45.37159486	45.45149412	45.27773513	45.77352678	45.1917593	45.16345897
14	Trae Young	45.34911082	45.37693405	45.170893	45.20887706	45.44118681	45.54766316
15	Rudy Gobert	45.22785997	45.85436742	45.75734665	44.33508902	44.82854514	45.36395162
16	Buddy Hield	45.09840652	45.18618692	45.04139486	45.18307225	45.00676511	45.07461344
17	Stephen Curry	44.48751817	45.22259715	44.9685183	43.04369126	43.42790262	45.77488154
18	Eric Bledsoe	44.3782547	44.27789875	44.13126718	44.09304573	44.88369255	44.5053693
19	Ben Simmons	44.2613513	43.60056963	43.45214718	44.70183921	44.54446334	45.00773714
20	Brook Lopez	43.91267474	44.21496538	44.11799664	43.26398037	43.94581234	44.02061898
21	Terrence Ross	43.61801176	43.33479775	43.23713063	44.17102096	43.94433243	43.40277702
22	Marc Gasol	43.57141054	43.99549522	43.86446295	42.52678455	42.97008434	44.50022565
23	Montrezl Harrell	43.22794607	43.07050002	43.02153036	43.37443534	43.56133626	43.11192836
24	Joe Ingles	42.88765933	43.31533466	43.17207138	42.25243087	42.69557507	43.00288467
25	Andre Drummond	42.87351399	44.39927017	44.31581935	41.19790871	41.54514083	42.90943087
26	Reggie Jackson	42.84863778	42.97245152	42.85295988	42.85507951	43.03938489	42.52331308
27	Mason Plumlee	42.7136468	43.28216106	43.22349764	41.44254518	42.46845527	43.15157483
28	Monte Morris	42.63926944	42.86262272	42.78834314	42.36271903	42.63894952	42.5437128
29	Blake Griffin	42.50111934	42.66272664	42.47948041	42.15748505	41.97344745	43.23245714
30	LaMarcus Aldridge	42.47975823	42.18314615	42.1270747	42.8133588	42.6134581	42.66175342
31	Luka Doncic	42.430138	42.22403841	42.0248544	42.42463587	42.92813139	42.54902995
32	Khris Middleton	42.37304986	42.53996784	42.39817758	41.85364279	42.76230185	42.31115923
33	Tobias Harris	42.1627449	42.34371358	42.24159054	42.22958249	41.78676594	42.21207194
34	Lou Williams	41.99323093	41.66358431	41.5131157	41.6947398	42.60280336	42.49191147
35	Klay Thompson	41.95130138	41.87018581	41.76752168	42.18188845	41.6905667	42.24634425
36	Terry Rozier	41.91290538	41.96084028	41.87065352	41.32819509	42.46828314	41.93655488
37	Kyrie Irving	41.90839093	42.17012678	41.96324789	40.95108618	41.42032462	43.03716919
38	Patty Mills	41.83797732	41.69753153	41.61284364	41.69176413	42.86943606	41.31831126
39	Willie Cauley-Stein	41.65177844	42.16732329	42.12652897	40.76459941	41.49750663	41.7029339
40	Donovan Mitchell	41.63166928	41.42878788	41.28645133	42.31890045	41.41745106	41.70675566
41	D.J. Augustin	41.43732167	41.7907663	41.67834786	41.08387638	41.62342795	41.01018985
42	Jeremy Lamb	41.4149122	41.53919783	41.46411113	41.22901547	41.49226466	41.34997191
43	Bam Adebayo	41.29593445	41.65207842	41.61722439	40.52630789	41.01701153	41.66705002
44	Mike Conley	41.17423643	41.21220019	41.03412892	40.78693342	41.33833002	41.49958958
45	Jae Crowder	41.14729618	40.88389725	40.8128826	41.61003842	41.40958282	41.02007983
46	Marcus Smart	41.06424248	41.12134009	41.03883	40.670251	41.73513819	40.7556531
47	DeMar DeRozan	41.03235508	40.05323909	39.95133617	42.49918114	41.51306949	41.14494952
48	Jordan Clarkson	41.01438212	40.87766959	40.81381625	41.4276905	41.05405055	40.89868369
49	Malik Beasley	40.87877705	40.77010488	40.72411322	41.03508194	40.77185572	41.09272948
50	Danny Green	40.87726066	40.44227954	40.37751224	41.31865893	41.05275428	41.19509829
51	Myles Turner	40.85775612	41.38617302	41.31733595	40.11266377	40.39543446	41.07717342
52	Kentavious Caldwell-Pope	40.7739601	40.59798383	40.55886412	41.13615656	40.90685277	40.66994326
53	Nemanja Bjelica	40.73227685	41.18212616	41.12085324	39.81432515	40.48939576	41.05468395
54	Pascal Siakam	40.58176731	40.64734834	40.5850634	40.71137255	40.48339648	40.48165579
55	Patrick Beverley	40.56573341	40.42049255	40.33676146	40.24123168	40.99706224	40.83311912
56	Ed Davis	40.55054855	41.8337679	41.81787933	38.79030341	39.76929346	40.54149866
57	Jusuf Nurkic	40.5029871	40.51894658	40.42542206	39.72217544	40.71529657	41.13309484
58	Jarrett Allen	40.47550834	40.66474548	40.64021094	40.47112823	40.48050589	40.12095113
