Would you like to know will your favourite team win the next game? And what the result will be? Well, mathematics has the answer and it is surprising.
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Football is a game full of surprises and lucky or unlucky breaks. After all, if it was easy to predict the winner of a match, there wouldn't be much reason to watch it. But a team of scientists says that football is actually a simple match in statistical terms. To demonstrate, they have derived a function that can predict the expected average outcome of a match in terms of the goal difference between the two competing teams.
As the scientists explain, a football match is equivalent to two teams throwing dice. Rolling a 6 means "goal", and the number of attempts of both teams is fixed at the beginning of the match, reflecting each team's fitness in that season. The higher its level of fitness, the more chances a team has to score a goal.
How to determine each team's fitness level is the main task of the scientists' analysis. To do this, the researchers analyzed data from all football matches in the German Bundesliga between the 1977-'78 season and the 2007-'08 season. In that league, every team plays 34 matches per season.
Based on the data, the scientists characterized team fitness as the goal difference within a game averaged over a season (in other words, the difference between number of goals scored and allowed by a team). The scientists' analysis showed that goal difference is an even bigger influence on team fitness than the number of goals. In addition, based on previous results, the home advantage could be taken into account by a team-independent but season-dependent constant. Overall, the researchers found that a team's fitness level remains constant throughout the season, although it changes between seasons.
Using team fitness values, the scientists derived a formula to estimate the expected value of the goal difference in a particular match. The actual number of goals in a match (just like rolling dice) could be described as Poissonian processes: the events occur randomly and, for the most part, independently of each other. Taking all analyzed matches into account, the goal distribution determined in this way agrees almost perfectly with the actual data.
The three key results are: the observation of constant team fitness during a season, the derivation of an equation which predicts the average outcome of a match, and the observation that the actual goal distribution can be very well described by a Poisson distribution, scientist say.
What does it mean in plain English? Although the researchers' equation was accurate in many areas, the researchers found that it became less accurate in cases where the goal difference was one or zero. Specifically, in the real data, there were more ties than predicted by the equation, and fewer one-goal differences.
As the researchers note, there are other random effects that influence goals. These effects include temporary injuries, fatigue, weather conditions that favour one time over another, red cards, and the probability of scoring a goal is increased when a team has already scored one or more goals in that game.
So, if you use the best mathematical and statistical methods there are still many unknown factors which make every match so exciting and unpredictable. ■