A few months ago, I examined what factors determined D.C. United’s home attendance over the last six seasons. What I found made a lot of sense: more fans come when the team is doing well or there’s a big-name opponent in town, and less fan comes for weekday games, holiday weekend games, and rain games. For my next project, I decided to flip the question on its head and see if attendance numbers influence the result on the field. We know that United typically have a pretty strong home-field advantage, and our players often list the support of the fans and supporters groups at RFK as helping to motivate them to perform well. With this study, I wanted to find out whether the magnitude of this advantage depends at all on the number of fans at RFK; will United play better with, say, 20,000 fans in the stands as opposed to 10,000?
I was able to use a lot of the same data as I collected earlier for this analysis. As before, I use an ordinary least squares regression to analyze the data. For my dependent variable, I used goal difference in each game to measure on-field performance. To control for the quality of each team, I added a variable for the difference of the season-ending point totals for each team (for example, a 2013 game against Houston, who racked up 51 points last season, would have a value of 16 – 51 = -35). This variable isn’t perfect, as it doesn’t take into account hot or cold streaks, injuries, or other factors that may affect an individual game, but it seems to do a good job of quantifying how much better or worse the opponent was relative to United in a given season. I also included data on weather, day of the week, United’s form (points earned in last five games), and the number of days since United’s last game.
The results were, well, pretty boring. The only variable I could find that had a statistically significant effect on goal differential was the difference in points on the season—not even United’s form could be used to predict performance in a given match. Every other variable was insignificant, including attendance. According to my data, for every point United finished higher than its opponent in a given year, goal differential increases by about 0.04 goals. One possible worry I had entering into the analysis was simultaneity, or that I would get a bogus effect because more fans come to games when the team is playing well, rather than the team playing well because more fans come to games. Not even this showed up in my analysis, though.
Before I ran the numbers, I was really hoping to find a positive and significant effect of attendance on performance. As fans, we have little if any control over the product on the field, but I know that at least I like to think that by going to a game and cheering on my team, I am motivating them to a better result in some small but not-non-existent way. Unfortunately, my simple analysis of D.C. United games provides no statistical evidence for this effect, so whether 9,000 or 30,000 people show up to a game, the result on the field is likely to be the same in any individual game. Of course, this doesn't mean that the supporters groups should pack up and go home, just that bringing in more fans doesn't necessarily translate into better results on the field.