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Chess Ratings - How They Work

  • erik
  • | Aug 23, 2007
  • | 118159 views
  • | 468 comments

Like it or not, we ALL have a chess rating. You may not care at all about your rating, or you may be whining every time it goes down in the slightest. You might be someone who plays a game a year, or someone who plays 1,000 a day. Still, there is a number out there that represents how well you play chess. Well, that's the theory, anyway.

To understand chess ratings you have to understand two things: #1 - that you have a TRUE rating that perfectly represents your strength of play, and #2 - that that TRUE rating will never be known and so we have to use statistics to get as close as possible to the truth. I'm writing this article in response to many people who ask about ratings and need a simple explanation of how they work. (I only know about all this because of a recent super-in-depth statistics course I took and my research in building Chess.com!)

There are two main rating systems, and each one has its merits.

The Elo System (used by the United States Chess Federation, FIDE, and many other online chess sites) is popular for two reason - it has been around for a long time, and it is simple. The idea is this: given two chess players of different strengths, we should be able to calculate the % chance that the better player will win the game. For example, Garry Kasparov has ~100% chance of beating my 4-year-old daughter. But he may only have a ~60% chance of beating another Grandmaster. So when playing that other Grandmaster, if he wins 6 games out of 10, his rating would stay the same. If he won 7 or more, it would go up, and 5 of less, his rating would go down. Basically, the wider the spread of the ratings, the higher percentage of games the higher rated player is expected to win. So to calculate a person's rating after playing a few games you calculate the average ratings of his opponents, and then how many games he was expected to win, and then plug it into a formula that spits out the new rating. Simple enough. Well, it turns out, that is maybe TOO simple.

The Glicko System (used by Chess.com, the Australian Chess Federation, and some other online sites) is a more modern approach that builds on some of the concepts above, but uses a more complicated formula. (This only makes sense now that we have computers that can calculate this stuff in the blink of an eye - when Elo created his system they were doing it on paper!) It is a bit trickier than the Elo system, so pay attention. With the Elo system you have to assume that everyone's rating is just as sure as everyone else's rating. So my rating is as accurate as your rating. But that is just not true. For example, if this is your first game on Chess.com and you start at 1200, how do we really know what your rating is? We don't. But if I have played 1,000 games on this site, you would be much more sure that my current rating is accurate. So the Glicko system gives everyone not only a rating, but an "RD", called a Rating Deviation. Basically what that number means is "I AM 95% SURE YOUR RATING IS BETWEEN X and Y." (Nerd Fact: In technical terms this is called a "confidence interval".) If this if your first game on Chess.com I might say, "I am 95% sure that your rating is somewhere between 400 and 2400". Well that is a REALLY big range! And that is represented by a really big RD, or Rating Deviation. If you have played 1,000 games and your rating is currently 1600 I might say "I am 95% sure your rating is between 1550 and 1650". So you would have a low RD. As you play more games, your RD gets lower. To add one extra wrinkle in there, the more recent your games, the lower your RD. Your RD gets bigger over time (because maybe you have gotten better or worse over time - I'm just less sure of what your actual rating is if I haven't seen you play recently). Now, how does this affect ratings? Well, if you have a big RD, then your rating can move up and down more drastically because your rating is less accurate. But if you have a small RD then your rating will move up and down more slowly because your rating is more accurate. The opposite is true for your opponent! If they have a HIGH RD, then your rating will change LESS when you win or lose because their rating is less accurate. But if they have a LOW RD, then your rating will move MORE because their rating is more accurate.

I wish there was some simple analogy to explain all this, but there isn't. It all comes back to this: you have a theoretically exact chess rating at any given moment, but we don't know what that is and so we have to use math to estimate what it is. There are really smart people out there who work on this stuff for a living, and at the end of it all we get to put their proven methods into our code so that we can all enjoy knowing what little numbers next to our name we deserve.

If you want to read more, check out these articles (WARNING - SEVERE NERD CONTENT AHEAD):

- The Glicko System by Professor Mark Glickman, Boston University

- Introduction to Chess Ratings (Elo mostly) on About.com

Comments


  • 3 years ago

    1plus1is4

    NO, if Kasparov plays with only a king and a pawn than he will only beat your daughter 9/10 times :)

  • 3 years ago

    driv4r

    Schroeder59, I think it's 3 or 4 moves by both players, at least in case of timeouts, so it might be same for resignations.

  • 3 years ago

    Schroeder59

    Is there a minimum number of moves for a game to be rated? E.g. if a player resigns after move 1, will the game be rated?

  • 3 years ago

    -rookie-

    Nice explanation.  Thank you!

  • 4 years ago

    sri301

    hi can u pls say me about ratins really i am confused on my rating......

  • 4 years ago

    driv4r

    I think people cheat here mainly because they want to gain high ratings and to feel good about it, they have low confidence or sth.

    But to lose on time, so that your opponent gains less rating points?? That would have to be some kind of weirdo. And it defo wouldn't be a problem if they didn't know about the difference between rating changes (and they probably wouldn't).

  • 4 years ago

    MikeDoyle

    If people cheat on here, they would certainly do that.

  • 4 years ago

    driv4r

    Well, those who lose could actually still lose same number of rating points, as I said I'm not sure about that. My main point is that winners should gain less. Do you think someone would really intentionally lose on time just to make the winner gains less points?? And I guess they wouldn't know about it anyway, so they wouldn't even think about it Wink

    Anyway, I didn't think about those issues, you mentioned MikeDoyle, before.

  • 4 years ago

    MikeDoyle

    But then, some people, knowing they are going to lose would simply time out on purpose in order to lose less points, and a few would do it so that their opponent would get less points.   There is no good way around that.

  • 4 years ago

    driv4r

    I see. I think it would actually be better if the timeout winner would gain less rating points. Why? Because if you win in this way you don't need to play better than your opponent, you just need to make some moves. Not sure about the rating change of the loser but I guess the loss could also be less severe...

  • 4 years ago

    MikeDoyle

    exactly the same.

  • 4 years ago

    driv4r

    Just wondering: does winning or losing due to a timeout affect your rating more or less severely than winning/losing by checkmate or the rating change is exactly the same?

  • 4 years ago

    Raghav

    Great.Thank's Erik for the information.

  • 4 years ago

    MikeDoyle

    i have a masters in math, so it ain't no thing to me, but to the lay man who has not had all that, it's a "thing." :P

  • 4 years ago

    Tazzyken

    Lol I cover this stuff in 7th form Statistics.

  • 4 years ago

    MikeDoyle

    Agree. Might as well just play some chess.

  • 4 years ago

    RavindraBabu

    Understanding of this rating calculation is like middle game of chess and confusing.

  • 4 years ago

    MikeDoyle

    High Glicko RD due to very few games played?

  • 4 years ago

    phizzer

    how can a 1388 rated player be a 1882 rated player after only three games played

  • 4 years ago

    vernmusic

    how can i change my unrated game to a rated game

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