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Chess Ratings - How They Work

  • erik
  • | Aug 23, 2007
  • | 149236 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


  • 23 months ago

    driv4r

    That's impossible.

  • 23 months ago

    fluffydinos

    I won a game and lost 300 elo is this a bug?

  • 24 months ago

    Nick987987

    One problem with the rating system is this: I often sit in the evening playing online chess in the bar drinking beer. At the beginning of the evening I will probably be playing close to my best. By the end of the evening I will be making the most elementary blunders!

  • 24 months ago

    shatrange_baaz

    What is the calculation at the begining which came to 150?

  • 2 years ago

    Timothy_P

    I just read the glicko system article and can see why it would be difficult to do by hand!

  • 2 years ago

    ticad02

    I don't understand any rating system and I don't want to.  I just want to know that there is one and that everyone I am playing is on the same rating system.  I wish this site used a system that was more used world wide, but it sounds like this one may end up being one that is.  I haven't played very many games here, but my rating is around what it was on another site where I played many games.  In a nutshell, if you beat someone that sucks its not as big a win as it you beat someone good, and vice verse with losses.  Having the same number of points for a winning game is rather stupid, since beating someone better should be worth more than beating a lesser player.  After all, you don't get the same sense of accomplishment when you beat a 3 year old in a foot race (assuming your at least a teenager or adult) versus beating a current Olympic Gold Medalist Sprinter.  If you do you are quite sad.  ENJOY CHESS!

  • 2 years ago

    peppapig4

    @ krunalgohil19 okay..i will try that..cheers ! :)

  • 2 years ago

    krunalgohil19

    @nen:go to live chess

  • 2 years ago

    peppapig4

    [COMMENT DELETED]
  • 2 years ago

    Divergentt

    Thanks CharlesRoberson , I just checked rated and unrated games, most were unrated, so I know now why my rating was not moving.

    Thanks a lot for the answer.

  • 2 years ago

    CharlesRoberson

    black-horseltu,

       sounds like you play some rated games and some unrated games. check the details in your game archive: home->game archive.

  • 2 years ago

    Divergentt

    My rating is not moving. Currently I won few games and lost one. Apparently loss was counted and wins no!!! What is going on?

  • 2 years ago

    driv4r

    What you mean jajr??

  • 2 years ago

    jajr

    why my rating don"tmove?

  • 2 years ago

    krunalgohil19

    @jhorlock:yeah......i understand......thanks......

  • 2 years ago

    jhorlock

    @Mr_Norm

    I think you have missed something fundemental in your understanding of the bell shaped curve.  Assuming there are 10,000 people online at any one time (and without doing exact calculations) If you are at the 95th percentile and you search for people +400 then there will be in the region of 475 better players than you available to play against, however, you are also searching for -400 of which there will be in the region of 5500 people. Thus if you get to play someone better than you once every 10 games you will be doing extremely well.  If you are at the 95th percentile you need to a much smaller lower search.  Try searching 400 above and 40 below - even with this you could still face similar problems (all depends on the standard deviation of the gausian curve).

     

    @krunalgohil19

    I would assume your rating goes down if you draw when you should have won.  If you are a grand master and yet you can only draw against a 3 year old then essentially you are not a grand master and you rating needs to drop considerably.  Equally if as a regular punter on here, I was able to get a draw against a grand master then I would seriously hope my rating would leap up.

  • 2 years ago

    krunalgohil19

    yeah may be you are right....driv

  • 2 years ago

    CharlesRoberson

      I have 30 years of programming experience. It is easy to fix their rating system. Just set the minimum impact of the RD so that two equally rated players gain no less than 16 rating points from a win.

     That gives you the ability to raise your rating when you play often and still sets your rating change higher after you've taken time off.

      Mr. Glickman has created two newer system to address the issues in the older system.

      Look at this to see that one of his two newer systems addresses the issue of a person with a low RD actually improving which isn't cover in system #1: http://www.glicko.net/ratings/glicko2desc.pdf

      As I stated a simple fix to system #1 is to set a minimum RD such that one gets a minimum of 16 points for a win against another person of equal rating.

  • 2 years ago

    driv4r

    Because your opponent has lower rating than you, no?

    I bet I sound like Mr Obvious now Laughing

  • 2 years ago

    krunalgohil19

    when a game is drawn......why my rating goes down?????

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