Is the "Three points for a win" rule actually efficient ? (Spring 2026)
Three points for a win is a standard used in many sports leagues and tournaments around the world, especially in football/soccer. According to this rule, 3 points are awarded to the team winning a match, with no points awarded to the losing team. If the match is drawn, each team receives 1 point. This rule was not the norm before the 1990’s. Most of the leagues originally awarded 2 points for a win and 1 point for a draw before switching to the new system. The new rule was first introduced in the English Football league in 1981, but became widespread after it was used in the 1994 Football World Cup. The change in the scoring system have resulted in a change of the results in many tournaments. For a recent example, Liverpool’s wait for an EPL title would have cut short by one year in the season 2018-19 under the old rule.
The rationale behind the new rule was to encourage more attacking play when compared to the two points for a win rule, as teams are less likely to settle for a draw if there was a prospect of gaining two points (instead of one) by winning. The second rationale is that it may reduce the chances of collusion among the teams needing only a draw to advance in the tournament or avoid relegation. Other than these justifications, the new (3, 1, 0) scoring rule has no other theoretical background. It is debatable how successful the new (3, 1, 0) rule have been in achieving its objectives in the past three decades since its widespread adoption --- with arguments and counter-arguments from both sides.
The goal of this project is to compare the new (3, 1, 0) rule against the old (2, 1, 0) rule (and possible other variants of these rules) in terms of efficacy. Here efficacy refers to the ability of a tournament to rank contestants according to their true strength. For example, one might consider the probability that the best player/team wins the tournament; see [3] for detailed discussions on different notions of efficacy considered in the literature. This requires the consideration of a probability model for predicting the outcome of the games as well as a framework for modeling the true strengths of the teams. The former objective is achieved by considering some variant of the popular Bradley-Terry model, see [1] for a survey on these probability models. For modeling the true strengths of the teams, see [1, 2] for some popular and useful choices.
Our target in this project can be summarized as follows. We shall only consider round-robin tournaments (as is common in most sports leagues).
Fix an appropriate notion of efficacy. Choose some probability model for true strengths and game outcomes. Simulate tournaments to compare the (3, 1, 0) rule against (2, 1, 0) rule in terms of the chosen notion of efficacy.
Continue with simulations to understand how robust are the comparison results to the change in the probability models.
Perform probabilistic analysis to get theoretical comparison between the two rules in terms of efficacy notion. See [2] for a similar kind of analysis one might expect in this situation.
Consider a general class of scoring systems: (a, 1, 0) where the teams are awarded a points for a win, 1 point for a draw and 0 for a loss, for some a > 1. By simulation / probabilistic analysis, try to optimize the efficacy over the choice of a.
For more information contact Souvik Ray (souvikr@iastate.edu)
People:
Souvik Ray (Postdoc)
Pre-requisites:
Students should have taken at least one proof-based mathematics course.
Some previous exposure to probability theory is required (Math/Stat 3410 or similar courses)
Basic programming experience is required.
References:
[1] David Aldous. Elo ratings and the sports model: A neglected topic in applied probability? Statistical Science, 32:616–629, 2017.
[2] Raphael Chetrite, Roland Diel, and Matthieu Lerasle. The number of potential winners in Bradley-Terry model in random environment. The Annals of Applied Probability, 27(3):1372–1394, 12 2017.
[3] Karel Devriesere, Laszlo Csato, and Dries Goossens. Tournament design: A review from an operational research perspective. European Journal of Operational Research, 324(1):1–21, 2025.