59	Cory Joseph	40.40992206	40.13742227	40.09260074	40.3761353	41.28362922	40.15982278
60	Darren Collison	40.32467197	40.63208786	40.5115106	40.18777158	40.3313902	39.96059961
61	Derrick Favors	40.32270265	40.679242	40.64051087	39.70204105	40.40570214	40.18601719
62	Kevon Looney	40.23788526	40.81406904	40.80017021	39.19999274	39.72282183	40.65237246
63	Hassan Whiteside	40.13392335	41.17549674	41.1233938	38.77035958	39.79113765	39.80922896
64	Jayson Tatum	40.09081781	40.00451905	39.94628358	40.46336725	40.46032444	39.57959474
65	Alex Len	40.08786988	40.61264725	40.56155829	39.17966598	39.8635698	40.22190807
66	Dario Saric	40.06502171	40.09839795	40.06597982	40.05568009	40.32891658	39.77613409
67	Aaron Gordon	39.94833161	40.06949483	39.98578216	39.98168402	39.44174528	40.26295174
68	Jamal Murray	39.89042404	40.13113945	40.01680555	39.58750339	39.4702552	40.24641662
69	Nerlens Noel	39.88770349	41.34528763	41.32293846	37.9014687	38.21950491	40.64931773
70	Bryn Forbes	39.85647563	39.39683609	39.35851132	40.89210172	40.26667155	39.3682575
71	Kelly Olynyk	39.82635242	39.91995391	39.86364098	39.28805756	40.30757966	39.75253001
72	DeAndre' Bembry	39.79634742	39.88609359	39.86539329	39.5349887	39.93092114	39.76434037
73	Ryan Arcidiacono	39.79294479	39.65795086	39.61969642	40.06470283	40.28258882	39.33978505
74	Miles Bridges	39.78909118	39.993497	39.98487491	39.33146835	39.71395853	39.92165711
75	Dennis Schroeder	39.74553097	39.57409068	39.49598911	40.53883785	40.13050417	38.98823302
76	Landry Shamet	39.70648779	39.2515106	39.21685902	40.46016027	40.01803222	39.58587685
77	Joel Embiid	39.69297865	40.02725955	39.87045642	38.90649547	39.33362341	40.32705838
78	Tomas Satoransky	39.68500488	40.34692299	40.2754169	39.02412928	39.23037365	39.54818157
79	Vince Carter	39.64321996	39.86377464	39.81054037	39.10690939	39.54994789	39.88492752
80	JaVale McGee	39.60745399	40.10962644	40.08595056	39.23821994	39.04769616	39.55577684
81	Al-Farouq Aminu	39.571592	39.19630589	39.17092443	39.80531749	39.92306986	39.76234234
82	Thaddeus Young	39.51714901	39.1834596	39.1693419	39.94957362	39.76568281	39.5176871
83	Mike Scott	39.44853802	39.66128842	39.64855142	38.95695736	39.23347875	39.74241417
84	Davis Bertans	39.38926749	39.26766129	39.21249447	39.36759014	39.5574145	39.54117702
85	Shai Gilgeous-Alexander	39.36939617	39.23276161	39.20687718	40.09868419	39.65760113	38.65105672
86	Royce O'Neale	39.36042257	39.1073084	39.11026162	39.33750707	39.60818496	39.6388508
87	Evan Fournier	39.34549437	39.25414089	39.19225215	40.10643544	39.44413203	38.73051133
88	Justin Jackson	39.28183956	39.25204264	39.24689916	39.3543988	39.30645692	39.24940028
89	J.J. Redick	39.21736935	39.10621438	39.0020366	40.01974426	39.32371308	38.63513841
90	Dwight Powell	39.19241987	39.5222913	39.48360947	38.60930588	39.0016115	39.34528121
91	Gorgui Dieng	39.15124031	40.44577844	40.41686546	37.07177571	37.75059948	40.07118246
92	Marco Belinelli	39.06952184	38.99743317	38.95226314	39.36546782	39.34950495	38.68294012
93	Jakob Poeltl	38.9717845	39.89151784	39.87331878	37.62970657	37.99325749	39.47112183
94	Bojan Bogdanovic	38.95510949	38.56423768	38.52243455	39.97881715	39.52952419	38.18053389
95	Julius Randle	38.92736913	38.67298318	38.5811552	39.20899804	38.94457792	39.22913133
96	Mikal Bridges	38.88401268	38.15742495	38.14909166	39.75779422	39.32498675	39.03076581
97	Domantas Sabonis	38.55263288	39.00534573	38.94069104	37.26327024	38.34005947	39.21379794
98	Dorian Finney-Smith	38.55133428	38.18075311	38.18308115	38.83142283	38.80104327	38.76037102
99	Justin Holiday	38.53641502	37.81580289	37.79940782	39.66983011	38.56911509	38.82791919
100	Delon Wright	38.47188156	39.06800061	39.00530407	37.36829504	38.08629695	38.83151113
101	Marvin Williams	38.45606461	38.1429107	38.10553377	38.75955869	38.56565249	38.7066674
102	Langston Galloway	38.42993813	38.22726156	38.20481479	38.93628929	38.45988375	38.32144126
103	Jerami Grant	38.34696056	37.91889119	37.91303118	38.99430703	38.68618073	38.22239265
