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Liverpool, Leicester or Man City for the title? Maths has the answer

Predicting where their team will finish in the Premier League or Championship is a national past time amongst football fans and pundits.

two players race for a football Now, researchers at Leeds Beckett University have come up with a formula that helps to forecast where teams will finish at the end of the season.

The academics have been able to show that all professional football leagues in England (Premier League, Championship, League One and League Two) obey the same underlying mathematical laws.

Worryingly for those near the foot of the table, or those hoping to close the gap on the leaders, the maths shows that end-of-season standings become 'fixed' surprisingly early on in the season.

Professor Clive Beggs, who led the research at the university’s Carnegie School of Sport, said: “By about round ten of the season, most teams become fixed in position, with relatively little change occurring thereafter.

“Regardless of the individual teams or the standard, leagues are governed by the competition structure and the points awarding system for a win or a draw.

“This means that, in practical terms, the weekly standings can be used to predict end-of-season league position with reasonable accuracy.

“For example, the team in first place in the Premier League after just ten games has a 77% chance of finishing in the top three.

“The team in last place after round ten has a 55% chance of being relegated.”

The majority of changes in league positions are settled as early as November, with 77% of final standings already predictable. After 20 games that rises to 87%, and by 30 games to 94%.

To determine the mathematical laws that govern league behaviour, the researchers computed the weekly standings for the four English leagues over 22 seasons between 1995-2017.

The research, Hidden dynamics of soccer leagues: the predictive ‘power’ of partial standings, have been published by Plos One, and could have far-reaching implications for club owners looking to change managers or boost their squads.

Researcher Dr Alexander Bond explained: “The implications for strategic decision-making within football firms are significant.

“It questions whether clubs should invest in new playing talent during the winter transfer window – which is often over-inflated.

“It also implies that firms need to consider the usefulness of managerial change mid-season or more realistic objective setting when changing managers mid-season.

“Furthermore, it demonstrates the blind optimism and unprecedented loyalty of football fans, who turn out week in week out so see if their team can beat the maths."

The findings of the study suggest that strategic interventions, such as changing manager, are probably best done early on in the season, as later on it becomes increasingly difficult to affect the outcome of the campaign.

Professor Beggs added: “When faced with relegation, waiting until the last eight games of the season before changing manager is probably not the best strategy.

“This is because the mathematics of the league are against you.”
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