On the convergence of the Elo rating system for a Bernoulli model and round-robin tournaments

Adrien Krifa , Florian Spinelli , Stéphane Junca (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

This report deals with limit properties of the Elo rating system. It is commonly believed that 30 games are enough to accurately rank a player but it is not always the case [1]. The Bernoulli model is first presented for 2 players. Then we'll study the N > 2 players case by numerically simulating Round-robin tournaments between the players. In all the case the Elo rating system correctly sorts people's strength.

Mots clés: AMS Classification: 60J20; 91D30 Ranking; Elo; rate; Markov chain; law of large numbers; ergodicity; least squares

Domaines: Equations aux dérivées partielles [math.AP]

Adrien Krifa, Florian Spinelli, Stéphane Junca. On the convergence of the Elo rating system for a Bernoulli model and round-robin tournaments. [Research Report] Université Côte D’Azur. 2021. ⟨hal-03286065⟩