Last week, only 298 days after Claudio Ranieri helped Leicester City win the Premier League title, a 5,000-1 triumph, Ranieri was sacked. But does sacking a football manager have an effect? Not very much of one, a growing body of evidence suggests. There is over a 90 percent correlation between teams’ wages and their results, according to analysis of teams’ spending and results from 1973 to 2010 in “Soccernomics,” a book by Simon Kuper and Stefan Szymanski. That leaves less than 10 percent to be decided by other factors — who its manager is, injuries, scouting and plain old luck. In English football from 1973 to 2010, Kuper and Szymanski found, only 10 percent of top-flight managers consistently overachieved when wages were taken into account. A very select few managers do make a difference, but most have a negligible impact on how a club performs.

Today, the average Premier League manager — except Arsene Wenger, in his 21st year at Arsenal — lasts a little over a year, slightly shorter than Ranieri’s reign. That doesn’t leave much time for a manager to leave a mark. Occasionally, innovations can help managers succeed immediately, as Antonio Conte has in reintroducing the 3-4-3 formation at Chelsea this season, to stunning effect. But in the overwhelming majority of cases, clubs’ complex systems of coaching, player analysis, scouting, youth development and training facilities far predate — and normally outlast — any new manager.

Take Leicester and Ranieri. There were several crucial aspects of their success last year: the brilliant end to the 2014-15 season, winning seven of the team’s last nine matches under a previous manager; sophisticated use of data analytics (several members of Leicester’s backroom team have subsequently been poached); and a brilliant scouting network. All of it was in place before Ranieri took charge. While Ranieri tweaked the side’s tactics and elevated the midfielder Danny Drinkwater from the substitutes’ bench, overall he changed relatively little about Leicester’s method.

What did change was Leicester’s luck, first for the better, and then for the worse. Last season, Leicester’s goal difference was 11.5 greater than predicted by a model of expected goals developed by David Sumpter, a sports economist, using Opta data that takes into account the location of shots; the team also benefited from the fewest total days lost to injury of any Premier League team. Until Leicester defeated Liverpool in its first match without Ranieri, it had been the unluckiest team in the league this season according to Sumpter’s model. When Ranieri was sacked, Leicester had conceded 9.6 goals more than expected, while scoring 0.8 fewer than expected, adding up to a goal difference of -10.4 compared to its actual figures, the lowest in the league.

“Sacking Ranieri now is stupid. It’s falling into the trap of underestimating randomness,” said Sumpter, author of “Soccermatics.” “This season’s run of bad form is partly down to a run of bad luck.” Football is particularly prone to randomness, because it is so low scoring; underdogs win more than in any other major sport.

So if Leicester continues to maintain its level of play for the remainder of the season, its results should improve, regardless of who the new manager is — or whether Ranieri had stayed.

Ranieri’s sacking is likely to lead to an upswing in Leicester City’s results, just not because a new manager is better than him. New Premier League managers generally enjoy “a short honeymoon period,” a study of sackings from 1992-2008 by Sue Bridgewater, director of the Centre for Sports Business at the University of Liverpool Management School, found — but this is not because of the new boss. Managers tend to be sacked when a team is at a low point, after which they tend to revert to their former level: Bridgewater found that an average team earns 1.3 points a match, which is what they earn in the three months after a sacking. The “bounce” a new manager enjoys is just regression to the mean. Bas ter Weel, a Dutch economist, has found the same phenomenon in the Netherlands.

In 2015-16, there were 58 sackings across the 92 clubs in the top four tiers in English football, a record. In most cases, teams would have been better off retaining their managers and using the saved cash on new players, or greater investment in scouting and youth development.

In recent years several unglamorous teams have thrived while adopting strategies that limit a manager’s importance. As Kuper and Szymanski note, Lyon won seven consecutive titles in France from 2002-08, as well as reaching the quarterfinals of Champions League in three consecutive seasons from 2003-04, with four different coaches – Jacques Santini, Paul Le Guen, Gérard Houllier and Alain Perrin — who subsequently had undistinguished records. Lyon recognized that a previous manager, Bernard Lacombe, was exceptional at spotting talent, so moved him to a director of football role, focusing on player recruitment while insulated from day-to-day pressure. More recently, Southampton has excelled in the Premier League despite repeatedly losing its coaches to other clubs. Southampton’s success, like Lyon’s, has been underpinned by excellent youth development and a philosophy for player recruitment that changes little depending on who the manager is.

Routinely branded the savior or destroyer of a club, the football manager is rarely either. Indeed, given how short his stints are and how many other staff members clubs now employ, perhaps the manager has never been less important. Ranieri’s unfathomable two years at Leicester might be best remembered as a reminder of the limits of a manager’s significance.

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