Optimizing K-factor in Elo Rating Systems

Abstract

The Elo rating system measures the relative skill of players of a zero-sum game. It assigns each player a rating that is updated based on their performances against other players and their respective ratings. This research investigates K-factor, a variable responsible for determining the sensitivity of ratings to change. In practice, it is often set heuristically. However, this paper seeks to optimize K-factor by minimizing the expected error between true skill and skill estimated by rating. This paper will address three main questions. Firstly, how should a new player be assigned an initial rating? Secondly, how does the player’s rating accuracy change after each game? Thirdly, what is the long-term accuracy of a player’s rating after many games? Evidence for the theoretical results obtained will also be shown through Monte Carlo computer simulation.

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