“I THINK I am a special one,” José Mourinho boasted in 2004. One of football’s most lauded managers, he won six domestic titles in his first 11 seasons in top leagues. But his powers have deserted him of late. He was sacked by Chelsea in 2015, and by Manchester United last month.

Fans lay most of the credit or blame for their team’s results on the manager. So do executives: nearly half of clubs in top leagues changed coach in 2018. Yet this faith appears misplaced. After analysing 15 years of league data, we found that an overachieving manager’s odds of sustaining that success in a new job are barely better than a coin flip. The likely cause of the “decline” of once-feted bosses like Mr Mourinho is not that they lost their touch, but that their early wins owed more to players and luck than to their own wizardry.

A manager’s impact is hard to gauge. How should credit be split between the boss and his charges? To separate their effects, we needed a measure of players’ skill. We found it in an unlikely place: video games. Electronic Arts’ “ FIFA ” series rates 18,000 players each year, based on their statistics and subjective reports from 9,000 fans. These scores yield reliable match forecasts. Using only pre-season FIFA ratings, we could predict the final table with an average error of eight league points.

By comparing actual results with these projections, we could see which clubs did better than their players’ ratings implied. Teams do over-perform for reasons other than their managers. But if coaching matters, the best bosses should continue to exceed expectations when they switch clubs.

Managers do carry over some impact. However, the effect is small. For a manager switching jobs after one year, we expect his new team to reap just 8% of his prior outperformance. Even after a decade of coaching, this figure is still only 45%, implying that the primary causes of a manager’s previous successes were beyond his control.

A few bosses have beaten expectations for long enough to deserve proper credit. Despite lacking the star power of La Liga’s titans, Diego Simeone led Atlético Madrid to a Spanish title. And Jürgen Klopp turned mid-table Borussia Dortmund into two-time German champions.

Conversely, Carlo Ancelotti has squandered resources. Although he has led the team with the best players in its league in eight of his past 12 seasons, he has won only three titles in that time. A top-league player who fared so poorly would have lost his job. But the market for coaches is inefficient. Mr Ancelotti keeps getting hired—perhaps because employers over-weight his three Champions League trophies, which required a much smaller number of wins.

Even the best tacticians cannot compete with those who contribute with their feet. Mr Simeone would improve an average club by four points, similar to the 50th-best player in the world. But greats like Lionel Messi can add twice as much or more.

Sources: Electronic Arts; Transfermarkt