NBA Win Shares | Basketball-Reference.com (2024)

I. Introduction

Win Shares is a player statistic which attempts to divvy up credit for team success to the individuals on the team. Full details are available below, but the important things to note are that it is calculated using player, team and league-wide statistics and the sum of player win shares on a given team will be roughly equal to that team’s win total for the season. Kareem Abdul-Jabbar’s total of 25.4 Win Shares in 1971-72 is the all-time single-season record and his 273.4 career Win Shares are the all-time career record. Abdul-Jabbar played long enough to compile many such career records. The all-time leader in Win Shares per 48 minutes is Michael Jordan (which falls in line with the prevailing wisdom on Jordan’s G.O.A.T. status).

This article will describe how I came up with the Win Shares system for basketball (stealing a page from baseball’s Bill James). If you believe that any attemptto attribute team success to individual players is an abomination, thenread no further, as this article will be of no interest to you.

II. What is a Win Share?

Bill James developed his system such that one win is equivalent to threeWin Shares. My system deviates from James's system in three key ways:

1. In James's system, one win is equivalent to threeWin Shares. In my system, one win is equivalent to one Win Share.
2. James made team Win Shares directly proportional toteam wins. In his system, a baseball team that wins 80 games will haveexactly 240 Win Shares, a baseball teamthat wins 90 games will have exactly 270Win Shares, etc. In my system, a basketball team that wins 50 games willhave about 50 Win Shares, give ortake.
3. James did not allow for the possibility of negative Win Shares. In hissystem, the fewest number of Win Shares a player can have is zero. In mysystem, a player can have negative Win Shares. I justify this by thinkingabout it in the following way: a player with negative Win Shares was sopoor that he essentially took away wins that his teammates hadgenerated.

III. Crediting Offensive Win Shares to Players

A. 1977-78 to present NBA

Offensive Win Shares are credited to players based on Dean Oliver's pointsproduced and offensive possessions. The formulas are quite detailed, so Iwould point you to Oliver's book Basketball on Paper forcomplete details. The process for crediting Offensive Win Shares isoutlined below (using LeBronJames of the 2008-09 ClevelandCavaliers as an example):

1. Calculate points producedfor each player. In 2008-09, James had an estimated 2345.9 pointsproduced.
2. Calculate offensivepossessions for each player. James had an estimated 1928.1offensive possessions in 2008-09.
3. Calculate marginal offensefor each player. Marginal offense is equal to (points produced) -0.92 * (league points per possession) * (offensive possessions). For Jamesthis is 2345.9 - 0.92 * 1.083 * 1928.1 = 424.8. Note that this formula mayproduce a negative result for some players.
4. Calculate marginal pointsper win. Marginal points per win reduces to 0.32 * (league pointsper game) * ((team pace) / (league pace)). For the 2008-09 Cavaliers thisis 0.32 * 100.0 * (88.7 / 91.7) = 30.95.
5. Credit Offensive Win Shares to the players.Offensive Win Shares are credited using the following formula: (marginaloffense) / (marginal points per win). James gets credit for 424.8 / 30.95= 13.73 Offensive Win Shares.

B. 1973-74 to 1976-77 NBA

The NBA did not track player turnovers until the 1977-78 season, and playerturnovers are needed to calculate player possessions. However, the NBA didtrack turnovers at the team level from 1973-74 to 1976-77. Since playerturnovers are the only thing holding us back from using the methodoutlined above, I have chosen to estimate player turnovers for this timeperiod. Player turnovers are estimated as follows (using KareemAbdul-Jabbar of the 1976-77 LosAngeles Lakers as an example):

1. Obtain an initial estimateof the player's turnovers. To do this use the following formula:

    -0.0005075172 * (minutes played) * (player age)- 0.0873982755 * (field goals)+ 0.0925506598 * (field goal attempts)+ 0.1566322510 * (free throw attempts)+ 0.0449241773 * (total rebounds)+ 0.2321637159 * (assists)+ 0.2040169400 * (personal fouls)

   Note that if this number is less than zero, then it should be rounded up tozero. Plugging Abdul-Jabbar's statistics into the formula above we get anestimate of 280.316 turnovers.
2. Find the sum of estimatedturnovers for the players on the given team. The sum for theplayers on the 1976-77 Lakers is 1448.057.
3. Calculate the player'sshare of this total. Abdul-Jabbar's share of the team total is280.316 / 1448.057 = 0.194.
4. Multiply the team's turnovers (adjusted for teamturnovers) by the player's share. As mentioned, the NBA trackedturnovers at the team level in these seasons. However, the team totalsinclude team turnovers (i.e., turnovers that are not attributed to anindividual player). Thus, we multiply the team's turnovers by 0.985, thenmultiply this adjusted figure by the player's share. For Abdul-Jabbar thisis 1538 * 0.985 * 0.194 = 293.9, which we round up to 294.

