Just how exceptional a manager is Ole Gunnar Solskjær? For all the praise lavished on the likeable Norwegian, I remain glued to the fence. Don’t get me wrong. He’s clearly doing well. It’s just that it is fiendishly tricky to separate the upturn in Manchester United’s mood and form since he took over – as reflected by that spectacular feat of alchemy in Paris – with the obvious fact that any club with that much money and world-class players should be winning most of their matches.

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Throw into the mix the astringency of José Mourinho’s last few months at Old Trafford, the effect of the new manager bounce and Solskjær’s previous record at Cardiff, and we are all playing guessing games about how good the Norwegian might be. Disentangling the skill of a manager – his special sauce, so to speak – from the quality of the players at his disposal and the club’s budget isn’t easy. After all, no one believes Roberto Di Matteo is a great coach, even though he led Chelsea to the 2012 Champions League after riding the sort of luck rarely seen outside a Euromillions jackpot winner. Avram Grant was also just a fluffed John Terry spot-kick away from conquering Europe in 2008.

However, a team of German academics believe they have found a way to separate the impact of a manager from the team effect after forensically examining every coach’s reign in Bundesliga from 1993-1994 to 2013-14. Their paper, published in the Journal of Sports Economics last August, looked at 6,426 matches, every club’s budget per season and even every coach’s playing career, and some of their findings were unsurprising. Representing the national team as a player, for instance, did not make someone a better manager. Similarly, there was no evidence that playing in any one position as a player made them a better coach later in life. But by paying particular attention to how the same managers performed at different clubs – and by applying similar statistical wizardry used to assess how much difference bosses make to productivity in the US – they made two intriguing findings.

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First, that the top 20% of managers over the 21-year period – which included Jürgen Klopp and Lucien Favre – improved a team by around 0.3 points a game on average over someone ranked in the bottom 20%, even after taking team strength and budget into account. That is 10.2 points on average over a 34-game Bundesliga season. Second, that measure of ability had a substantial predictive power for future performance of the teams employing the respective manager.

The research, incidentally, appears to back up what I and others have written before about managerial talent. In essence it is like a U-curve, with the best and worst coaches having a bigger impact on results – and those in the middle tier relying on the quality of their players, their club’s recruitment strategy and luck to succeed or fail. And, of course, relative success is only one measure a club should look at when bringing in a new manager. Their personality, how they develop and improve young players, and their style of play are all essential too.

Facebook Twitter Pinterest Neither José Mourinho nor Brendan Rodgers had successful careers as professional footballers. Photograph: Tom Jenkins/The Guardian

Incidentally, the academics found something else that teams might bear in mind. Bundesliga sides whose managers were former professional players who had played in the top two tiers of German football tended to perform worse, on average, than managers who had either not played professionally at all or played no higher than the third tier. One explanation, according to Dr Gerd Muehlheusser of the University of Hamburg, is that managers who have not been former star players themselves need to be substantially better coaches in order to secure a job as a head coach in the top leagues. “In other words, they must start their managerial career in low divisions and hence have already proven to possess some managerial quality beforehand,” he says.

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Maybe that shouldn’t surprise us. After all, Arrigo Sacchi was an amateur player and shoe salesman before revolutionising football at Milan, while Mourinho, Gérard Houllier and Brendan Rodgers are among many successful coaches who never played the game professionally. Still, as Omar Chaudhuri, the head of football intelligence at football consultancy 21st Club, points out it might mean that football undervalues coaches who have not played the game professionally.

“It’s not possible to know, unfortunately, if there was the same number of non and ex-pros, whether the non-ex-pros would be better on average,” says Chaudhuri, who works with several top clubs. “Still, the main thing it suggests is that potentially non-ex-pros are less of a risk than perceived by the market. The question is whether a club can use that – if non-ex-pros still have to ‘prove’ themselves, you potentially don’t know if they’re any good until they’ve proved themselves.”

Interestingly, it is a different story in the NBA, where top players tend to do better as coaches than non-players. That is probably because those players do not usually get head coach positions right away. Instead they have to prove their talent first. Maybe there is a lesson there for football clubs as well as former players.

In the meantime, 36 managers have now left their jobs in English football this season. Incredibly, 20 of those appointments lasted less than a year, including Solskjær’s old teammate Paul Scholes at Oldham, and it suggests that large parts of the game still have a problem evaluating what a good manager looks like.