Three Points for a Win in Soccer: Is It Fair?

• Activity Number: 154
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Sports
• Author(s): Marcus Thuresson and Johan Bring*+
• Companies: Statisticon AB and Statisticon AB
• Keywords: Soccer ; Simulation ; Scoring system ; Fairness ; Poisson

Abstract

In the season 1981-82, England changed the rules in its soccer leagues. A victory was now rewarded with 3 points instead of 2 points. During the next 15 years, the rest of the world followed England's model. The choice of scoring system can effect which team will win the league, e.g. in the season 2006-2007, Barcelona would have won the Spanish league instead of Real Madrid, if the 2-point scoring system had been used. We present a simulation study that investigates the correctness with the 2- and 3-point systems. The assumptions in the simulation study are based on data from the major European soccer leagues. In the simulation model, we assumed that the number of goals scored by a team in a match followed a Poisson distribution with pre-specified scoring intensities. We use three different measures to evaluate the correctness: correlation between intensities and ranking, the probability that the best teams qualify to the UEFA Champions' League, and the probability that the worst teams will be relegated. The results showed a small advantage for the 2-point compared to the 3-point system. In addition the results show that 380 games per season are too few to do justice.