Lecturer's maths model simulates Euro 2012 final

Research news

Friday 29 June 2012

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Spain is the team most likely to score first in Sunday’s UEFA European Football Championship final, but Italy has more chance of following up a successful strike with a second and third goal.

That is the prediction of a group of academics from Coventry University and the universities of Heidelberg, Mainz and Leipzig, who have devised a mathematical model which takes into account national teams’ goal scoring tendencies in international tournaments dating back to 1968.

The researchers have used historical data (which is weighted towards more recent championships) to calculate a team’s initial scoring probability, before calculating if – and by how much – each goal increases or decreases the chance of that team scoring again.

Spain, according to these ‘goal distribution’ statistics, is more likely to score first against Italy – but historically it is weaker than Italy when it comes to translating a goal into an increased probability of scoring again. This increase or decrease in probability is referred to by the researchers as the ‘football fever’.

The football fever factor can also be affected by a number of outside influences, from a country’s cultural or political circumstances to whether they are playing at home or away – although in the case of Sunday’s final, both teams will be away.

Overall, the data indicates that Spain is the team most likely to win Sunday’s final.

Dr Martin Weigel, an academic in Coventry University’s Applied Mathematics Research Centre and one of the creators of the model, said:

Rather than simply looking at the teams’ recent form, which is what the pundits will be doing ahead of Sunday’s final, we’re trying to offer a rather different perspective on what might happen in the match based on in-depth statistical trends over a number of years. By analysing the whole tournament, we take into account not only the individual strength of each team, but also which teams have less chance of reaching the final due to the calibre of the opponents they need to beat on their way.

It actually raises some interesting talking points – for example, why is the Spanish team less likely than Italy to get a morale boost from a goal? This would hint at them being very efficient at becoming more defensive to protect their advantage – a skill traditionally associated not with the Spanish, but rather with the Italian system of the ‘Catenaccio’.



Some of the more interesting trends emerging from the academics’ analysis of past data include the following:

  • Spain, despite having the highest initial probability of any team in the Euro 2012 championship of scoring a goal (2.6% per minute), does not improve its scoring chances with each goal scored – in fact, at 0.8 the statistics indicate that their chances of scoring reduce by 20% after each goal.
  • Host nation Ukraine is the least likely team to score initially (the probability being around 1.3% per minute), though if it does score a goal its chances of scoring again are increased by 34% which is more than most other teams.
  • England has a high initial chance of scoring (around 2.2% per minute), but the increase in scoring probability after a goal is just 6% – one of the lowest in this tournament.


The mathematical model was also used to calculate the probability of any given team winning at each stage of the Euro 2012 tournament.

Ahead of the qualifying stages, Germany had the highest probability of winning based on historical data, followed by the Netherlands and Croatia. Entering the last eight, Germany still had the highest chance of winning, but the Czech Republic and France emerged as the second and third strongest contenders.

England’s probability of winning was at its highest point after the first quarter-final in which the Czech Republic was knocked out by Portugal – the researchers’ model indicated that Roy Hodgson’s squad had a 15% chance compared with Germany’s 26%.

How does it all work?

The researchers use the ‘goal distribution’ data to simulate a 90 minute game between combinations of national teams – in this case, Spain versus Italy. Simulations are based on a given team scoring with a probability ‘p’ per minute, with ‘p’ increasing or decreasing after each goal depending on how likely a team is to score again. Click here for further details.

For more information, please contact Alex Roache, External Press & Media Relations Officer, Coventry University, on 024 7679 5050 or email alex.roache@coventry.ac.uk.