Get to know the rating system in the model Glicko vs Elo Get to know the rating system in the model Paritosh Walvekar Akshay Chopra

Elo Rating System

What is Elo? Named after its creator Arpad Elo, a Hungarian-American physics professor. The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess.

General Idea Everybody gets a number which is used by system to predict the odds of the player beating the other player based on difference between the player’s number and that of someone else.

If a player wins a game, he is assumed to have performed at a higher level than his opponent for that game. Conversely if he loses, he is assumed to have performed at a lower level. If the game is a draw, the two players are assumed to have performed at nearly the same level.

Major Assumption The central assumption was that the chess performance of each player in each game is a normally distributed random variable. Although a player might perform significantly better or worse from one game to the next, Elo assumed that the mean value of the performances of any given player changes only slowly over time.

Elo waved his hands at several details He did not specify exactly how close two performances ought to be to result in a draw rather than a decisive result.

How to compute Elo? Notations R-A : Rating of Player A R-B : Rating of Player B E-A : Expected outcome of player A ( Percentage of win) E-B : Expected outcome of player B (Percentage of win) K : Weighing Factor S-A : Outcome of game for player A ( win - 1, Draw 0.5, Loss-0) S-B : Outcome of game for player B R’A : New Rating of player a R’B : New Rating of player b

Steps Involved Finding the E-A and E-B ( Percentage of win) Finding the new rating of both players

Calculating the E-A and E-B Note :

Calculating New Rating

Different Values of K Players below 2100: K-factor of 32 used Players between 2100 and 2400: K-factor of 24 used Players above 2400: K-factor of 16 used.

Issues with ELO Rating Accurate Distribution System Normal Distribution used by ELO does not accurately represent the result achieved particularly by low rated players. Most Accurate K Value Statistician Jeff Sonas believes that if the K-factor coefficient is set too large, there will be too much sensitivity to just a few, recent events, in terms of a large number of points exchanged in each game. Too low a K-value, and the sensitivity will be minimal, and the system will not respond quickly enough to changes in a player's actual level of performance.

Can there be another rating system?

Glicko Rating System

Introduction to Glicko Developed in 1995 by Mark Glickman Currently implemented on the FICS Coincidentally, Elo turns out to be a special case of Glicko Why Glicko? Elo balances out for the outcome Reliability of ratings Situations aren’t so extreme, but you get the intuition! Glicko is a best guess along with an uncertainty measure

Getting Started Rating RD - Rating Divergence Ratings affected with the game outcome RD affected with the game outcome as well as time for which player doesn’t/does play Rating changes after the game is governed by both player’s RD The player has both rating and a rating divergence

How to compute Glicko? Algorithm If the player is unrated, set the rating to 1500 and the RD to 350. These are default reasonable choices, but the RD of 350 in particular can be determined through optimizing predictability of game outcomes (not described here). Otherwise, use the player’s rating from the last period, and calculate the new RD from the RD at the last period (RDold) by the formula...

Can we replace Elo with Glicko? Glicko solves the problem in a different way Communicating how Glicko works is difficult than Elo How to prove if a rating system really reflects the accurate ability? Ratings is a touchy issue! Will the GMs (top 100 players) still remain in the reckoning after we replace Elo with Glicko

Should we really change the ranking system?

Thank you!