Still More on Pulling the Goalie
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Interfaces, 21(2), 1991, pp. 59-64.Once again the goalie is taken to task for staying in the game too long. This time dynamic programming is used to get around a questionable assumptio made in previous analyses. The rules of hockey specify that only six players can be on the ice at any one time. Normally a team will find it prudent to devote one of these players (the goalie) entirely to goal defense. The rules do not require this, however, so whichever team is behind may elect to "pull its goalie" in order to devote all six skaters to the task of scoring on the opponent. This can clearly be done too early, since the maneuver is more likely to result in a score by the opponent than by the pulling team but may nonetheless prove fruitful in the waning moments of a game that will otherwise be almost surely lost. Morrison and Wheat  attribute the US victory in the 1980 Winter Olympics to employment of the tactic in the game with Sweden. The question to be examined here is "What is the optimal time to pull the goalie?"