(http://www.basketball-reference.com/about/ws.html)
I. Introduction
Stealing a page from baseball’s Bill James, I decided to attempt to calculate basketball Win Shares. This article will describe how I came up with the Win Shares system for basketball. If you believe that any attempt to attribute team success to individual players is an abomination, then read 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 three Win Shares. My system deviates from James’s system in three key ways:
- In James’s system, one win is equivalent to three Win Shares. In my system, one win is equivalent to one Win Share.
- 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.
- 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 this system, a player can have negative Win Shares. This can be justified by acknowledging a player with negative Win Shares was so poor that he essentially took away wins that his teammates had generated.
III. Crediting Offensive Win Shares to Players
Offensive Win Shares are credited to players based on Dean Oliver’s points produced and offensive possessions. The formulas are 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 LeBron James of the 2008-09 Cleveland Cavaliersas an example):
- Calculate points produced for each player. In 2008-09, James had an estimated 2345.9 points produced.
- Calculate offensive possessions for each player. James had an estimated 1928.1 offensive possessions in 2008-09.
- Calculate marginal offense for each player. Marginal offense is equal to (points produced) – 0.92 * (league points per possession) * (offensive possessions). For James this is 2345.9 – 0.92 * 1.083 * 1928.1 = 424.8. Note that this formula may produce a negative result for some players.
- Calculate marginal points per win. Marginal points per win reduces to 0.32 * (league points per game) * ((team pace) / (league pace)). For the 2008-09 Cavaliers this is 0.32 * 100.0 * (88.7 / 91.7) = 30.95.
- Credit Offensive Win Shares to the players. Offensive Win Shares are credited using the following formula: (marginal offense) / (marginal points per win). James gets credit for 424.8 / 30.95 = 13.73 Offensive Win Shares.
IV. 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 (please see Oliver’s book for further details). Here is a description of the process (once again using LeBron James in 2008-09 as an example):
- Calculate the Defensive Rating for each player. James’s Defensive Rating in 2008-09 was 99.1.
- 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) – ((Defensive Rating) / 100)). For James this is (3054 / 19780) * 7341 * ((1.08 * 1.083) – (99.1 / 100)) = 202.5. Note that this formula may produce a negative result for some players.
- Calculate marginal points per win. Marginal points per win reduces to 0.32 * (league points per game) * ((team pace) / (league pace)). For the 2008-09 Cavaliers this is 0.32 * 100.0 * (88.7 / 91.7) = 30.95.
- Credit Defensive Win Shares to the players. Defensive Win Shares are credited using the following formula: (marginal defense) / (marginal points per win). James gets credit for 202.5 / 30.95 = 6.54 Defensive Win Shares.
V. Putting It All Together
The final step of the process is to add Offensive Win Shares to Defensive Win Shares. In our examples, LeBron James total in 2008-09 is 13.73 + 6.54 = 20.27 Win Shares and Oscar Robertson 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 in terms of wins, it makes sense to see if the sum of player Win Shares for a particular team closely matches the team win total. For the 2008-09 Cavaliers the sum of player Win Shares is 67.9, while the team win total is 66, an error of 66 – 67.9 = -1.9 wins. For the 1964-65 Royals the sum of 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 have complete player splits), the average absolute error is 2.74 wins and the root mean squared error is 3.41 wins.
