Understanding draws in Elo rating algorithm

This work is concerned with the interpretation of the results produced by the well known Elo algorithm applied in various sport ratings. The interpretation consists in defining the probabilities of the game outcomes conditioned on the ratings of the players and should be based on the probabilistic rating-outcome model. Such a model is known in the binary games (win/loss), allowing us to interpret the rating results in terms of the win/loss probability. On the other hand, the model for the ternary outcomes (win/loss/draw) has not been yet shown even if the Elo algorithm has been used in ternary games from the very moment it was devised. Using the draw model proposed by Davidson in 1970, we derive a new Elo-Davidson algorithm, and show that the Elo algorithm is its particular instance. The parameters of the Elo-Davidson are then related to the frequency of draws which indicates that the Elo algorithm silently assumes games with 50% of draws. To remove this assumption, often unrealistic, the Elo-Davidson algorithm should be used as it improves the fit to the data. The behaviour of the algorithms is illustrated using the results from English Premier League.

OPTIMAL POLICIES IN TWO-STEP BINARY GAMES UNDER SOCIAL PRESSURE AND LIMITED RESOURCES

In this paper, we propose a model where binary games with many players are implemented at two subsequent dates. An external authority sets incentives to maximize the gain deriving from the project. We show that the interplay between the optimal participation shares at the two subsequent dates makes the optimal strategy nontrivial and, to some extent, unexpected. As an application, in the context of an insurgence muting into an armed rebellion, we study the emergence of escalation effects when many actors interact taking into account social recognition.