Football referees are unfair when awarding penalty kicks

After the controversial referee call that decided yesterday’s World Cup football match between Brazil and Croatia, I wondered if professional football referees had any consistent biases when they make these potentially controversial calls. After all, referees are forced to make match-altering decisions in just minutes, so it’s highly likely that these snap decisions are affected by inherent human biases. It just so happens that one German researcher, Wolf Schwarz, published a report on this topic a few years ago. The results are bound to shock you.

Croatian players argue with the referee over his controversial penalty kick call

Croatian players argue with the referee over his controversial penalty kick call
in the 2014 Brazil vs. Croatia World Cup match

If referees awarded penalty kicks in a completely unbiased manner, we would expect the distribution of matches with penalty kicks to follow a Poisson distribution: Most matches with no penalty kicks, a good number of matches with 1 penalty kick, a handful of matches with 2 penalty kicks, and so on. Instead, Schwarz found a peculiarity in the data: There are far more 2-penalty kick matches than would be expected by chance. It appears that referees have a bias to turn some of these 1-penalty kick matches into 2-penalty kick matches.

The burning question is: Why?

penalty-kick-dist

To explore this question a little further, Schwarz looked at the breakdown of which teams are awarded the penalty kicks. Surprisingly, the Home team has a considerable advantage when it comes to penalty kicks: 70.6% of all penalty kicks were awarded to the Home team. So not only do Home teams have the advantage of more fans cheering them on, but it appears that the referees are on their side too.

penalty-kicks-team

Using the above breakdown as a baseline, Schwarz then focused in on the 2-penalty kick matches to see what was going on. Could it be that referees are trying so hard to be fair to both teams that they’re trying to give both teams an even number of penalty kicks? The data seems to suggest that this is the case: If the Home team received the first penalty kick, then the Away team received the second penalty kick 48% of the time — a marked increase from the baseline 29.5%. Similarly, if the Away team received the first penalty kick, then the Home team received the second penalty kick 92.5% of the time — an incredible display of referee bias.

penalty-kicks-by-first-penalty

But what if the first penalty kick wasn’t converted? Would the referee still feel pressured to award the other team a penalty kick to “even things out”? When Schwarz split the data up by whether the first team converted its penalty kick (here, for the Home team only), it seems the answer is “no.” If the first team didn’t convert its penalty kick, referees awarded the second penalty kicks as normal (68.4% Home, 31.6% Away). But when the first team did convert its penalty kick, the referee bias popped up again (46.5% Home, 53.5% Away).

penalty-kicks-first-home-converted

Clearly, professional football referees are trying so hard to be fair when awarding penalty kicks that they’re actually unfair in making their calls. These findings could have sweeping implications for professional football, and especially the World Cup going on this week, if players start taking advantage of this referee bias to score an easy penalty kick.

Schwarz looked at several other aspects of the referee bias in his research paper, for example showing that the second penalty kick is awarded much faster than the first penalty kick, which indicates that referees are lowering their standard for what deserves a penalty kick after they awarded the first one. I highly recommend giving his paper a read.

Dr. Randy Olson is a Senior Data Scientist at the University of Pennsylvania, where he develops state-of-the-art machine learning algorithms with a focus on biomedical applications.

Posted in data visualization Tagged with: , , , , ,
  • Morten k

    I think you are a little too “enthusiastic” when you use the word “clearly” in your conclusion.

    The whole data set completely neglects to examine what penalties does to the flow of the game. The observation that the second penalty is given along the same rates as normal, if the first it wasn’t converted, might just be because the fact that no goal was scored, kept the game in a “normal” state, as far as who were being offensive or not.

    And home teams get more penalty kicks than away teams because they on average play more offensively on home ground. Just like good teams get more penalties than bad teams – they are simply more in the penalty areas.

    And using the poisson distribution is a bit of a problem, because the events are not independent of each other. So we would not “expect” it to follow it.

    All in all there are a ton of aspects that are not considered – some so obvious that it seems almost omitted on purpose to suit a wanted conclusion – and consequently some serious problems with the conclusions you make about what the data says about the referees.

    • The whole data set completely neglects to examine what penalties does to the flow of the game.

      The research paper actually addresses this. See page 444.

      And home teams get more penalty kicks than away teams because they on average play more offensively on home ground. Just like good teams get more penalties than bad teams – they are simply more in the penalty areas.

      Sure, that makes sense. Which is why the distribution shown is used as a baseline for the rest of the study; we do not expect there to be an even 50/50 split of penalty kicks.

      And using the poisson distribution is a bit of a problem, because the events are not independent of each other. So we would not “expect” it to follow it.

      Aren’t football matches typically refereed by a different referee each time? So wouldn’t they technically be independent events, as far as looking at referee decisions?