What is a Point Share?
Bill James developed his system such that one win is equivalent to three Win Shares. My system deviates from James' in three key ways:
In James' system, one win is equivalent to three Win Shares. In my system for hockey, one point is equivalent to one Point 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 for hockey, a team with 100 points will have about 100 Point 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 my system, a player can have negative Point Shares. I justify this by thinking about it in the following way: a player with negative Point Shares was so poor that he essentially took away points that his teammates had generated.
III. Marginal Goals For and Marginal Goals Against
The Point Shares system is based on the fact that marginal goals for and marginal goals against are linked to team points. At the team level, marginal goals for and marginal goals against are equal to:
MGF = (team goals) - (7 / 12) × (team games) × (league goals per game)
MGA = (1 + (7 / 12)) × (team games) × (league goals per game) - (team goals against)
* Why 7/12? At even strengh a team has six players on the ice, five skaters and one goalie. Imagine each of these players having two chips to contribute to one of two buckets: offense and defense. Collectively the skaters will contribute five chips to the offensive bucket and five chips to the defensive bucket. However, the goalie will contribute both of his chips to the defensive bucket, giving the defensive bucket seven of the twelve chips.
Marginal goals for and marginal goals against can be converted into expected points using the following formula:
Expected Points = (league points per goal) × (MGF + MGA)
For example, here is the calculation for the 2009-10 Pittsburgh Penguins:
MGF = 257 - (7 / 12) × 82 × 2.765 = 124.74
MGA = (1 + (7 / 12)) × 82 × 2.765 - 237 = 121.99
Expected Points = 0.4059 × (124.74 + 121.99) = 100.15
Actual Points = 101
Doing the same calculation for all team seasons from 1917-18 to 2009-10 produces an average absolute error of 4.43 points per 82 games and a root mean squared error iof 5.95 points per 82 games.
Crediting Goalie Point Shares to Goalies
Goalies will receive 2/7 of the team's defensive point shares, on average, although that fraction is adjusted upward or downward in seasons where shots against are available.
* Why 2/7? Go back to the chips analogy above: of the seven chips contributed to the defensive bucket, two came from the goalie.
Shots against were not officially recorded until the 1983-84 season, so there is one method for 1983-84 to the present and another method for 1917-18 to 1982-83.
