Chess is an interesting game for artificial intelligence research and an entertaining hobby and sport for a growing number of people. However, humans differ greatly in their ability to play. Typically, the Elo rating is used to determine a player's skill and to predict who will win. When differences in Elo are too great the weaker player is almost guaranteed to lose. While on one hand, the Elo rating allows players to be matched to equally well-playing opponents, it also to some degree restricts the games to be played between equally strong opponents since otherwise the result is known beforehand. Here a handicap system where stronger players remove pieces at the start of the game is evaluated. Specifically, the effect each removed piece or combination of pieces have on a player. Interestingly, pieces do not always reduce the Elo of a player by a predefined amount, but their effect depends strongly on the player's current Elo. The results presented here are from playing the computer engine Stockfish because data about humans playing this scheme is limited. However, the results make direct predictions about the effect of piece removal on Elo.

This work studies how the Elo rating system can be applied to score-based sports, where it’s gaining popularity, and in particular for predicting the result at any point of a game, extending its statistical basis to stochastic processes. We derive some new theoretical results for this model and use them to implement Elo ratings for basketball and soccer leagues, where the assumptions of our model are tested and found to be mostly accurate. We showcase several metrics for comparing the performance of different ratings systems and determine whether adding a feature has a statistically significant impact. Finally, we propose an Elo model based in a discrete process for the score that allows us to obtain draw probabilities for soccer matches, and has a performance competitive with alternatives like SPI ratings.