104	Serge Ibaka	38.27928878	38.53491362	38.49204426	37.99900586	38.31107278	38.05940738
105	P.J. Tucker	38.07972689	36.29180098	36.30892405	40.02077454	38.93776088	38.83937402
106	Jrue Holiday	38.02220579	38.69132564	38.50644383	36.88087664	37.08045382	38.95192904
107	Danilo Gallinari	37.97704355	37.86904178	37.74872512	38.00591872	38.47718586	37.78434629
108	Al Horford	37.97668707	38.27335926	38.17207054	37.04906925	38.03763334	38.35130296
109	Steven Adams	37.97073626	37.55260696	37.5681881	38.46270254	38.68303791	37.58714579
110	Marcus Morris	37.93416456	37.97139473	37.91153662	38.11327278	38.03580384	37.63881482
111	Josh Jackson	37.92157626	38.20218365	38.17797966	37.62381833	37.70745684	37.8964428
112	Quinn Cook	37.83868083	38.10537835	38.06234915	36.97439375	37.60831211	38.44297078
113	Dwyane Wade	37.77130117	37.81980224	37.72527767	37.56038481	38.10273699	37.64830412
114	Jonas Jerebko	37.76681719	38.22560955	38.19757803	36.72211948	37.55622164	38.13255724
115	Kyle Lowry	37.76409456	38.5896231	38.40198057	36.41888398	37.35855457	38.05143056
116	Zach Collins	37.70154034	38.09226035	38.08705688	36.9242007	37.52726936	37.87691439
117	Jonathan Isaac	37.54356889	37.35328214	37.33201381	37.99160519	37.82298795	37.21795533
118	Gordon Hayward	37.44464555	37.32035504	37.26817668	37.4550922	37.92332681	37.25627703
119	Thomas Bryant	37.43841801	38.2112473	38.17225277	36.31459724	36.70806517	37.78592759
120	T.J. McConnell	37.33855968	37.7407123	37.71359465	36.68287221	37.18619341	37.36942585
121	Gerald Green	37.20241359	37.07717521	37.04039594	37.23283622	37.28895625	37.37270432
122	Josh Richardson	37.07570181	37.66366241	37.57514776	36.69328524	36.47367207	36.97274158
123	Jeff Green	36.96102064	36.85594369	36.83285082	37.45778685	37.16742469	36.49109716
124	Bogdan Bogdanovic	36.86801712	37.06706941	36.97643143	36.62217519	37.02290545	36.6515041
125	Torrey Craig	36.75623582	36.58436458	36.59249796	36.7876752	37.003148	36.81349333
126	Joe Harris	36.69211578	36.49547499	36.43961401	37.43112527	36.83403402	36.26033062
127	Maxi Kleber	36.58858054	36.76153813	36.74758632	36.15882923	36.60632583	36.6686232
128	Kevin Huerter	36.58214729	36.45357524	36.40788929	36.93206379	36.63490405	36.48230409
129	Harrison Barnes	36.56224636	35.94575388	35.90417928	37.92838111	37.05338231	35.9795352
130	Collin Sexton	36.52132277	36.12786642	36.11919424	37.89279604	36.94068429	35.52607288
131	Jaylen Brown	36.51535878	36.32823416	36.31032732	37.0815773	36.68176921	36.17488591
132	Paul Millsap	36.48628588	36.61491667	36.56538089	36.21395493	36.66956201	36.3676149
133	Malik Monk	36.34289367	36.68174607	36.62656847	35.66811371	36.2242663	36.51377376
134	Jeremy Lin	36.28385146	36.82539598	36.76198855	35.36062534	36.09864495	36.37260245
135	Nicolas Batum	36.28091842	36.08439513	36.04964958	36.35360859	36.26206395	36.65487484
136	CJ McCollum	36.23085568	36.03307901	35.95042225	36.75799099	36.19619017	36.21659597
137	Evan Turner	36.10822734	36.04244794	36.01922281	35.86142064	36.32799272	36.29005258
138	Draymond Green	36.07849295	35.85128338	35.74391058	35.21832229	36.45329909	37.12564941
139	Larry Nance	36.07003799	36.46289825	36.41452013	35.08328831	35.92533842	36.46414485
140	Kyle Korver	36.05943134	35.7434065	35.7111145	36.19092424	36.71791397	35.93379749
141	Shaquille Harrison	35.97213794	36.25163521	36.23548017	35.50043093	35.66362515	36.20951825
142	Richaun Holmes	35.96383022	36.63995542	36.61417909	35.07745499	35.29985046	36.18771112
143	Seth Curry	35.95521611	35.65529372	35.65065775	36.3878257	36.20391858	35.87838478
144	Mitchell Robinson	35.90502597	36.50623171	36.48231816	35.30831875	35.15234039	36.07592086
145	Rudy Gay	35.77670386	36.24189439	36.18056322	34.80506049	35.70822037	35.94778082
146	Deandre Ayton	35.77462318	35.78340441	35.76812444	35.7654944	35.89384357	35.66224907
147	Kawhi Leonard	35.7326853	35.56746529	35.44828589	35.86432949	35.72462058	36.05872523
148	Anthony Davis	35.63547904	37.22814343	37.06852163	32.79083256	33.97065471	37.11924288
