Sunday, May 22, 2011

More evidence for referee bias in soccer

Commenter "Millsy" was kind enough to send me a couple of academic studies on soccer refereeing bias. Both of them have pretty solid evidence that referees favor the home team.

The first one is "Favoritism Under Social Pressure," (.pdf) by Luis Cariciano, Ignacio Palacios-Uerta, and Canice Prendergast. The authors looked at how much extra time the referees added to the end of soccer games (to compensate for time lost to injuries, substitutions, and so on). Looking at games in the Primera Division in Spain over two specific seasons (1994-95 and 1998-99), they found that, in games where the score difference was exactly one goal, referees awarded almost twice as much extra time when the home team was trailing as when it was leading. More time, of course, benefits whichever team is behind, as it gives them a better chance to tie the game.

The difference was about 1.8 minutes, even after controlling for yellow cards, red cards, substitutions, and several other things. In round numbers, home teams got four extra minutes to tie the score, but visiting teams got only two minutes. The difference was very statistically significant (at least 15 SDs).

Those two situations -- home team ahead by one goal, and visiting team ahead by one goal -- were the two most significant deviations from the mean of about three minutes. The full data, as read off the authors' chart, arranged by home team lead:

4+ goals ... 3.0 minutes
3 goals .... 3.0 minutes
2 goals .... 2.5 minutes
1 goal ..... 2.1 minutes
0 goals .... 3.3 minutes
-1 goal .... 4.0 minutes
-2 goals ... 2.8 minutes
-2+ goals .. 3.0 minutes

This seems like pretty solid evidence that something is going on ... I can't think of anything that would cause this other than referee bias, but if you can think of anything, let us know.

By the way, the authors estimate that the bias changes the result of about 2.5% of games -- presumably from a loss to a tie. That means it changes home winning percentage by 0.0125. That's less than 10% of the overall home field advantage in soccer, but it's still pretty significant.


However, there's one thing that's a bit strange -- you'd expect that if it's referee bias, some refs would be aware of it and consciously try to avoid it. The authors checked individual referees, though, and they all seemed to be about the same:

" .... we found that most referees appear to be equally biased. Only 3 of the 35 referees in the sample show statistically significant individual effects at the 10% level."

That, to me, seems very unusual, that all the refs would be breaking their vows of fairness in exactly the same way. So I still have some reservations that it's all just unconscious bias, even though I honestly can't think of any other explanation.

Also, I find it interesting that the paper I reviewed last week argued that differences in referees confirms the hypothesis of bias. This paper found *no* differences in referees -- but does not consider this to *refute* the hypothesis of bias.


The second paper is called "Favoritism of agents -- The case of referees' home bias," by Matthias Sutter and Martin G. Kocher (.pdf). The authors looked at the 2000-2001 season in Germany, and found a similar, though less extreme, result:

1 goal ..... 2.2 minutes
0 goals .... 1.8 minutes
-1 goal .... 2.7 minutes

The +1/-1 difference is just 30 seconds, instead of the 100 seconds the Spanish study found. It's still significant at just over 2 SDs. (The difference between -1 and 0 is 3 SDs.)

This study checked a couple of other things that were interesting. In the first half, the pattern was reversed: there was more extra time when the home team was ahead (20 seconds, 2 SDs). The authors think that's because, in the first half, it's to the home team's benefit to have play stop earlier, so they can regroup for the second half.

Also, the authors note that a German magazine, "Kicker Sportmagazin," reviews all games and posts an opinion on which penalty calls were correct and which were incorrect (both actual and missed calls). It turns out that for penalties called in favor of the home team, 5 out of 55 were illegitimate. But for visiting teams, it was only 1 out of 21. So referees favored the home team by about twice as many false positives.

False negatives also favored the home team. There were 12 cases where home team should have been awarded a penalty, but wasn't; there were 19 such cases for the visiting team.

Overall, if you add those up, the visiting team was "cheated" out of about 10 penalty kicks.

Assume 9 of those would have been goals. Nine goals out of 306 games equals 0.03 goals per game. The overall goal difference between home and road was 0.62 goals. So, this particular manifestation of referee bias equals about 5 percent of home field advantage.

That seems plausible to me.

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At Saturday, March 03, 2012 8:09:00 AM, Anonymous foot lyon said...

Sure referee bias exists, but isn't it a part of soccer's charm ? It's precisely because nothing is sure in this sport more than in any other that it's so exciting to watch a match on TV, don't you think so ?


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