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.

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?

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.

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.

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).

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.