149	Cedi Osman	35.62181498	35.13031074	35.10606141	36.6319881	35.92105819	35.31965646
150	Ricky Rubio	35.40116428	35.67850833	35.56488362	35.08483378	35.46191619	35.21567949
151	Tony Snell	35.26572826	35.25089695	35.2410498	35.17704761	35.46012752	35.19951943
152	LeBron James	35.22641988	35.46857856	35.27919552	33.59600272	34.72935231	37.05897031
153	Wayne Selden	35.20081139	35.22285091	35.23587145	35.29926174	35.24266788	35.00340497
154	Doug McDermott	35.14184192	35.22661681	35.22937707	35.26947377	35.00019987	34.98354211
155	Jalen Brunson	35.12841099	35.41237542	35.36489152	34.65797351	35.12738105	35.07943342
156	Spencer Dinwiddie	35.12310447	35.04370233	34.93726243	35.20491575	35.49422612	34.93541573
157	Austin Rivers	35.03377974	34.39737983	34.39844814	36.21390973	35.63194541	34.52721557
158	Robin Lopez	34.98058531	34.57670717	34.60505675	35.82734698	35.44834529	34.44547038
159	Lance Stephenson	34.9717226	35.2968112	35.24985065	34.26515158	34.89643285	35.15036675
160	Yogi Ferrell	34.95366381	35.52874795	35.49961621	33.88565614	34.49008677	35.364212
161	DeAndre Jordan	34.95142702	35.15893598	35.12759611	34.42655239	34.80002944	35.24402117
162	Damyean Dotson	34.94149938	34.82483521	34.80542661	35.12215959	35.14021834	34.81485713
163	Tyus Jones	34.89748241	35.46026805	35.38842373	34.41556607	34.91444575	34.30870846
164	Andre Iguodala	34.89477703	34.8264404	34.78391334	34.55406086	35.41281028	34.89666027
165	Devin Booker	34.89052049	34.42059626	34.26342664	35.87389862	34.46072639	35.43395454
166	Josh Okogie	34.84692728	34.33606464	34.34260052	35.52244881	35.30248899	34.73103344
167	Clint Capela	34.73327663	34.79971791	34.76884502	34.66241538	35.0427913	34.39261354
168	Jimmy Butler	34.59786885	34.54174287	34.43718546	34.72938896	34.48906373	34.79196325
169	Kent Bazemore	34.5943151	34.73304504	34.68699063	34.25614022	34.6733616	34.62203803
170	Jake Layman	34.5757383	34.62482835	34.62495911	34.49126509	34.42794582	34.70969311
171	Andrew Wiggins	34.46419413	34.28803456	34.24769828	35.39461077	34.47265201	33.91797504
172	Tyreke Evans	34.43550182	34.86071133	34.81434585	33.74505595	34.31063658	34.44675937
173	Trevor Ariza	34.39312898	34.51158494	34.43914616	34.28310871	33.99844932	34.73335577
174	Kevin Knox	34.34086562	34.12418751	34.1255308	35.21532075	34.37944519	33.85984385
175	Chris Paul	34.28602556	34.77748682	34.59667226	33.36537444	34.30232563	34.38826865
176	Derrick White	34.28577848	34.55533365	34.50732001	33.7623222	34.42224558	34.18167097
177	Garrett Temple	34.26400311	33.42255719	33.44667548	35.77619568	34.70547829	33.96910889
178	Bruce Brown	34.25322216	33.90694611	33.94134452	34.8126815	34.52805482	34.07708384
179	Dewayne Dedmon	34.22714423	34.69428697	34.63727678	33.51900571	34.09620343	34.18894829
180	Kelly Oubre	34.21397779	34.22277917	34.16762271	34.49091193	34.35889568	33.82967947
181	Devin Harris	34.14954747	34.68831129	34.66033863	33.11004897	34.01090036	34.27813812
182	Eric Gordon	34.14463579	33.61945286	33.56177492	35.42517078	34.2259131	33.8908673
183	Daniel Theis	34.12277002	34.67780872	34.65448484	33.06080164	33.61808367	34.60267125
184	Alfonzo McKinnie	33.97499307	34.52580472	34.52869261	33.02580084	33.38519097	34.40947622
185	Taj Gibson	33.93290245	33.99467541	33.99187155	33.93244481	33.97596614	33.76955431
186	Kyle Kuzma	33.89028329	33.82582771	33.76985569	34.3014469	33.70944417	33.84484195
187	Jordan Bell	33.88983525	34.34995706	34.34141833	32.84964946	33.27962037	34.62853104
188	Juan Hernangomez	33.68339043	33.67986894	33.67642619	33.61591567	33.65124182	33.79349955
189	Justise Winslow	33.65271593	33.66931794	33.59565379	33.46880084	33.94368263	33.58612447
190	Noah Vonleh	33.57744561	33.65923751	33.61842353	33.33619226	33.52468037	33.74869437
191	Fred VanVleet	33.50455534	33.65724528	33.55744736	33.45505673	33.62599868	33.22702864
192	Ersan İlyasova	33.30423092	33.45962337	33.45047736	32.84255524	33.37461657	33.39388208
193	Darius Miller	33.29972732	32.82665948	32.79935381	34.37615309	33.63356206	32.86290817