Now that we have this estimate, the method above is used to complete thecalculation of Offensive Win Shares.

C. 1946-47 to 1948-49 BAA and 1949-50 to 1972-73 NBA

Because so many statistics are missing prior to the 1973-74 season(offensive rebounds, turnovers, etc.), we will not use Oliver's pointsproduced and offensive possessions for this time period, although thebasic framework will remain the same. Here is the process for creditingOffensive Win Shares prior to the 1973-74 season (using OscarRobertson of the 1964-65 CincinnatiRoyals as an example):

1. Calculate the player'smodified points. The formula is:

    2.0 * (field goals) * (1 - ((team assists) / (team field goals)))+ 1.5 * (field goals) * ((team assists) / (team field goals))+ 1.0 * (free throws)+ 0.5 * (assists)

   Plugging Robertson's statistics into the formula above we get 2495.93 modifiedpoints.
2. Calculate the player'smodified shot attempts. The formula is:

    1.00 * (field goals) * (1 - ((team assists) / (team field goals)))+ 0.50 * (field goals) * ((team assists) / (team field goals))+ 1.00 * ((field goal attempts) - (field goals))+ 0.44 * (free throw attempts)+ 0.50 * (assists)

   Plugging Robertson's statistics into the formula above we get 2246.85 modifiedshot attempts.
3. Calculate league points pershot attempt. League points per shot attempt is equal to (leaguepoints) / (league field goal attempts + 0.44 * (league free throwattempts)). For the 1964-65 NBA this is 79641 / (71882 + 0.44 * 25604) =0.9578.
4. Calculate marginal offensefor each player. Marginal offense is equal to (modified points) -0.92 * (league points per shot attempt) * (modified shot attempts). ForRobertson this is 2495.93 - 0.92 * 0.9578 * 2246.85 = 515.06. Note thatthis formula may produce a negative result for some players.
5. Calculate marginal pointsper win. Marginal points per win reduces to 0.16 * (team points pergame + opponent points per game). For the 1964-65 Royals this is 0.16 *(114.2 + 111.9) = 36.176.
6. Credit Offensive Win Shares to the players.Offensive Win Shares are credited using the following formula: (marginaloffense) / (marginal points per win). Robertson gets credit for 516.06 /36.176 = 14.27 Offensive Win Shares.

IV. Crediting Defensive Win Shares to Players

A. 1973-74 to present NBA

Crediting Defensive Win Shares to players is based on Dean Oliver'sDefensive Rating. Defensive Rating is an estimate of the player's pointsallowed per 100 defensive possessions (please see Oliver's book forfurther details). Here is a description of the process (once again usingLeBronJames in 2008-09 as an example):

1. Calculate the DefensiveRating for each player. James's Defensive Rating in 2008-09 was99.1.
2. Calculate marginal defensefor each player. Marginal defense is equal to (player minutesplayed / team minutes played) * (team defensive possessions) * (1.08 *(league points per possession) - ((Defensive Rating) / 100)). For Jamesthis is (3054 / 19780) * 7341 * ((1.08 * 1.083) - (99.1 / 100)) = 202.5.Note that this formula may produce a negative result for someplayers.
3. Calculate marginal pointsper win. Marginal points per win reduces to 0.32 * (league pointsper game) * ((team pace) / (league pace)). For the 2008-09 Cavaliers thisis 0.32 * 100.0 * (88.7 / 91.7) = 30.95.
4. Credit Defensive Win Shares to the players.Defensive Win Shares are credited using the following formula: (marginaldefense) / (marginal points per win). James gets credit for 202.5 / 30.95= 6.54 Defensive Win Shares.

