## Hockey and Math

Sports commentators on soccer and hockey games will often make their winning predictions as soon as the first goal is scored. Now, Canadian mathematicians have worked out a formula for spotting the winning team that could make the pundits redundant. In a paper of two halves, they reveal all in the International Journal of Operational Research.

Jack Brimberg and Bill Hurley of The Royal Military College of Canada, Kingston, Ontario, wanted to find out whether that first goal is really important or not. They have done this by calculating the probability of the first-goal team winning at discrete points in the match after the first goal is scored based on the number of minutes remaining in the game. They also take overtime into account to adjust the weighting on their formula appropriately.

Their formula breaks down as follows: From the first whistle, team X has a 50:50 chance of winning. However, if the team scores at just 5 minutes of play, with 55 minutes left to play in the first period of a hockey match, then the team’s chances rise to 7 to 3 (70%). However, if they score the first goal much later in the game, with say, 25 minutes remaining in the second period, then their chances of winning the match rises to 4 to 1 (80%).

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Of course, probability and statistics are notoriously difficult to pin down in real life, so it is best to take any such mathematical punditry with a pinch of salt when watching the fortunes or misfortunes of your team. That applies whether you’re playing in Redwood City, catching the Toronto Maple Leafs, or your flight of fancy is UK football’s black and white army, The Magpies.

Jack Brimberg, & W.J. Hurley (2009). A note on the importance of the first goal in a National Hockey League game Int. J. Operational Research, 6 (2), 282-287