Elo, I Love You Won’t You Tell Me Your K

Abstract

Elo is a rating schema used for tracking player level in individual and, sometimes, team sports, most notably – in chess. Also, it has found use in the area of tracking learner proficiency. Similar to the 1PL IRT (Rasch), Elo rating schema could be extended to serve the most demanding needs of learner skill tracking. Elo’s advantage is that it has fewer parameters. However, the computational efficiency side of the search for the best-fitting values of these parameters is rarely discussed. In this paper, we are focusing on questions of implementing Elo and a gradient-based approach to find optimal values of its parameters. Also, we compare several variants of Elo to learning modeling approaches like Bayesian Knowledge Tracing. Our results show that the use of analytical gradients results in computational and, sometimes, statistical fit improvements on small and large datasets alike.