I’ve long had my eye out for intriguing papers that cover my two favorite areas of research, causal inference and sports statistics. For unfamiliar readers, causal inference tools allow for the estimation of causal effects (i.e., does smoking cause cancer) in non-experimental settings. Given that almost all sports data is inherently observational, there would seem to be opportunities for applied causal papers to answer questions in sports (here’s one).
It was with this vigor in mind that I read a paper, the Midweek Effect on Performance: evidence from the Bundesliga, recently posted and linked here. The authors, Alex Krumer & Michael Lechner – the latter of which has done substantial causal inference work – use propensity score matching to estimate the effect of midweek matches on home scoring.
The authors conclude that:
Playing midweek leads to an effect of about half a point in total, resulting from the home team losing about 0.2 points, while the away team gains about 0.3 points (the asymmetry results from the ‘3 points rule’)..it becomes clear that the home team loses all its home advantages in midweek games.
Interestingly, although matching is used as the primary method, selection effects (i.e., how much the weekend and weekday games differ) are weak. Primarily, conclusions are drawn as a result of the varying point totals described above.
As the authors discuss, several factors could be at play here, most notably referee bias and attendance. The authors also (gulp) suggest that testosterone levels could be linked to the poorer home team performance. In conclusion, Krumer & Lechner recommend that Bundesliga officials work to balance midweek game assignments.
All together, these findings would have a substantial place in sports literature with respect to the drivers of home advantage in sports. The results were so cool, in fact, that my first thought was: let’s replicate them.
Thanks to James Curley’s awesome engsoccerdata package, results from several professional soccer leagues are right at the R users fingertips. I started by trying to replicate the findings of Krumer and Lechner using the Bundesliga. Matching aside, our outcome of interest is a difference in difference: the average home point difference between weekend and weekday, minus the average away point difference between weekend and weekday.
In the paper linked above, the author’s found a gap of about 0.5 (in favor of weekend games) using the last 8 years of data.
As good news, so did I.
Using all years since 1960, I estimated the yearly average home weekend advantage. Sure enough, while there didn’t appear to be much of a difference prior to the year 2000, the last 15 years have seen a notable spike; teams are winning more points at home during weekend games. The blue line reflects the trend over time, which has roughly stabilized at at half a point over the last decade. The red dotted line reflects no difference.
Teams performed better on home weekday games in all but one of the last 10 years (2011). Meanwhile, in three of those years was the difference in point totals greater than 1. This difference is both statistically and practically significant (although it is important that only about 10% of a team’s games are weekday ones). Indeed, the author’s conclusions seem reasonable.
But replication on the data used by the authors is one thing; validation on another data set (e.g., another league) would go a long way towards confirming a weekday effect in professional soccer.
Fortunately, Curley’s R package contains more than the Bundesliga. I chose the English Premier League (EPL), Spain’s La Liga, and Italy’s Serie A to try and apply the paper’s approach elsewhere. If you want to try another league, feel free to expand upon it using my code posted here.
Long story short, I couldn’t replicate our initial findings in any of the three leagues. There wasn’t a single time-span in any of the EPL, La Liga, or Serie A where there was an additional benefit to teams playing home games on weekends.
Here are the three graphs, made similar to the one above. Note that there are varying x-axes: each league has had different numbers of seasons with weekday games. I went as far back as I could within each league (while also trying to assure continuity).
First, the home weekend advantage in Italy. By and large, there have been no differences.
Second, the home weekend advantage in England. Arguable, the weekday advantage was actually a disadvantage for a while.
Finally, the home weekend advantage in Spain. Again, if anything here, there has been a disadvantage.
To conclude, Krumer and Lechner find evidence of a difference in the home versus away point totals when comparing weekend and weekday games. Over the last decade, this magnitude of these differences has been fairly large – half a point, on average.
That said, while it was encouraging to replicate their findings, it is disconcerting the replications failed in three other top European leagues. There are obviously differences between the Bundesliga and each of the EPL, Serie A, and La Liga, including the types of weekdays on which each league plays its games (Serie A appears most similar to the Bundesliga in this respect, in not playing Monday games). However, there doesn’t appear to be anything else unique about the Bundesliga which would lend that league, and that league only, to a weekday effect.
That said, returning to the author’s original approach, this isn’t to say a midweek effect can be entirely discounted. If other leagues have assigned specific teams to midweek games based on past performances, it would mean our approach (a simple difference in difference one) was inappropriate. However, in absence of this other information, it seems more than plausible that the observed midweek effect in the Bundesliga could be accounted for due to chance.