One of the biggest questions in football is whether the amount of rest a team has matters. With four competitions available to English teams, it's actually pretty rare to get a full week off in between games: only 37% of matches are played with at least seven days' rest. Obviously, players get tired when told to take the field day after day, but it's not clear how much impact this has on a team at large, as there are roster management techniques managers can employ in order to minimise fatigue across the board.
If a large 'rest' effect exists, can we find it? If we assume that the goal of a league match is to maximise points, determine the amount of points expected versus those actually earned, and then look at the days between matches, might that give us an answer?
Yes, albeit not a definitive one.
I took the fixture list each team in the top half of the league for the 2009/10 season (290 Premier League games in total) and determined the rest days between each match. Then I looked at the result, tallied up points, and compared them to expected points.
To get expected points, I compared each team's record on attack and defence to come up with a goals per game distribution, then gave the home team +0.25 goals scored and -0.25 goals conceded per the typical home field advantage adjustment. We may then use Poisson distributions to figure out the win/draw/loss probabilities for each match, and multiplying win probability by three and adding it to the likelihood of a draw gives you total point expectancy. It's then just a matter of subtracting that from points earned to see whether a team over-performed (a positive number) or under-performed (negative).
Once we have expected points we can compare them with a team's rest days*:
Figure 1: Days off vs. Points - expected Points, for the top 10 Premier League teams in the 2009/10 season.
That bar chart is vulnerable to the whims of our sample size, though. There were very few games played with four days rest last year, and even fewer with two. How can we find the actual relationship between days off and performance? Statistics offers us a great tool here in the correlation coefficient. Essentially, this tells you how much you can infer about one variable based on another. Running a correlation analysis on my dataset, which is substantial, but not huge, gives us a correlation of virtually zero (R-squared is something like 0.0006, for those curious).
In other words, given the fixtures played by the top teams in the Premier League last year, I can't find any positive or negative effects on performance related to the amount of days between games. It's not definitive by any means, but if there was a large impact I would have expected to find it here.
It may be worthwhile looking at how specific competitions affect team performance - I mentioned in my post yesterday that the league leaders take a huge hit during the more difficult rounds of the Champions League, and it might be that a broad-picture analysis just isn't picking it up. However, given the data here I'd be very surprised if that dredged up a large effect either.
*Using games played in last 30 days yields similar results.