Youtor
The Elo Rating System for Chess and Beyond
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=AsYfbmp0To0
The Elo Rating system is a method to rate players in chess and other competitive games. A new player starts with a rating of 1000. This rating will go up if they win games, and go down if they lose games. Over time a player's rating becomes a true reflection of their ability - relative to the population. • My video was mostly based on A Comprehensive Guide to Chess Ratings by Prof Mark E Glickman http://www.glicko.net/research/acjpap... • Below are some of the things I wanted to talk about, but cut so the video wasn't too long! • Some explanations of the Elo rating system say it is based on the normal distribution, which is not quite true. Elo's original idea did model each player's ability as a normal distribution. The difference between the two players strengths would then also be a normal distribution. However, the formula for a normal distribution is a bit messy so today it is preferred to model each player using an extreme value distribution. The difference between the two players strengths is then a logistic distribution. This has the property that if a player has a rating 400 points more than another player they are 10 times more likely to win, this makes the formula nicer to use. Practically, the difference between a logistic distribution and the normal distribution is small. • Logistic distribution on Wikipedia https://en.wikipedia.org/wiki/Logisti... • We replace e with base 10, s=400, mu=R_A - R_B and x=0 in the cdf. • For the update formula I say that your rating can increase or decrease by a maximum of 32 points, and I said there was no special reason for that. This value is called the K-factor, and the higher the K-factor the more weight you give to the players tournament performance (and so less weight to their pre-tournament performance). For high level chess tournaments they use a K-factor of 16 as it is believed their pre-tournament rating is about right, so their rating will not fluctuate as much. Some tournaments use different K-factors. • In the original Elo system, draws are not included, instead they are considered to be equivalent to half a win and half a loss. The paper by Mark Glickman above contains a formula that includes draws. Similarly the paper contains a formula that includes the advantage to white. • Another criticism of Elo is the reliability of the rating. The rating of an infrequent player is a less reliable measure of that player's strength, so to address this problem Mark Glickman devised Glicko and Glicko2. See descriptions of these methods at http://www.glicko.net/glicko.html • On the plus side, the Elo system was leagues ahead of what it replaced, known as the Harkness system. I originally intended to explain the Harkness system as well, so here are the paragraphs I cut: • In the Harkness system an average was taken of everyone's rating, then at the end of the tournament if the percentage of games you won was 50% then your new rating was the average rating. • If you did better or worse than 50% then 10 points was added or subtracted to the average rating for every percentage point above or below 50. • This system was not the best and could produce some strange results. For example, it was possible for a player to lose every game and still gain points. • • This video was suggested by Outray Chess. The maths is a bit harder, but I liked the idea so I made a in-front-of-a-wall video.
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