B. 1951-52 to 1972-73 NBA

Prior to the 1973-74 season, the NBA did not track defensive rebounds,steals, or blocks, so allocating defensive credit is a difficult task.Nevertheless, here is the process for crediting Defensive Win Shares inthose seasons (once again using Robertson in 1964-65 as an example):

1. Calculate team marginaldefense. Team marginal defense is equal to 1.08 * (league pointsper shot attempt) * (team field goal attempts + 0.44 * (team free throwattempts)) - (opponent points). If you're wondering why we're using teamshot attempts as opposed to opponent shot attempts, the answer is (a) wedon't have opponent shot attempts prior to 1970-71 and (b) the systemworks better using team shot attempts. For the 1964-65 Royals we get 1.08* 0.9578 * (7797 + 0.44 * 2866) - 8952 = 417.854.
2. Calculate the player'sshare of the team's marginal defense. The player's share of theteam's marginal defense is equal to 0.25 * ((minutes played) / (teamminutes played)) + 0.5 * ((total rebounds) / (team total rebounds)) + 0.25* ((assists) / (team assists)). How did I get those weights? ModernDefensive Win Shares are most dependent on minutes played, defensiverebounds, steals, and blocks. I regressed DWS on those stats and thenfound the relative importance of each regressor (approximately 25% forminutes played, 35% for defensive rebounds, 25% for steals, and 15% forblocks). Since those defensive statistics are not available for pastseasons, I used total rebounds as a proxy for defensive rebounds andblocks; and assists as a proxy for steals. A couple more notes: (1) priorto the 1964-65 season, team minutes played were not an official statistic,so for those seasons estimate the team's minutes played using the formula5 * 48 * (team games) + 125; and (2) prior to the 1967-68 season, teamtotal rebounds included team rebounds, so to account for this multiply theteam total by 0.875. Getting back to our example, Robertson's share on the1964-65 Royals is equal to 0.25 * (3421 / 19325) + 0.5 * (674 / (0.875 *5387)) + 0.25 * (861 / 1843) = 0.2325.
3. Calculate marginal defensefor each player. Marginal defense is equal to (team marginaldefense) * (player share). For Robertson this is 417.854 * 0.2325 =97.151. Note that this formula may produce a negative result for someplayers.
4. Calculate marginal pointsper win. Marginal points per win reduces to 0.16 * (team points pergame + opponent points per game). For the 1964-65 Royals this is 0.16 *(114.2 + 111.9) = 36.176.
5. Credit defensive Win Shares to the players.Defensive Win Shares are credited using the following formula: (marginaldefense) / (marginal points per win). Robertson gets credit for 97.151 /36.176 = 2.69 Defensive Win Shares.

B. 1950-51 NBA

Prior to the 1951-52 season, the NBA did not track minutes played, soallocating defensive credit is an even more difficult task. Nevertheless,here is the process for crediting Defensive Win Shares in the 1950-51season (using GeorgeMikan as an example):

1. Calculate team marginaldefense. Team marginal defense is equal to 1.08 * (league pointsper shot attempt) * (team field goal attempts + 0.44 * (team free throwattempts)) - (opponent points). If you're wondering why we're using teamshot attempts as opposed to opponent shot attempts, the answer is (a) wedon't have opponent shot attempts prior to 1970-71 and (b) the systemworks better using team shot attempts. For the 1950-51 Minneapolis Lakerswe get 1.08 * 0.8553 * (5590 + 0.44 * 1989) - 5264 = 708.023.
2. Calculate the player'sshare of the team's marginal defense. The player's share of theteam's marginal defense is equal to 0.25 * ((field goal attempts) / (teamfield goal attempts)) + 0.5 * ((total rebounds) / (team total rebounds)) +0.25 * ((assists) / (team assists)). How did I get those weights? ModernDefensive Win Shares are most dependent on minutes played, defensiverebounds, steals, and blocks. I regressed DWS on those stats and thenfound the relative importance of each regressor (approximately 25% forminutes played, 35% for defensive rebounds, 25% for steals, and 15% forblocks). Since those defensive statistics are not available for pastseasons, I used field goal attempts as a proxy for minutes played; totalrebounds as a proxy for defensive rebounds and blocks; and assists as aproxy for steals. Note that prior to the 1967-68 season, team totalrebounds included team rebounds, so to account for this multiply the teamtotal by 0.875. Getting back to our example, Mikan's share on the 1950-51Lakers is equal to 0.25 * (1584 / 5590) + 0.5 * (958 / (0.875 * 3049)) +0.25 * (208 / 1408) = 0.2873.
3. Calculate marginal defensefor each player. Marginal defense is equal to (team marginaldefense) * (player share). For Mikan this is 708.023 * 0.2873 = 203.415.Note that this formula may produce a negative result for someplayers.
4. Calculate marginal pointsper win. Marginal points per win reduces to 0.16 * (team points pergame + opponent points per game). For the 1950-51 Lakers this is 0.16 *(82.8 + 77.4) = 25.632.
5. Credit defensive Win Shares to the players.Defensive Win Shares are credited using the following formula: (marginaldefense) / (marginal points per win). Mikan gets credit for 203.415 /25.632 = 7.94 Defensive Win Shares.

