EXAMPLE 5.20 English Premier League Goals
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Consider data on the total number of goals scored per soccer game in the English Premier League (EPL) for the 2013–2014 regular season.12 Over the 380 games played in the season, the average number of goals per game is 2.768.
The Poisson distribution has a unique characteristic in that the standard deviation of the Poisson random variable is equal to the square root of the mean. In turn, this implies that the mean of a Poisson random variable equals its variance; that is, . This fact provides us with a very convenient quick check for Poisson compatibility—namely, compare the mean observed count with the observed variance. For the goal data, we find the sample variance of the counts to be 3.002, which is quite close to the mean of 2.768. This suggests that the Poisson distribution might serve a reasonable model for counts on EPL goals per game.
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Figure 5.10 shows a JMP-produced graph of a Poisson distribution with overlaid on the count data. The Poisson distribution and observed counts show quite a good match. It would be reasonable to assume that the variability in goals scored in EPL games is well acounted by the Poisson distribution.
