IB Extended Essay — Chess Rating Systems
Evaluates Elo vs Glicko for how well ratings reflect chess performance, focusing on expected score, rating deviation, and responsiveness.
Research question: To what extent do the Elo and Glicko rating systems reflect a player’s performance in chess?
Overview: The essay analyses Elo’s normal-distribution premise (σ≈200) to derive draw probabilities and expected scores, then reformulates expected score as a logistic curve based on rating differences (≈400 points ≙ 10× odds). It contrasts this with Glicko’s introduction of rating deviation (RD) and update dynamics (constant $c$, RD bounds), showing how uncertainty and game volume affect rating adjustments.
Highlights
- Derives intersection area of two normal distributions to interpret draw likelihood at a given rating gap.
- Recasts Elo expected score into logistic form $E_A = \frac{1}{1+10^{(R_B-R_A)/400}}$.
- Explains Glicko’s RD, its growth via constant $c$, and how RD contracts with recent results, yielding more responsive ratings.
Special thanks to Dr. Mark Glickman for responding to my inquiry about his Glicko rating system and sharing valuable insights.