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Calculating Win Shares

Note: This article was edited on August 4, 2008. I made some major modifications to the Win Shares system to address two primary concerns with the old system: (1) that the results were expressed in "shares" rather than "wins" (i.e., that there was a 3:1 ratio of Win Shares to wins rather than a 1:1 ratio) and (2) that players who played on poor teams were being unfairly penalized. Please read the explanation below for complete details.

Introduction

Stealing a page from baseball's Bill James, I decided to attempt to calculate basketball Win Shares. Due to data limitations the current system only works for the 1973-74 season forward, but at some point I hope to modify the system for seasons prior to 1973-74. This article will describe how I came up with the Win Shares system for basketball.

What is a Win Share?

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

  1. In my system, one win is equivalent to one Win Share.
  2. James made team Win Shares directly proportional to team wins. In his system, a baseball team that wins 80 games will have exactly 240 Win Shares, a baseball team that wins 90 games will have exactly 270 Win Shares, etc. In my system, a basketball team that wins 50 games will have about 50 Win Shares, give or take.
  3. James did not allow for the possibility of negative Win Shares. In his system, the fewest number of Win Shares a player can have is zero. In my system, a player can have negative Win Shares. I justify this by thinking about it in the following way: a player with negative Win Shares was so poor that he essentially took away wins that his teammates had generated.

Crediting Offensive Win Shares to Players

Offensive Win Shares are credited to players based on Dean Oliver's Offensive Rating. Offensive Rating is an estimate of the player's points produced per 100 offensive possessions. The formula is quite detailed, so I would point you to Oliver's book Basketball on Paper for complete details. The process for crediting offensive Win Shares is outlined below (using Tim Duncan of the 2003-04 Spurs as an example):

  1. Calculate the Offensive Rating for each player. In 2003-04, Tim Duncan's Offensive Rating was 107.385.
  2. Calculate offensive possessions for each player. Once again, I would point you to Oliver's book for complete details on calculating player offensive possessions. Tim Duncan had an estimated 1373.19 offensive possessions in 2003-04.
  3. Calculate marginal offense for each player. Marginal offense is equal to (player possessions) * ((player Offensive Rating) / 100) - 0.92 * (league points per possession)). For Tim Duncan this is 1373.19 * ((107.385 / 100) - 0.92 * (1.02929)) = 174.26. Note that this formula may produce a negative result for some players.
  4. Calculate league marginal points per win. League marginal points per win reduces to 0.32 * (league points per game) . For the 2003-04 NBA season this is 0.32 * 93.3966 = 29.8869.
  5. Credit offensive Win Shares to the players. Offensive Win Shares are credited using the following formula: (player marginal offense) / (league marginal points per win). Tim Duncan gets credit for 174.26 / 29.8869 = 5.83 offensive Win Shares.

Crediting Defensive Win Shares to Players

Crediting defensive Win Shares to players is based on Dean Oliver's Defensive Rating. Defensive Rating is an estimate of the player's points allowed per 100 defensive possessions. I know I'm sounding like a broken record, but please see Oliver's book for further details. Here is the process, once again using Tim Duncan as an example:

  1. Calculate the Defensive Rating for each player. Tim Duncan's Defensive Rating in 2003-04 was 88.501.
  2. Calculate marginal defense for each player. Marginal defense is equal to (player minutes played / team minutes played) * (team defensive possessions) * (1.08 * (league points per possession) - ((player Defensive Rating) / 100)). For Tim Duncan this is (2527 / 19755) * 7353.42 * ((1.08 * 1.02929) - (88.5001 / 100)) = 213.18. Note that this formula may produce a negative result for some players.
  3. Calculate league marginal points per win. League marginal points per win reduces to 0.32 * (league points per game) . For the 2003-04 NBA season this is 0.32 * 93.3966 = 29.8869.
  4. Credit defensive Win Shares to the players. Defensive Win Shares are credited using the following formula: (player marginal defense) / (league marginal points per win). Tim Duncan gets credit for 213.18 / 29.8869 = 7.13 defensive Win Shares.

Putting It All Together

The final step of the process is to add offensive Win Shares to defensive Win Shares. In our example, Tim Duncan's total is 5.83 + 7.13 = 12.96 Win Shares.

Does This Work?

Because this metric is designed to estimate a player's win contribution, it makes sense to see if the sum of player Win Shares for a particular team closely matches the team win total. For the 2003-04 Spurs the sum of player Win Shares is 61.76, while the team win total is 57, an error of 57 - 61.76 = -4.76 wins. This error is actually larger than the "typical" error; looking at all NBA teams since the 1973-74 season, the root mean squared error (rmse) is 3.466 wins.

Feedback

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