Edit: I’ve received some questions about the statistical significance of the differences between the home and away means. The data I was able to pull were already aggregated at the team per season, all teams per week, and per referee levels. I would need the per game data in order to calculate the 95% confidence intervals (because I need the standard deviations), but I don’t have access to these data. So in lieu of error bars, the best I can do is to run paired two-sample t-tests on the data at the aggregated levels using a hypothesized difference between the means of 0. I did run a Shapiro-Wilk test and the data are normally distributed. The t-tests show that, even at the aggregated levels (which have smaller sample sizes), the p-values are «0.05, and the t statistics exceed the critical values for each paired set. As such, we can reject the null hypothesis (that the means are equal), and conclude that the differences between the means are real. So I can’t be certain, but I’m guessing that at the per game level, where the sample sizes would be significantly larger, the confidence intervals would show the differences to be statistically significant.
No matter who you root for, you’re bound to witness calls against your team that you think are bogus. That’s just the nature of sports. Did anyone see that penalty against Ahmad Brooks where he apparently made an illegal tackle on Drew Brees last Sunday? That was a clean hit! If the game had been played in SF, would the call still have been made? And therein lies the question behind this post.
There have been many studies about official/referee/umpire bias in sports. Some claim it exists, others say it doesn’t. For this set of graphs, I simply took the raw data from the past three complete regular seasons of each sport (four for football because there are fewer games and I wanted a robust sample size), and calculated the averages for the home/away split. It turns out that, for every statistic over which an official has direct control, the home team outperforms the away team. Coincidence? Probably not. Of course, there could be other factors at play; it’s possible that most teams just play better at home. But the fact that it occurs in all categories across all sports makes me a tad suspicious.
So the next time you see a ridiculous call made against your team, just remember it might be because they are on the road. If they’re at home, well, you’ve got no one to blame but your lousy team.