Corruption and quid pro quo behaviour in professional soccer

In their book Freakonomics, Steven Levitt and Stephen Dubner described research (from this article by Levitt and Mark Duggan - ungated earlier version here) that showed evidence of rigged matches in sumo wrestling. Specifically, wrestlers who were approaching their eighth win (which comes with much greater earnings and ranking) were more likely to win against those who already had eight or more wins, than would be expected based on their relative ability. And that was in Japan - a country not known for widespread corruption (Transparency International ranks Japan 18th out of 180 countries in its Corruption Perceptions Index). How bad could things be in other, less honest or trustworthy, countries?

A 2018 article by Guy Elaad (Ariel University), Alex Krumer (University of St. Gallen), and Jeffrey Kantor (Ariel University), published in the Journal of Law, Economics, and Organization (ungated version here), provides a window to widespread corruption in domestic soccer. [*] They look at games in the final round of the season, in domestic soccer leagues, where one of the teams needed to win (or draw) in order to avoid relegation, and where the match was inconsequential for the other team. They have a database of 1723 such matches in 75 countries over the period from 2001 to 2013. Most interestingly, they look at how the win probability (controlling for a range of factors, including the strength of the opposition and home advantage) varies by the level of corruption of the country. They find that:

...the more corrupt the country is according to the Corruption Perceptions Index (CPI), the higher is the probability of a team (Team A) to achieve the desired result to avoid relegation to a lower division relative to achieving this result in non-decisive games against the same team (Team B)... This finding is robust when controlling for possible confounders such as differences in abilities, home advantage, and countries’ specific economic, demographic and political features.

Then, there is evidence that the winning team in that game returns the favour (quid pro quo) in the following season, since they find that:

...in more corrupt countries the probability of Team A to reciprocate by losing in the later stages of the following year to Team B is significantly higher than losing to a team that is on average better (stronger) than Team B. This result strengthens the suspicious of corrupt norms, since in the absence of any unethical behavior, we would expect the opposite result, since naturally the probability of losing increases with the strength of the opponent.

There's clearly a lot of mutual back scratching going on in professional soccer. It is worth noting, though, that the top divisions in Europe (Premier League, Ligue 1, Bundesliga, etc.) were not included in the analysis, which focused on the second-tier leagues in Europe, and top leagues outside of Europe.

An interesting follow-up to this study would be to look at betting odds. Do the betting markets price this corruption into their expectations (so that the team needing to avoid relegation has betting odds that suggest a higher probability of winning than would be expected based on home advantage, strength of opponents, etc.)? If not, then there may be opportunities of positive expected gains available from betting on those games.

[HT: Marginal Revolution, last year]

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[*] Or football, if you prefer. To me, football involves shoulder pads and helmets.