194	Stanley Johnson	33.27128809	33.29492764	33.29556558	33.17516085	33.18419453	33.40659186
195	Malcolm Brogdon	33.010333	33.19041283	33.12056468	32.69230913	33.00240986	33.04596852
196	DeMarre Carroll	32.95256402	32.7089132	32.68520987	33.29639679	33.55092491	32.52137533
197	Sindarius Thornwell	32.87821756	32.52826704	32.53391725	32.84002361	33.06510365	33.42377628
198	Thon Maker	32.83458422	33.28090325	33.26888654	32.16674284	32.4096606	33.04672789
199	Enes Kanter	32.79690288	33.4527459	33.39608933	31.73339362	32.25093396	33.15135159
200	JaMychal Green	32.77475911	32.99327486	32.96439635	32.47339081	33.08377474	32.35895879
201	Wesley Matthews	32.704194	32.34667633	32.3213707	33.75645734	32.92518809	32.17127751
202	Cheick Diallo	32.67057709	33.12428669	33.12279375	31.8126216	32.18882673	33.10435669
203	Jamal Crawford	32.62477979	32.93060333	32.88578275	32.25066775	32.84834275	32.20850237
204	Rodney Hood	32.61535389	32.39196535	32.37849949	33.32456685	32.6221369	32.35960084
205	Zaza Pachulia	32.56753334	33.26921214	33.259842	31.3034602	31.98401156	33.02114077
206	Nik Stauskas	32.55832209	32.9446093	32.93481651	31.77941358	32.28640411	32.84636695
207	Josh Hart	32.46827471	32.08810936	32.08151909	32.91704136	32.63343619	32.62126756
208	John Collins	32.31658028	32.60883768	32.56720782	32.02008846	31.93105746	32.45570996
209	Zach LaVine	32.23011087	31.88108663	31.78400007	33.06803519	32.28689167	32.1305408
210	Trey Lyles	32.15124462	32.63155781	32.59919025	31.43872731	31.65464725	32.43210045
211	Tim Hardaway	32.03418405	31.86485577	31.78769756	32.83959841	32.28387523	31.39489328
212	Mike Muscala	31.84134558	31.93778872	31.90138051	31.43558705	31.91754708	32.01442456
213	OG Anunoby	31.78880223	31.46478579	31.47890656	31.9921032	32.06282913	31.94538646
214	Pat Connaughton	31.70897149	31.77656524	31.73994012	31.2241152	32.02695102	31.77728586
215	Rodney McGruder	31.65727261	31.25970712	31.26041374	32.235316	31.83776821	31.69315799
216	Iman Shumpert	31.41827012	31.09534429	31.08712686	31.54451106	31.8710354	31.49333299
217	Meyers Leonard	31.31463209	31.92706014	31.90444175	30.17762666	30.80366729	31.76036461
218	Jabari Parker	31.28391874	31.40296141	31.36513905	31.2000103	31.36810224	31.08338068
219	Alec Burks	31.19248707	31.60154178	31.56467702	30.56686927	30.82273755	31.40660975
220	Marvin Bagley	31.08872315	31.31862353	31.29204571	30.94911564	31.10255523	30.78127566
221	Michael Kidd-Gilchrist	30.89529851	31.26599456	31.27114855	30.54515803	30.39631504	30.99787636
222	Anthony Tolliver	30.79670086	30.69167332	30.67970495	30.71873363	31.09356337	30.79982903
223	Luke Kennard	30.69121663	30.57694033	30.54320831	30.8514177	30.87567536	30.60884143
224	Dante Cunningham	30.67333783	30.6325387	30.63481029	30.40224414	30.77899132	30.91810469
225	Abdel Nader	30.58987954	30.65722043	30.66709264	30.20007652	30.38037078	31.04463732
226	Wesley Iwundu	30.57805976	30.50445155	30.51558169	30.68760242	30.85562582	30.32703732
227	Tyrone Wallace	30.34513075	30.52627958	30.53975536	29.73557595	30.03611091	30.88793197
228	Tim Frazier	30.26000475	30.63032037	30.58640117	29.498896	30.27917162	30.30523462
229	Norman Powell	30.12287167	30.19822625	30.18535442	30.06441914	30.19709978	29.96925877
230	Shabazz Napier	30.11123016	30.39594339	30.34126566	29.58530779	30.17363819	30.05999577
231	Trey Burke	30.09799103	30.23677037	30.18589308	29.74069412	30.09951139	30.22708621
232	Rodions Kurucs	30.05202722	30.12236552	30.12229449	29.92492021	30.0472367	30.04331918
233	Ian Clark	30.05169093	30.06881214	30.06011814	29.93922784	30.08794606	30.10235048
234	Ivica Zubac	29.90729841	30.34391536	30.32717709	29.19332863	29.41824531	30.25382563
235	Boban Marjanovic	29.80038479	30.45652908	30.43237041	28.43533806	29.08503511	30.59265129
236	Shaun Livingston	29.77451295	30.16948251	30.17184363	29.23284799	29.54201972	29.7563709
237	Jahlil Okafor	29.75639325	29.85677832	29.85491278	29.46423273	29.52771859	30.07832382
238	Tony Parker	29.66189126	29.69107264	29.68256427	29.14404163	29.93486547	29.85691229
