WHEN Emmanuel Adebayor (pictured) played for Manchester City in a match against Arsenal in 2009, there was little love lost. The Togolese striker had once been an Arsenal favourite, but left the club in acrimonious circumstances. The Arsenal fans that had previously lauded him, spent the match giving him the bird and singing rude songs about his family. Inevitably, Mr Adebayor scored the clinching goal. He promptly ran 100 metres to the other end of the ground to celebrate—sliding to his knees, arms outstretched—in front the stand in which his tormentors were concentrated. It was ever thus. Former players always seem to come back to haunt the clubs they leave. Geoff Brown, a football writer, had a phrase for it: “the immutable law of the ex”. But is the effect real, or just an example of confirmation bias? Does the very fact that we expect former players to exact revenge make us more likely to notice it when they do? Three management professors, led by Federica Pazzaglia of University College Dublin, decided to investigate. In a paper published in Human Resource Management, which takes Mr Brown’s remark as its title, they tested whether former players really do perform better against their old teams.

The study looked at English Premier League matches between 2000-2005 that featured players lining up against former clubs. They then analysed the marks they received in the player ratings published by the Sun and Mirror, two tabloid newspapers. According to this system, players did indeed tend to perform better when pitted against former teammates. The paper explores two hypotheses, one more plausible than the other. The first is that a player’s familiarity with his former team's modus operandi gives him an advantage. The researchers inferred this because a player’s ratings went up more if his ex-club had the same coach as when he left—the implication being that the tactics would not have changed much. The trouble with this hypothesis is that it ignores the fact that such insider knowledge works both ways. Many hours spent on the training pitch might, for example, make a striker aware of a defender’s vulnerability to pace on his outside. But equally the defender might know that the departed striker always tends to cut inside to shoot with his right foot. There seems no reason why one player’s knowledge would outweigh the other’s.

A more obvious explanation is that a departed player feels he has something to prove to the coach who sold him, and tries harder as a result. This is the researchers’ central hypothesis. Indeed, by studying press reports, they determined which transfers appeared to be harmonious and which bitter. Where a transfer was accompanied by press articles that included words such as “vendetta”, “bad blood” or “grudge”, the player’s performance rating duly went up further when he returned. Players who left in anger got, on average, a 6% higher rating than the rest of his team. They did even better when compared with players who left on good terms: a 10.5% higher rating.

The researchers’ findings are, for the most part, intuitive. Nonetheless, there do seem to be striking flaws to the paper. Firstly, using player ratings given by tabloid newspapers is not the robust measure that the authors claim. There is no reason why football hacks will be any more immune to confirmation bias than an average fan. Indeed, they may be more susceptible. Newspapers love the narrative of a disgruntled ex-player exacting revenge. They may be likely—consciously or not—to overplay his contribution. Even if one disregards this, it only compares a player’s ability to that of his teammates. Better players may simply be more likely to get transfers, and would have higher ratings regardless of their employer.

The authors also overstretch themselves by trying to apply the immutable law of the ex to managers who swap firms in every day life. But Premier League football is a rarefied arena with little relation to the real world. A manager who moves from Starbucks to Greggs will rarely find the same direct competition as adversaries on the sports field do. A consultant moving from Bain to McKinsey may use inside knowledge to secure a client that both are wooing; he may even put in longer hours to secure the contract. But will he necessarily work any harder for that client once it is secured?

In any case, he will probably not have to deal with 30,000 Bain fanatics casting aspersions about his parenthood as he does so. That, one suspects, makes revenge all the more worth working hard for.