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The Marginal Benefit of Goals Scored and the Marginal Cost of Goals Allowed

By Kevin Mongeon and J. Michael (Mike) Boyle - Sep. 2011


It is well known among professional hockey executives that each goal scored and goal allowed during a game contributes different amounts to determining the eventual winner of the game.  However, economic rationale that supports the idea that different goals contribute varying amounts to winning has not been documented.  Nor, to the best of the authors’ knowledge has a formula been developed that industry professionals can use to calculate the value, in terms of winning, of a goal scored or goal allowed.  Therefore, this paper has the following two objectives.  The first is to demonstrate the economic rationale that explains the reasoning behind the idea that different goals contribute varying amounts to winning.  The second is to provide hockey professionals with a formula they can use to calculate the value, in terms of winning, of a goal scored or goal allowed.


To achieve these objectives we pursue the following three stages of analysis:


First, using data from the 2008-09 (2008), 2009-10 (2009), and the 2010-11 (2010) National Hockey League (NHL) season we calculate the probability of a home team and visiting team win for each possible score of the game, where the score of the game is determined by the difference (or margin) in goals of the two competing teams.  Using these results we calculate the average marginal benefit probabilities, in terms of winning, of a goal scored and the average marginal cost probabilities, in terms of winning, of a goal allowed.


Second, to demonstrate the importance of incorporating time remaining in the game into the determination of the value of a goal calculation, we calculate the probability of a home team and visiting team win for each possible period specific score of the game.  Using these results, we calculate the marginal benefit probabilities, in terms of winning and the marginal cost probabilities, in terms of winning of time remaining in the game for each possible score state.


Finally, we use regression analysis to develop a formula that calculates the probability of a home team and visiting team win for each possible score of the game and time remaining in the game.  Then using these results, we develop a formula that calculates the marginal benefit probability of a goal scored and the marginal cost probability of a goal allowed for each possible score of the game and time remaining in the game.


If the game is won during regulation play, the winning team is awarded two points and the losing team is not awarded any points.  If the game is won in overtime or after a shootout, the winning team is still awarded two points, but the losing is team awarded one point.  However, if we assume for the sake of simplicity that teams play to win games rather than for an overtime loss, we can more straight forwardly calculate the value of a goal, in terms of probabilities of winning.  Assuming the objective of the two teams competing in the game is to win the contest, the winner of the game is determined by the difference in goals at the end of regulation time or overtime (including the shootout).  Therefore, scoring a goal on an opponent or having a goal scored upon one’s own team affects the probability of winning because it alters the margin in goals (difference in goals; henceforth called score) of the two teams competing.  Furthermore, because the winner of the game is determined by the difference in goals at the end regulation time or overtime, the probability of either team winning the game at any point during the game is a function of both the difference in goals at that point in time during the game and the time remaining in regulation play.


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