239	Reggie Bullock	29.56471786	29.22028555	29.18931579	30.40089694	29.71148847	29.30160256
240	Rondae Hollis-Jefferson	29.45878945	29.7801613	29.78321293	28.94054298	29.18563436	29.60439567
241	Derrick Jones	29.35917319	29.30019911	29.2994751	29.38567326	29.3906257	29.41989278
242	T.J. Leaf	29.33855581	29.82921651	29.83118013	28.53009891	28.75423387	29.74804961
243	Willy Hernangomez	29.31891803	30.14582023	30.11181749	27.7475521	28.77179977	29.81760056
244	Maurice Harkless	29.2785238	29.26257546	29.25783664	29.05712447	29.41128716	29.40379525
245	Sterling Brown	29.21432682	29.26759221	29.26720778	28.92313773	29.1392272	29.47446918
246	Georges Niang	29.20144851	29.68647343	29.68048136	28.20344907	28.70157552	29.73526319
247	Allonzo Trier	29.12858922	28.98719666	28.98005061	29.55799084	29.36050541	28.75720257
248	Otto Porter	29.08507011	29.36007684	29.30534201	28.66052797	28.78238785	29.31701585
249	Cristiano Felício	29.06723878	29.41809285	29.43126717	28.44364955	28.54155322	29.50163112
250	Harry Giles	29.05765667	29.53127739	29.52105124	28.15579541	28.44141928	29.63874004
251	Jerian Grant	29.02595609	29.31059548	29.27253966	28.21313366	29.24698876	29.08652291
252	Markieff Morris	29.00907417	29.16163453	29.13254487	28.76462617	28.92025152	29.06631375
253	George Hill	28.99427169	28.82112285	28.81538765	29.26685825	29.38200122	28.68598847
254	Emmanuel Mudiay	28.89912328	28.87658931	28.8222011	29.26206655	29.01459106	28.52016836
255	Patrick Patterson	28.78412302	28.83883211	28.84325717	28.44475627	28.75621837	29.03755119
256	Frank Jackson	28.73803954	28.5616576	28.56479844	29.26906528	28.72616317	28.56851319
257	Jaren Jackson	28.72221796	28.75031997	28.73325804	28.92840988	28.74381807	28.45528386
258	Tyler Johnson	28.56294161	28.50631719	28.46417797	28.81772946	28.81034555	28.21613787
259	Ish Smith	28.44271777	28.6462416	28.61691248	28.04894183	28.43733104	28.46416192
260	Taurean Waller-Prince	28.09756271	28.02843387	28.00540517	28.58266469	28.16881482	27.70249503
261	Avery Bradley	28.03547671	27.17901373	27.19364401	29.75425704	28.72616127	27.32430748
262	Mario Hezonja	28.01564089	28.11807374	28.11423338	27.79087593	27.78381729	28.2712041
263	Ante Zizic	27.95730515	27.98721421	27.99050376	27.95892924	27.95349864	27.89637992
264	Shelvin Mack	27.58002373	27.60626394	27.58280141	27.62422841	27.79623024	27.29059462
265	Jonathon Simmons	27.46579428	27.4454302	27.45500936	27.73450965	27.62348079	27.07054141
266	Lauri Markkanen	27.28093675	27.67117258	27.59908535	26.86614626	27.09595254	27.17232701
267	Gary Harris	27.23630064	27.02995378	27.0146606	27.74909027	27.37657589	27.01122266
268	Derrick Rose	27.13162061	27.17662121	27.12017878	26.82651062	27.07864273	27.45614974
269	Wayne Ellington	26.85689966	26.56079401	26.51330255	27.17197999	27.02506646	27.01335526
270	Jared Dudley	26.73680572	26.49530896	26.50321808	26.95666243	27.08583348	26.64300564
271	Ekpe Udoh	26.64863813	26.84150797	26.82837327	25.92716279	26.52372056	27.12242606
272	Antonio Blakeney	26.55635238	26.6442289	26.64492818	26.35942641	26.46262808	26.67055032
273	Troy Brown	26.54763697	26.91114256	26.90860747	25.8281365	26.16600464	26.92429369
274	Jonas Valanciunas	26.4195107	26.80953564	26.7693966	26.08926463	26.01490123	26.41445539
275	Dennis Smith	26.37027097	26.32577018	26.28146589	26.8621701	26.5113001	25.87064857
276	C.J. Miles	26.3681533	26.33783513	26.33232576	26.1981267	26.45897712	26.51350176
277	James Johnson	26.31799195	26.59504132	26.55503733	25.74878954	26.30288488	26.3882067
278	Dirk Nowitzki	26.13626875	26.68365571	26.65518767	25.16684807	25.56519559	26.61045673
279	Bismack Biyombo	26.12601423	26.55394941	26.54672016	25.31635529	25.62326588	26.58978041
280	Bobby Portis	26.09305425	26.23426987	26.1819172	25.89658096	26.10422077	26.04828245
281	James Ennis	25.77827637	25.5631504	25.55595076	26.18559293	25.95077426	25.63591352
282	Elie Okobo	25.77715217	25.80781491	25.80388229	25.81457721	25.98828673	25.47119973
