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Chess Ratings - How They Work

  • erik
  • | Aug 23, 2007
  • | 149555 views
  • | 490 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


  • 9 months ago

    pfred42

    Go down 2 from there to ohpunky81, 2nd paragraph.  Says beginning.  Perhaps chess.com can tell us.

  • 9 months ago

    LegoPirateSenior

    @pfred42 -- look 9 posts down from yours for the answer.

  • 9 months ago

    pfred42

    Thanks for the reply.  But from other posts I read it sounds like the points for W/L/D are set by the opponents' (and your own for them) rating at the date you start.  Is that true or are the points a moving value as you play?

  • 9 months ago

    spanishfly25

    yes, you get the same amount of points, no difference.  only problem when is you win due to time and your opponent was playing 50 games. his rating would decrease very fast and you probably would not get that many points. 

  • 9 months ago

    pfred42

    Are the points one gets for a win the same whether the win is by mate, resignation or time?

  • 9 months ago

    hettor

    Guru_2, i´ve seen that depends of the rating of your opponent, if you play and win against a player with a higher rating than yours you will get very good points, but if you lose you won´t lose much; the other is, if you play and lose against a player with a lower rating than yours you will lose a lot of points, but if you win you´ll get a few points. It must be a tab in some place, i´ll try to find it and share ...

  • 10 months ago

    Punky81

    Potential changes to rating are stated in the chat box at the beginning of each game. It's the line that says, "win +8, draw 0, loss -8" or something similar.

  • 10 months ago

    pbeckett

    Guru_2,you have played many blitz games.Your strength seems fairly constant,so you only gain /lose 2 pts or so per win/loss.

    Don't think of ratings as a measure of your worth as a human being!

    They are a tool to ensure you get a good match with a fairly equal opponent

  • 10 months ago

    Guru_2

    Please help in understanding, how many points will be acquired or deducted in case of win or a loss respectively? ( In 10!0 game)

  • 10 months ago

    spanishfly25

    thanks.

  • 10 months ago

    LegoPirateSenior

    @spanishfly25  - at the end

  • 10 months ago

    spanishfly25

    I am sorry, I don't feel like reading all the post and the many pages to see if anyone ask my question so here I go again, does anyone in here know if a rating is calculated base on your rating at the begining of the game or at the end of the game,  example at the begginning of the game, I am at 1600 and playing at guy with a rating of 1400, but after 3 months, our ratings are now at 1500, and if the game was going to end now.  would the rating adjustment would be done base on the  1600-1400 rating or the 1500 rating.

  • 10 months ago

    Punky81

    jjpbetterboy, if your opponents rating changed 100 points that quickly, it seems like they fall in the category of new players. In the article, it mentions how their rating will change quickly because the system recognizes that there is a lot of uncertainty in their rating. However, your rating changes less when playing these opponents because of that same uncertainty.

    Also, the rating is based on the rating at the beginning of a game based on the fact that at the beginning of every game it tells you in the chat box exactly how much your rating will change for a win, draw, and loss.

  • 10 months ago

    pbeckett

    play several games

    don't stop playing

    play people with a similar rating,

    and then all our ratings will be accurate enough!

  • 10 months ago

    jjpbetterboy

    I was wondering the same thing as you IvoryGambit. As I was in the process of losing to my opponent over a few weeks of a long game, his rating increased about 100 points. I would have liked to have known how he learned so much in that space of time, and maybe gotten some credit for his newfound skill.Wink

  • 10 months ago

    IvoryGambit

    C.c.needs to explain whether one,s rating change post game is calculated on the basis of the opponent,s rating at the game start or end.There can be a considerable change in this over the course of a long game,significantly altering one,s own rating change,win or lose.

  • 10 months ago

    Firdiansyah

    ok

  • 10 months ago

    whitepawn1

    I have just lost by checkmate my opponent was rated as 858 after the game his/her rating grew to 918 yet the game was 4 point loss to me so surely it should have been only a 4 point increase to the winner

  • 10 months ago

    42rick42

    Still doesn't explain how I can be challanged, make a move, and get 0 pts. on a resignation! What the heck! An early exit shouldn't be worth less points than a win and a draw should be worth something. It is the inferior system, having played both (USCF active in the '80s) that

    And really, would it kill you to add spell check to this site? I don't know anybody still in this situation...unless you want us all to look like English is our second language!

  • 11 months ago

    GiridharaRaam

    that was really useful

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