Sack a soccer manager by equation

The Cambridge University formula says Chelsea's Vialli should not have been fired

LONDON, England (CNN) -- The formula for success for the world's top soccer clubs has been revealed by an English academic from Cambridge University.

Dr. Chris Hope has devised a simple mathematical equation which tells football club chairmen exactly when the time is right to part company with a manager or coach whose eyes are simply just not on the ball.

The equation: perf (m) = 0.121 (result (m)) + 0.879 (perf (m - 1)) has been tested on the English Premier League but its author hopes to use it throughout Europe and the rest of the soccer world. (The equation in action)

It could settle once and for all whether underperforming Barcelona of Spain should dismiss coach Carles Rexach or could say whether Italy's Lazio should really have sacked Dino Zoff or Spain's Real Sociedad fired John Toshack.

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What the formula -- which took a month to work out and has examined 380 million matches -- does reveal is that some soccer clubs sack their manager too early.

Hope's equation says that, based on performance, Chelsea was wrong to sack both Ruud Gullit and Gianluca Vialli.

Though it says that, after strings of poor results Aston Villa of the English Premier League kept on John Gregory a year too long and fellow-midtablers Everton should have let Walter Smith walk through football management's revolving door three years before he actually left the club.

The formula if applied, Hope says, will stop clubs from sacking good coaches because of a sudden bad run or sticking with a manager or coach who really should go.

"We have checked it and Arsene Wenger of Arsenal and Alex Ferguson of Manchester United would definitely have stayed," says Hope, of the Judge Institute of Management. "So it does work."

Unsurprisingly, 'double' winners Arsenal were right to keep Wenger, says Hope

The equation gives a manager a "honeymoon period" of eight weeks.

Then it holds that a manager should automatically be sacked if his percentage of points per game, weighted in favour of recent results, drops below a figure of 0.74.

Clubs who followed the formula would do better, in the English Premiership getting an average of 56.8 points a season rather than the current average of 51.8 -- the extra five points possibly saving them from relegation.

That is actually bad news for managers -- or perhaps good news for them and bad news for chairmen since there would be many more payoffs -- with each club having a turnover of 5.7 managers every 10 years.

In the formula, perf (m) -- or the rating after m number of matches -- is the bottom line. If that goes below 0.74 the trapdoor opens under the manager's feet.

Result (m) is the number of points scored in the most recent match and perf (m - 1) is the total perf (m) score after the previous match.

The figures of 0.121 and 0.879 are Hope's "smoothing" figures to give increased importance to the most recent games -- the last five matches making up 50 percent of the rating.

Hope, 47, said: "I've seen the work of both good and poor managers at close quarters, and know how difficult it is to decide when a manager has to go.

Hope -- whose usual work is in management quality control and climate change -- says his formula is deadly serious and is genuine "management science."

Chelsea were also wrong to sack Gullitt, says the maths program

"This model is very simple to use, so any club considering the future of its manager might find it worthwhile at least to take a few minutes to check how close his performance is to the trapdoor before pulling the lever that consigns him to the sack."

But although he says he would like sponsors to help him look at the Italy's Serie A, Germany's Bundesliga and Spain's Primera Leagua, Hope has no plans yet to apply his equation to the performance of top business managers and CEOs.

That may be not long in coming, however, with DaimlerChrysler chief Jurgen Schrempp on record as describing Bayern Munich coach Ottmar Hitzfeld as a role model for German business leaders.

With the World Cup imminent David Bolchover who has just written the book "The 90-Minute Manager" told CNN's Business International that company heads could learn a lot from the man-motivation of soccer successes like Marcello Lippi of Juventus.

"Many business managers are starting to look at soccer managers as a model which will provide lessons for them," Bolchover told CNN's Becky Anderson.

"Sir Richard Greenbury who used to be chairman of Marks and Spencer referred to Alex Ferguson is the greatest man manager in Britain.

"This business model is increasing in popularity and in relevance."