B. 1946-47 to 1948-49 BAA and 1949-50 NBA

Prior to the 1950-51 season, the NBA did not track total rebounds, soallocating defensive credit is an almost impossible task. Nevertheless,here is the process for crediting Defensive Win Shares in those seasons(using BobFeerick in 1946-47 as an example):

1. Calculate team marginaldefense. Team marginal defense is equal to 1.08 * (league pointsper shot attempt) * (team field goal attempts + 0.44 * (team free throwattempts)) - (opponent points). If you're wondering why we're using teamshot attempts as opposed to opponent shot attempts, the answer is (a) wedon't have opponent shot attempts prior to 1970-71 and (b) the systemworks better using team shot attempts. For the 1946-47 Washington Capitolswe get 1.08 * 0.6528 * (5794 + 0.44 * 1391) - 3836 = 680.412.
2. Calculate the player'sshare of the team's marginal defense. The player's share of theteam's marginal defense is equal to 0.25 * ((field goal attempts) / (teamfield goal attempts)) + 0.5 * ((personal fouls) / (team personal fouls)) + 0.25 * ((assists) / (team assists)). How did I get thoseweights? Modern Defensive Win Shares are most dependent on minutesplayed, defensive rebounds, steals, and blocks. I regressed DWS on thosestats and then found the relative importance of each regressor(approximately 25% for minutes played, 35% for defensive rebounds, 25% forsteals, and 15% for blocks). Since those defensive statistics are notavailable for past seasons, I used field goal attempts as a proxy forminutes played; personal fouls as a proxy for defensive rebounds andblocks; and assists as a proxy for steals. Getting back to our example,Feerick's share on the 1946-47 Capitols is equal to 0.25 * (908 / 5794) +0.5 * (142 / 1144) + 0.25 * (69 / 378) = 0.1469.
3. Calculate marginal defensefor each player. Marginal defense is equal to (team marginaldefense) * (player share). For Feerick this is 680.412 * 0.1469 = 99.953.Note that this formula may produce a negative result for someplayers.
4. Calculate marginal pointsper win. Marginal points per win reduces to 0.16 * (team points pergame + opponent points per game). For the 1946-47 Capitols this is 0.16 *(73.8 + 63.9) = 22.032.
5. Credit defensive Win Shares to the players.Defensive Win Shares are credited using the following formula: (marginaldefense) / (marginal points per win). Feerick gets credit for 99.953 /22.032 = 4.54 Defensive Win Shares.

V. Putting It All Together

The final step of the process is to add Offensive Win Shares to DefensiveWin Shares. In our examples, LeBronJames total in 2008-09 is 13.73 + 6.54 = 20.27 Win Shares and OscarRobertson total in 1964-65 is 14.27 + 2.69 = 16.96 Win Shares.

VI. Does This Work?

Because this metric is designed to estimate a player's contribution interms of wins, it makes sense to see if the sum of player Win Shares for aparticular team closely matches the team win total. For the 2008-09Cavaliers the sum of player Win Shares is 67.9, while the team win totalis 66, an error of 66 - 67.9 = -1.9 wins. For the 1964-65 Royals the sumof player Win Shares is 43.5, while the team total is 48, an error of 48 -43.5 = 4.5 wins. These errors are actually close to the "typical" error;looking at all NBA teams since the 1962-63 season (the last season we havecomplete player splits), the average absolute error is 2.74 wins and theroot mean squared error is 3.41 wins.

VII. Feedback

If you have any comments or questions about the Win Shares methodology,please send me some feedback.

VIII. Revision History

Version 4.0

• Extended Win Shares back to the 1946-47 BAA season.

Version 3.1

• Changed the calculation of marginal points per win. Prior to this updatethe league average marginal points per win was used for all players, butnow the pace-adjusted league average is used instead.

Version 3.0

• Extended Win Shares back to the 1951-52 NBA season.

Version 2.0

• Changed the ratio of Win Shares to team wins from 3:1 to 1:1.
• Removed the adjustment that forced team Win Shares to add up to teamwins.
• Modified the formulas to allow for the possibility of negative WinShares.

Version 1.0

• Initial release.