Another dubious sports statistic

I believe it is against Canadian law for a televised hockey game to be completed without the announcer mentioning, somewhere amid his (sic) endless recitation of players' hometowns, that getting the first goal is all-important, since the team that gets the first goal wins such a high percentage of games.

This belief seems to have come from a study of all major league baseball games between 1966 and 1987 which found that 66% of the games were won by the team that scored first. That’s an interesting finding because in baseball the visiting team is more likely to score first (since it bats first). However, the home team was still more likely to win, so the importance of the first run was still questionable. In 1998 Tom Ruane published an article in which he showed that teams scoring the first run were less likely to win than teams who were the first to score each of the second through ninth runs. The first run, it seemed, was actually the least important run to score. How can that be?, you may be asking. How can a run associated with 66% of victories be unimportant?

The reason it’s unimportant is most likely that the winning team scores more runs than the losing team. Consequently, it’s more likely to score the first run. So even if scoring the first run has no effect on the chances of winning a game, the winning team is still more likely to score the first run.

To examine this possibility I chose data from another sport in which teams don’t alternate offensive and defensive sessions. I collected scores from 110 National Hockey League games played from November 30, 2006 to December 14, 2006. I included games settled by shootout, but gave no credit to the winning team for the goal awarded for the shootout. The team scoring the first goal won 70% of these games (77 of the 110). However, the winning team also scored 68% of the goals (439 of 649). So, if scoring the first goal did not improve a team’s chances of winning a game, you’d still expect the winning team to score the first goal in 68% of the games, or 75 games. The improvement here is all of two percentage points.

But is it an improvement? You can’t reasonably expect that teams scoring 68% of the goals will necessarily win exactly 68% of the games. Other factors have some effect on the outcome, so you’d expect them to win a number around 75. Fortunately, we can estimate the probability that:

• if scoring the first goal does not increase a team’s chances of winning and
  
• if winning teams score 68% of the goals then
• the team scoring the first goal will win 77 games.

That probability is 44%. Conventional standards of statistical signficance would reject the idea that the first goal is of any importance when the percentage is that high. However, arguing that the probability of the difference being real is still greater than 50% is entirely reasonable. But if we look at the difference that way, we still have to conclude that there is only a 56% chance that scoring the first goal increased the likelihood of winning a game, and that if it did increase the probability of winning a game, it increased it by only 2 percentage points (aka one chance in 50). Either way, that first goal doesn’t seem all that important.

I propose an alternative to the Law of the All-Important First Goal/Run. I modestly call it FitzGerald's Law: the first team to score the winning goal will win. My law has as much explanatory value as the Law of the Fatal First Goal/Run, but is logically more elegant. It also reminds me of another statistical topic which baffles me: why, in a baseball game which finishes with a score of 11-10, can the player who drove in the first run for the winning team get credit for the game-winning RBI? Hm?

Another dubious sports statistic © 1995, 2006 John FitzGerald
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