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):
1. Calculate the Defensive Rating for each player. James's Defensive Rating in 2008-09 was 99.1.
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) - ((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.
3. 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.
4. 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.