I have not crunched the numbers on this but am pretty sure that holding [football] player quality [...] constant, players on lower-quality teams commit more fouls due to a) weaker teams having possession of the ball less often combined with b) players being much more likely to commit a foul when their team is not in possession.Another reason to suspect this is that players may sometimes commit fouls because they're frustrated about losing.
I now have crunched some numbers on this. Via EPL Talk I found the English Premier League's fair play table for the season just finished (which, for some reason, does not include data for the last two days). It contains a substatistic for red and yellow cards received (higher values mean less cards received; yes, I've counter-checked that). Although the score could theoretically vary between 0 and 360, the actual minimum and maximum are 271 and 313, respectively. Not holding player quality constant, I related it to the amount of points the clubs gained last season.
It turns out that the correlation between the "card score" and points is .365 - not spectacular, but noteworthy. If you run a linear OLS regression, you get the following equation:
FAIR PLAY SCORE = 283.281 + .211*POINTS
R-squared is .134; in other words, there is a lot left to explain. Both calculations are not statistically significant at conventional levels (p = .113). This isn't too surprising given a sample size of 20, but it also means you shouldn't put too much faith in the generalizability of the results.
Even so, this is some evidence that my previous intuition was correct. Not that I think you should kneel down and hail me; nine out of ten football fans would probably have told you the same.
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