Caveats and pitfalls in crowdsourcing research: the case of soccer referee bias

In a recent crowdsourcing project, 29 teams analyzed the same data set to address the following question: “Are football (soccer) referees more likely to give red cards to players with dark skin tone than to players with light skin tone?” The major finding was that the results of the individual teams varied widely, from no effect to highly significant correlations between skin color and the rate of red cards, which some teams interpreted as indicative of a referee bias. We analyzed the same data using a Poisson log-linear regression model and obtained an odds ratio of 1.34 (95%-CI, 1.13–1.59), which means that players with a darker skin tone have in fact a slightly higher odds of receiving a red card. This result is in agreement with the median odds ratio of 1.31 from all 29 teams. We then extended the original study by investigating the likelihood of receiving yellow cards. If a referee bias was in fact present, it would be plausible to see a similar association. However, players with darker skin tone were significantly less likely to receive a yellow card, with an odds ratio of 0.94 (95%-CI, 0.91–0.97). The risk of receiving a card is most strongly affected by a player’s position, and there are significantly more players with darker skin tone at center back and defensive midfield where receiving red cards is generally more likely. Taken together, our results do not support the hypothesis of a referee bias. Our most important finding, however, is that the perceived diversity of results from the crowdsourcing teams is due to placing too much emphasis on dichotomous decisions (significant vs. nonsignificant). When we focus on point estimates and their reasonable bounds, the individual substudies predominantly reinforce each other. We argue that data scientists should put less emphasis on statistical significance and instead focus more on the careful interpretation of confidence intervals or alternative methods for measuring the effect size and its precision.