Foxes' formula for success

Posted by ap507 at May 16, 2016 12:45 PM |
University of Leicester mathematicians create equations that capture Leicester City’s monumental achievement in winning the English Premier League

Issued by University of Leicester Press Office 16 May 2016

Mathematicians at the University of Leicester have created the perfect formula to describe the historic achievement of Leicester City Football Club who won the English Premier League with 5000-1 odds at the start of the season.

Dominic Cortis and Jeremy Levesley, from the Department of Mathematics at the University of Leicester, worked out the formula after Leicester played the final game of the season, drawing 1-1 at Chelsea.

Just as Leicester City has demonstrated on the pitch, the clever clogs at the University have shown that anything is possible and have used numbers – with the benefit of hindsight and some tampering with the stats - to convey the incredible success that has catapulted the team – and the city- to global fame.

Dominic and Jeremy added several factors to create the formula – even including the world-renowned discovery of King Richard III by University of Leicester archaeologists as the club achieved its success after the reinterment of the King in the city.

Other factors that came into play included:

  • Match statistics
  • Betting information
  • The team’s total wage bill
  • The value of the ‘Vardyquake’ which was a measurement taken by University of Leicester students into the earth tremors caused by the fans celebrating Leicester’s success

Dominic said: “Leicester City Football Club’s (LCFC) ascent to the top of the Premier League has captured the hearts of many in the UK and abroad. Testament to the fascination with the David versus Goliath story is the number of visitors to the city, including bus-loads coming directly from Milan’s San Siro Stadium to celebrate the awarding of the cup during the last home match (http://calciatoribrutti.com/macchinata-ignorante-pullman/ ).

“Today the team is having a victory celebration culminating at Victoria Park, just on the University of Leicester’s doorstep (http://www.visitleicester.info/things-to-see-and-do/sport-fitness/lcfc/lcfcparade/).  On this occasion all campus buildings are being renamed to the team’s players (http://www2.le.ac.uk/news/blog/2016-archive/may/university-buildings-renamed-after-english-premier-league-champions).”

Jeremy added: “No prediction model could have foreseen this conclusion at the start of the season. With the benefit of hindsight, significant bending of the laws of statistics and some convenient rounding we produced an equation that calculates the number of points obtained this season.”

Dominic Cortis, a lecturer in the Department of Mathematics at The University of Leicester and an assistant lecturer at The University of Malta, is an associate actuary and his research focuses on sports analytics as well as financial and betting derivatives.  Jeremy Levesley is Professor of Applied Mathematics at the University of Leicester.

Dominic said: “Since I started the PhD at Leicester in 2012, I have gone to see a couple of matches each season and adopted LCFC as my team. It has been an amazing journey from the pain of losing that championship playoff to Watford to this jubilant season.  I am also a proud Ulloa shirt fan -which I am wearing right now!”

Dominic Cortis and Professor Levesley said the formula is dependent on three components: match statistics, betting information and other statistics.

The following is a breakdown of how the mathematicians arrived at the formula:

Match Stats

The match statistics component we formed is as follows:

The team has played some great defensive football with fifteen clean sheets (matches in which no goal is conceded) out of which seven were 1-0 wins. Playing at home, the team has scored 1.84 and conceded 0.95 goals per match, resulting to a home ratio of 1.94 (1.84÷0.95). Claudio Ranieri’s squad also amazed us with their clinical precision – they had only 13.7 shots per game, 6th best in the league, with only Manchester United (11.3) in the top six teams less than them. Their counterattacking power and pace was lauded through the season; only Leicester together with West Ham and Southampton FC had a possession average below 50%, with Leicester least at 45%.

Betting Information

LCFC were considered ultimate outsiders at the outset of the season with odds of winning the league of 5000:1. However, if you had placed a wager of £1 on winning for every match, you would have pocketed £22.98. It seems like bookmakers will not underestimate the Foxes again; for the upcoming season the best odd on offer is 29:1 at time of writing.

The formula for the betting market component has been evaluated as:

The Brier score is a function that measures the accuracy of probabilistic predictions and is typically used for weather prediction modelling. In simple terms a smaller Brier Score indicates a better prediction, with zero being a perfect prediction. Using odds from betting markets, the two biggest Brier scores obtained this season were the home draws versus Manchester City (0-0 on 29th December 2015) and West Bromwich Albion (2-2 on 1st March 2016). These upsets can be explained by the fact that LCFC were expected to lose the former and win the latter (we should also take into account the fact that draws are the hardest outcome to predict in football).

5.jpg

Other Stats

Finally we plug six statistics together for the other stats component, namely

  • Riyad Mahrez rumoured transfer purchase fee paid by Leicester in 2014. The PFA player’s player of the year winner is now rumoured to be valued well above £30million: £400,000
  • The team’s total player wage bill in millions which is quite small seeing that six teams had a wage bill well over £100million: £48.2million
  • The maximum Vardyquake value reached. This is the value measured by a seismometer installed at Hazel Community School by University of Leicester Geology students measured during home matches : 0.4 during the game versus Everton (http://www2.le.ac.uk/news/blog/2016-archive/may/leicester-fans-produce-biggest-vardyquake)
  • The founding year of the team: 1884
  • The capacity of King Power Stadium: 13,262.
  • Age of King Richard III as at today. The King was discovered in the car park by University of Leicester academics and the team has achieved success since the reburial: 563

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Summing it up

Hence the sum of the three components is 4.40, and we can plug this in the formula to obtain the exponential of this value which at 81.45 can be rounded down to 81.

Dominic said: “Working this out was easy peasy but the traditional disclaimer must apply here - this was meant just as a fun exercise with some major stats.”

Jeremy added: “We look forward to welcome European teams to the city of Leicester as well as students to work on actual prediction models.”

Ends

Notes to editors:

For interviews with Dominic Cortis, please email: dc156@le.ac.uk

Twitter handles:

@domcortis

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