Two of the great issues of our age are: what impact does inequality have upon economic performance? and: should Arsenal give Robin van Persie a massive pay rise to hold onto him? A new paper bears upon both questions. It studied serie A games in 2009-10 and 2010-11 and found:

Pay dispersion has an overall negative impact on team performance…doubling pay dispersion [as measured by the Theil index] decreases by 6% the probability of winning a match.

This is a big effect. The authors estimate that if a team changes from everyone being paid the same wage of €600k pa (the average in their sample) to a superstar earning €1.5m pa and everyone else in the team getting €510k, the chances of the team winning a game falls by 20 percentage points. That’s almost as big an effect as having to play every game away from home.

This adverse effect comes because pay dispersion worsens individuals’ performance, as measured by newspapers’ (highly subjective) ratings. And it seems that the highly paid players’ performance suffers as much as that of regular players. It seems that the “pressure of expectations” can depress superstars’ performance, whilst other players’ do worse because they (subconsciously?) relinquish responsibility as they look to the superstar to win them the game.

All this confirms what all sentient beings already knew - that Arsene Wenger knows best. There’s a logic behind his traditionally relatively egalitarian wage structure.

Or is there? All this applies to the pay of the players who appeared on the pitch. Looking at the dispersion among the entire squad, which includes non-playing members, things are different. Pay dispersion here might actually have a positive effect upon performance. This suggests that the optimum structure is one of relatively equality among first-team players, but inequality between first-teamers and squad players.

However, whilst this is an important caveat for football, it hardly applies to companies generally where all employees are in effect players. This, then, is more evidence that paying huge wages to superstars can often backfire. And it’s evidence that inequality can be economically damaging.