283	Tyson Chandler	25.66255558	25.76330799	25.76908935	25.38968794	25.5948062	25.79588644
284	De'Anthony Melton	25.66222525	25.78874557	25.7714232	25.24526199	25.85518439	25.65051112
285	Timothe Luwawu-Cabbarot	25.53769471	25.26470631	25.27629378	25.76946919	25.74325053	25.63475373
286	Semi Ojeleye	25.33896673	25.55018944	25.54392823	24.88118652	25.0817611	25.63776837
287	Aron Baynes	25.18081864	25.54649619	25.53459249	24.50036231	24.97872261	25.34391963
288	Gary Clark	25.09501346	25.20669677	25.20014442	24.5535286	25.07819296	25.43650458
289	Quincy Pondexter	25.06569436	24.92421932	24.916489	24.94980558	25.06302923	25.47492868
290	Nikola Mirotic	25.03513238	25.18310545	25.09842011	24.96717333	25.03754573	24.88941726
291	Troy Daniels	24.91696925	25.01727018	24.99972464	24.44735024	24.80699976	25.31350142
292	Justin Anderson	24.90982782	25.10540787	25.10449426	24.40791155	24.82436362	25.10696178
293	David Nwaba	24.87276386	24.96790634	24.98279431	24.76189413	24.69045977	24.96076476
294	Amir Johnson	24.85592191	25.37978462	25.36883764	23.84812625	24.21111664	25.47174437
295	Aaron Holiday	24.83006941	25.13945963	25.10987185	24.20884291	24.77534424	24.9168284
296	Wilson Chandler	24.82301483	24.66904003	24.6749069	24.92940645	24.8190235	25.02269726
297	Cody Zeller	24.78506903	24.89185879	24.89105701	24.43409361	24.79042678	24.91790897
298	Lonzo Ball	24.68942911	24.94207125	24.87581952	23.87496217	24.70850957	25.04578305
299	Thabo Sefolosha	24.55919597	25.06695322	25.04699233	23.77349487	23.88008502	25.02845442
300	Chasson Randle	24.45536829	24.86110908	24.84636636	24.00469638	24.19763806	24.36703155
301	Luke Kornet	24.43915428	24.943295	24.89768535	23.46983956	23.94598937	24.93896212
302	Rajon Rondo	24.30291393	24.71365897	24.62514062	23.20104889	23.90282882	25.07189235
303	E'Twaun Moore	24.28560961	23.95363254	23.9467335	25.19343554	24.26074588	24.07350056
304	Frank Kaminsky	24.25082917	24.63617109	24.60150519	23.46150126	24.01957454	24.53539376
305	Matthew Dellavedova	24.23413019	24.48827805	24.45814685	23.742203	24.57733871	23.90468435
306	D.J. Wilson	24.22413732	24.30304946	24.28771545	23.7861823	24.39835628	24.3453831
307	Mo Bamba	24.21431487	24.66645142	24.65497368	23.52891648	23.81040484	24.41082794
308	Khem Birch	24.16921658	24.81961081	24.79831751	23.35044552	23.39190281	24.48580625
309	Furkan Korkmaz	23.94990428	24.33721379	24.31796921	23.22579559	23.55980751	24.30873529
310	Ivan Rabb	23.91183976	24.23632436	24.22498619	23.21776022	23.56591941	24.31420865
311	Jose Calderon	23.63428476	23.73313443	23.72614826	23.47630857	23.97167175	23.26416077
312	Kenrich Williams	23.58806521	23.29366731	23.28931161	23.5924747	23.92229492	23.84257754
313	Brandon Ingram	23.50421456	23.27637216	23.28515321	24.04731383	23.85085414	23.06137947
314	Omari Spellman	23.28076674	23.52090496	23.51246104	22.69446589	23.12319533	23.55280645
315	Hamidou Diallo	23.24583615	23.35076638	23.35538927	23.11366138	22.98976536	23.41959834
316	Kris Dunn	23.19479326	23.30433382	23.24283679	23.0745252	23.42560643	22.92666406
317	Kyle O'Quinn	23.09127717	23.290307	23.27867644	22.42494139	22.93128883	23.5311722
318	Jeff Teague	22.97326876	23.29487384	23.22697658	22.9761797	22.96061491	22.40769874
319	Elfrid Payton	22.82334768	22.95361916	22.88716158	22.49269622	22.66837529	23.11488616
320	Sam Dekker	22.75131241	23.00766349	23.02564957	22.33314356	22.3761276	23.01397784
321	Tyler Dorsey	22.67196996	23.01881663	22.98257063	21.96544542	22.40411066	22.98890646
322	Marcin Gortat	22.49148108	22.74799717	22.74319407	22.05246331	22.10947713	22.80427371
323	Joakim Noah	22.45766346	22.93062172	22.91284594	21.55485555	21.97668792	22.91330618
324	Dion Waiters	22.43083273	22.42351118	22.37369103	22.46197543	22.5106787	22.38430732
325	Devonte' Graham	22.29751112	22.65174557	22.59698991	21.63721494	22.25509536	22.3465098
326	Jonah Bolden	22.02107238	22.2505366	22.21449473	21.40667144	21.84712051	22.38653862
327	Dragan Bender	21.98006447	21.87928708	21.87044103	21.96245135	22.01594568	22.17219719
