New Insights on Football Strategy: Data analysis suggests that wins should be worth more , The most popular sport in the world has more than 250 million players in over 200 countries. Every week he fills stadiums with many more millions. This sport, soccer, is played by two teams of 11 players who cooperate to score goals while preventing their opponents from doing so. For each team, the game can have one of three outcomes – win, draw or lose.
This kind of game is usually part of a larger business of determining the best team. The most common process is a league structure where teams play against each other and are then ranked by results. The winner is the team that leads the standings at the end of the season.
This kind of ranking seems quite easy, but it actually hides some subtle but important questions. Chief among them is the question of the value of victory. In most professional leagues, the answer is that a win is worth 3 times as much as a draw, while a loss is worth nothing, recorded as (3-1-0).
It wasn’t always like that. Before 1981, a win in professional football was worth only two points under the system (2-1-0). So a win was twice as valuable as a draw. However, the sport’s governing body increased the value of winning to increase the motivation to win.
However, these numbers are essentially arbitrary, decided by committee in the (metaphorically) smoke-filled boardrooms of yesteryear. But if winning is the goal, why isn’t it 5 times more valuable than a draw, or 10 times, or 100?
Play to win
And that raises an interesting question. Is there an objective way to determine the value of the profit, and if so, what is its value?
Today we have an answer thanks to the work of Leszek Szczeczinski of the Institut National de la Recherche Scientifique in Montreal, Canada. Szczeczinski has developed a probabilistic model of game outcomes and the rankings they produce.
In this model, there is a free parameter that corresponds to the value of win versus tie. Its idea is to use real-world results from pro football to determine its value. And when he does, the answer, he says, is 5.
Szczecinski’s model is relatively simple. It is based on the idea that teams have inherent abilities that determine whether they will beat other teams. However, this inherent ability is hidden in the real world and can only be determined by repeatedly comparing teams. In other words, by playing games to see who wins.
Also, the games have an element of luck – sometimes the weaker team can win their due. Regardless, the league’s process must ultimately rank teams according to their latent inherent ability.
So in his model, Szczecinski assigns each team a probability of victory that is related to its hidden inherent ability. Teams then “play” against each other with these probabilities determining whether the game ends in a win, loss, or tie.
The question Szczecinski addresses is what scoring system ensures that league rankings best reflect the hidden inherent abilities the process is designed to reveal.
Of course, there’s no way to know the inherent ranking in real life, so Szczeczinski used data from professional soccer leagues since 1981 in England, Germany, and Spain to help calibrate his model.
It turns out that the ideal scoring scheme varies across these leagues. For example, in the English Premier League, perhaps the toughest league in the world, a win is 3.9 times more valuable than a draw. In Spain’s top league, La Liga, which is largely dominated by just two teams, Real Madrid and Barcelona, a win is 7.5 times more valuable than a draw.
A sore spot
“The results show that the nominal football scoring rules do not match the empirical data,” says Szczecinski. Instead, the data shows that the value of a win is close to 5 points.
Of course, Szczecinski acknowledges that changing the win value itself affects the nature of the game. He points out that this is exactly what happened when the football authorities changed the value of a victory from 2 to 3 points in 1981 in England and in 1994 in Germany. At that time, the data showed that the tie was worth nothing and the scoring system should be (1-0-0).
“It seems that the governing body, by introducing the (3-1-0) scoring rule, managed to change the pattern of results: the (conditional) probability of wins is now less than the probability of draws,” he says.
This suggests that further changes should be made with caution. Szczeczinski says this should involve an iterative process – make a change and use the results over time to calculate a new profit value, etc. “For example, the rule might first be set to (4-1-0),” he suggests
The message is that if the purpose of these leagues is to determine the best team, then the scoring system should be based on continuous evaluation of data, not random numbers. An interesting idea, for sure. Five points for a win, anyone?
Reference: Why winning a football match is worth 5 points: arxiv.org/abs/2303.15305