FOR FANS OF Tottenham Hotspur, the past week has seemed like a strange dream. On the morning of November 19th the Premier League club’s manager was still Mauricio Pochettino. The Argentine is adored by Spurs fans, since under his leadership a squad of cheaply assembled youngsters has been transformed into world-beaters, even reaching the final of the Champions League, football’s premier knock-out tournament. Real Madrid have often tried to hire Mr Pochettino. Tottenham endured a poor start to the season, tumbling to 14th place, but most supporters expected him to turn things around.

By November 23rd the club had fired the beloved Argentine, and done the unthinkable by hiring José Mourinho. The Portuguese manager’s two trophy-laden stints at a rival London club, Chelsea, have hardly made him popular among Tottenham fans. Nor has his reputation for arrogance, hostility—he once gouged an opposing manager in the eye—and spectacular downfalls. Though most of his tenures have started with great success, including league titles in four different countries and two Champions League trophies, they have usually ended acrimoniously. His tendency to alienate supporters, players and eventually his employers has become known as his “third-season syndrome”. Most Manchester United fans were relieved when the club sacked him 11 months ago.

How quickly Tottenham’s groans have turned to cheers. Mr Mourinho’s first match ended in a thrilling 3-2 victory against West Ham, another local rival. Spurs fans last saw their club lift a trophy in 2008. Perhaps this regular (though ungracious) winner might bring them glory once again?

Mr Mourinho certainly believes he will. The man who once dubbed himself the “Special One” has lost some of his invincible sheen, after failing to win the league at Manchester United. But he remains as self-confident as ever. In his first press conference for Tottenham, he explained: “I was always humble. The problem is you never understood that.”

But will the Humble One actually prod Tottenham to perform at a higher level than their talented players ought to reach? Earlier this year, The Economistcrunched the numbers from 15 years of top-division matches in England, Spain, Germany, France and Italy (football’s “big five” leagues), to measure Mr Mourinho’s worth. Our findings suggest that, after adjusting for the quality of the players that they have available to them, even the most decorated managers make comparatively little difference to their teams’ results. And those who have overachieved at their last club have about the same chance as a coin flip of doing so in their next job.

The hand of Poch

That assertion seems like heresy to most football fans, who balk at the idea of inexplicable, random patterns. When their team goes on an unforeseen run of wins or losses, they look for a simple cause. Generally, they turn to the person who decides the tactics and selection of players. Just down the road from Tottenham, at Arsenal’s stadium, the spectators showered praise on Unai Emery, a manager appointed last season, when he led the team on a streak of 22 games without a loss. Now that they are seventh in the table, most are calling for his dismissal. Such arguments often include the claim that the manager has lost the backing of his squad.

This cognitive bias is reinforced by the fact that a team’s performance often does improve when a new manager comes in. However, several studies have shown that this is simply a reversion to the team’s typical level of performance, after a temporary slump. One group of Dutch academics found that clubs which endure such rough patches tend to come through them, regardless of whether they change their coach. Mr Mourinho may receive plenty of credit just for getting Spurs to return to their usually dominant selves, when Mr Pochettino might also have overseen such a turnaround.

Because football teams so often go through ups and downs—and chairmen fire their coaches with such regularity—measuring long-term managerial performance is tricky. The most comprehensive research has been conducted by Stefan Szymanski, an economist, who obtained wage data for clubs in England’s four professional divisions between 1973 and 2010. Of the 700 managers to have appeared in that time, Mr Szymanski reckoned only 40-70 had consistently achieved better results than expected, given their financial resources. (Sir Alex Ferguson and Arsène Wenger, stalwarts at Manchester United and Arsenal respectively, both ranked highly.)

We wanted to produce a similar study to Mr Szymanski’s, updated for more recent seasons—but could not, because today’s elite managers often switch between countries, and few clubs are as forthcoming with their accounts as those in England are. So, rather than using financial resources as a benchmark, we looked for a widely available measure of players’ ability. Football analysts have only recently developed statistics that can do this for all positions, and such data exists for just the last few seasons. Instead, we turned to an unconventional source: video games.

Mr Mourinho would scoff at being evaluated via PlayStation. But we have found that the player ratings used in the FIFA game series—which are available online from as early as 2005, and are maintained today by a selection of 9,000 “superfans”—are very accurate predictors of real-life results. We fed them into a statistical model, which assigned weights for each position, and created a hypothetical starting 11 (plus a couple of substitutes) for each club.

We then plugged these line-ups into the 38 games a year that clubs play in their domestic leagues. (We could not find a readily available database of Champions League matches going back 15 years, but will try to build one in the future.) When we simulated entire seasons, we found that our predictions were nearly as good as those made by betting markets. The wisdom of the gambling crowds is the gold standard of forecasting in sports, since punters can price in factors that statisticians overlook. Gamblers on Sporting Index, a website that offers wagers on the final number of points each team will achieve, have had an average error of 7.6 points in the last four Premier League seasons (when comparing their predictions on the starting day to the eventual results). Our dinky model scored 8.3.

No way, José

Now that we had a reasonable proxy for player quality across leagues, we could see which coaches had consistently inspired their squads to unexpected heights. The data are sobering for believers in managerial omnipotence. Of the 131 coaches who overachieved during their first tenure and secured a second job, only 57 (or 44%) of them outperformed again. Of those serial winners, just 56% who made it to a third job repeated the feat once more. At the fourth hurdle—where Mr Mourinho fell, as his second stint at Chelsea ended with his team near the relegation zone—the survival rate was 31%.

This suggests that football managers who are excelling at their clubs cannot control most of the determinants of their success, or replicate them elsewhere. The players clearly make most of the difference. Might the serial overachievers merely have stumbled upon several groups of footballers who “clicked” together at just the right time, and thus have lucked their way through several rounds of sporting roulette?

Not quite. We did find a link between overperformance in the past and the future, but it was very weak. Because managers regress so quickly to the mean, our best predictions came from blending their actual results with 11 seasons’ worth of average ones (see the chart at the top of this article). In his 13 years of management in the “big five” leagues, Mr Mourinho’s teams have overachieved by 2.1 points per season, relative to what an average manager would get. Our best guess of his future contribution is therefore roughly 1.1 points. For Mr Pochettino, his 2.9 points per season so far give us a prediction of about 1.4 going forward.

Even the coaches with the most impressive records, such as Liverpool’s Jürgen Klopp and Atlético Madrid’s Diego Simeone, should add less than four points per season. That is dwarfed by the nine points that Lionel Messi contributes, relative to an average striker. Harry Kane, Tottenham’s acting captain and best striker, is worth about five.

Those fans who still worship Mr Mourinho will find it hard to believe that such a reliable champion adds barely a point per year, and a fifth as much as his new skipper. But Tottenham’s spending on the Humble One suggests that the club expect a similar return. After factoring in the severance pay for Mr Pochettino, the annual bill for employing Mr Mourinho is about £19m. According to 21st Club, a sports consultancy which has translated playing ability into wins and losses, adding one point’s worth of talent on the pitch costs an elite team about £17m per year in transfer fees and wages.

Perhaps Mr Mourinho will finally deliver the trophies that Spurs fans so desperately want. He has never finished a job without winning at least two of them. But our number-crunching suggests that almost all the credit for the Humble One’s glory so far belongs to the exceptionally talented footballers he has had at his disposal, rather than his personal wizardry.