An enhancement of the Glicko-2 algorithm applied to matchmaking in chess games

ABSTRACT: This study aimed to enhance the Glicko-2 algorithm by improving its responsiveness to rating updates, addressing consecutive draws, and applying correct inactivity penalties. Three key issues were identified: (1) reliance on rating periods, which delays updates and reduces matchmaking fairness and accuracy; (2) failure to account for consecutive draws in rating deviation (RD) calculations; and (3) poor handling of inactivity. To address these, the following solutions were implemented: (1) Real-time updates using provisional ratings that updated after every match until the end of the rating period, resulting in players being matched based on their real-time ratings. (2) Consecutive draws were classified using a Hidden Markov Model (HMM) to refine RD calculations. (3) The RD penalty was adjusted based on the simulated RD decrease and also considered the length of each period to give a more accurate rating when the player returned. Results on both single and multiple simulations demonstrated the enhanced algorithm’s effectiveness. (1) Real-time updates enabled real-time matchmaking, with accuracy improving from 38.22% to 86.32% across 100,000 simulations, averaging a 5.31% improvement in rating (553.41 (±0.27) to 582.79 (±0.44). (2) Consecutive draws increased RD by 5.10% across simulations (63.73 (±0.00) vs 67.16 (±0.20)). This led to a 4.24% rating improvement overall (377.04 (±0.65) vs. 361.70 (±0.79)), all achieved with an HMM Accuracy over Performance State of 92.23%. (3) Enhanced inactivity handling resulted in a 25.37% increase in the Average Mean Rating Deviation (502.0286 ±1.7907 vs. 629.6958 ±2.3192), along with a significant rise in Average Captured RD Change, from 6.56% (±0.14%) to 91.41% (±0.06%) in simulated RD increase. The enhanced Glicko-2 algorithm improved matchmaking, addressed consecutive draws, and applied more accurate inactivity penalties, leading to more precise rating assessments.

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