328	Wendell Carter	21.86016352	21.78359846	21.77069369	21.95954323	22.0766097	21.71037253
329	Marquese Chriss	21.53934444	21.91032332	21.91375675	20.95724474	21.03115724	21.88424013
330	T.J. Warren	21.44617571	21.34325052	21.31714607	21.57508166	21.73076367	21.26463661
331	Allen Crabbe	21.0500218	20.58979894	20.58287177	21.66995787	21.41575372	20.99172671
332	Moritz Wagner	20.9690086	21.13815126	21.12054486	20.66464684	20.79269778	21.12900226
333	Glenn Robinson	20.9131555	21.06766081	21.07578704	20.64719912	20.71999749	21.05513303
334	Will Barton	20.88149085	20.80446848	20.77668267	20.88046593	21.20156927	20.74426792
335	Greg Monroe	20.77796002	21.12011884	21.11013431	20.29054312	20.24928586	21.11971794
336	Tristan Thompson	20.73056451	21.02791655	21.01989197	20.34687252	20.39810006	20.86004146
337	Kosta Koufos	20.66175383	21.28012987	21.2694843	19.648233	19.98161981	21.1293022
338	Nene Hilario	20.63428052	21.18826088	21.20275182	19.90309932	19.93214252	20.94514806
339	Dwayne Bacon	20.59285182	20.60718885	20.59656404	20.61075525	20.40715855	20.74259242
340	Lance Thomas	20.45540158	20.45000988	20.4833482	20.46766663	20.35611087	20.51987233
341	Kyle Anderson	20.24338354	19.89243607	19.88883537	20.74937546	20.63033325	20.05593754
342	Frank Ntilikina	20.12126641	20.06203941	20.04609376	20.18922996	20.36319278	19.94577613
343	Solomon Hill	19.99772527	19.73604793	19.75519112	20.25084038	20.18651899	20.06002795
344	Chandler Hutchison	19.66435971	19.4428897	19.46570549	19.95048766	19.79996384	19.66275187

As mentioned earlier, durability impacts cumulative true win shares. Furthermore, two players can have the same average true win shares, but different ranges of true win shares. If two players average the same high number of true win shares, you might prefer the more consistent player.

To show more sensitive results, we created an interactive R Shiny app. This lets you compare the true win shares of any two players in a couple different ways. First, you can look at the distribution of true win shares, which shows some form of consistency. For example, if you compare Russell Westbrook and James Harden, you’ll see that Westbrook has a lot of games with low true win shares. So, he’s a polarizing player.

Along with the distribution of true win shares, you can look at the cumulative win shares over time. So, you can see if one player was keeping pace with another, but then got hurt, preventing him from racking up more true win shares. Finally, on the last tab, you can see each player’s individual game log and the true win shares earned for that game. The link is:

http://dribbleanalytics.shinyapps.io/true-win-shares/

Discussion of results

As expected, durability influences cumulative true win shares. So, it’s not exactly a top players list, as several superstars like LeBron, Curry, and Kawhi missed games. The average true win shares looks a lot like a reasonable ranking of the top players. Though no one would rank Westbrook #2, most have Harden, LeBron, Giannis, Curry, and AD among their top players.

The one top player who ranks low is Kevin Durant. This is likely because his counting stats took a hit as a result of playing with the Warriors. This sheds light on the primary issue of the model: though it tries to estimate wins, it does so exclusively through counting stats. For the most part, this gives us a good idea of performance. But, this overvalues some players (like Westbrook) and undervalues others (like Durant). Still, it’s a simple way to measure player impact game-by-game.

Conclusion

NBA teams use analytics to gain an edge in finding players that will help them win. By its construction, true win shares gets to the core of this goal. This is because it’s constructed to predict whether a team will win or lose given a player stat line. Given that it uses counting stats, it has its flaws. But, these counting stats are all we have that’s publicly available on a game-by-game basis.

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