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Statistical analysis of World Cup fouls

Craig Depken has posted a nifty analysis of fouls and cards, using data from the last two World Cups. His findings:

[O]n average over the two tournaments there was one Yellow Card issued for every 5.5 fouls committed, ceteris paribus. A couple of interesting results from the first stage regression: the host team receives 4 fewer Yellow Cards over the course of their participation in the tournament and the more fouls committed against a team the fewer Yellow Cards issued to the victim team, ceteris paribus. This suggests (to me) that referees might let the victim exact some revenge on the pitch without punishing the victim for their redress.

....Based on the 2002 and 2006 World Cups, there is one Red Card issued for approximately every 12-13 Yellow Cards. There also seems to be a little home cooking for the host team above and beyond what consideration the team gets from the Yellow Cards issued.

....What I found interesting is that the U.S. team received 2 Red Cards on 5 Yellow Cards. Given the estimation results, the U.S. should have received 0.39 Red Cards (round down to zero) and yet received two. Was there bias against the U.S.? Hard to tell without more data. From these two tournaments (2002 and 2006), the 95% confidence interval of the number of Yellow Cards per Red Card is [0.89, 24.12], centered on 12.5.

This is cool stuff. I encourage Craig to go ahead and estimate a count model, rather than linear regression. That might tighten up the standard errors. [Craig links to the data here, in Stata format, for anyone who wishes to take a crack at it.]

Also, the talk is about the differential rate of cards being issued in 2006, which doesn't show up independently in Craig's statistical model. If both the commentary and the model are correct, then the extra cards are mostly a function of extra fouls being called. For example, the bookings issued for picking up the ball to delay free kicks, etc., which have been given warnings and a shake of the finger in the past.

On another World Cup note, here is co-blogger Brian Goff, talking with SI's Bill Syken about Tivo, commercial interruptions, soccer, and the NFL's problem with game length. Bill suggests that the NFL should go to a continuous clock. Perhaps, but that is part of what drives soccer players to feign injury, in order to give themselves and their teammates a rest. (Prediction for Craig's number crunching machine: stoppages for injury increase with time during the game, since the players are more tired late in the game).