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Chess Ratings - How They Work

  • erik
  • | Aug 23, 2007
  • | 137163 views
  • | 483 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

    CharlesRoberson

    black-horseltu,

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

  • 23 months 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?

  • 23 months ago

    driv4r

    What you mean jajr??

  • 23 months ago

    jajr

    why my rating don"tmove?

  • 23 months ago

    krunalgohil19

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

  • 23 months 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.

  • 24 months ago

    krunalgohil19

    yeah may be you are right....driv

  • 24 months 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.

  • 24 months ago

    driv4r

    Because your opponent has lower rating than you, no?

    I bet I sound like Mr Obvious now Laughing

  • 24 months ago

    krunalgohil19

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

  • 2 years ago

    AlexZhang001

    Thanks

  • 2 years ago

    Skeptikill

    if you notice in the thread, it is only very low rated people complaining....

    This is a fair system. It makes sense to me and many people. If you play alot your RD will decrease and if you dont it means there are more uncertain unknown/known factors which mean it is harder for it to determine a rating. Therefore RD increases to allow for this uncertainty. 

    Im going to stop here since it really is just repeating what is above.

    Just keep reading it until you understand it fully or else discuss it with someone who understands it in real life.

  • 2 years ago

    niels5x9

    this articel states that you have one real rating that doesn't go up and down but i get better in playing chess while im am playing frecuently so actually I am Punished for playing frecuently

  • 2 years ago

    PCL91

    I completely agree lads, it is not fair at all!!

  • 2 years ago

    CharlesRoberson

    You are correct, it does penalize you for playing often. There is a simple fix. The staff should modify the code so that it never allows the RD value to drop below a certain point. That value should be one that allows you to get 16 points for winning against an opponent with the identical rating as yours. Allowing the RD to grow during inactive periods is good and letting it shrink as you play is good as long as it doesn't go below the previously stated minimum.

  • 2 years ago

    tennesseebunny

    this rating system is bullshit and frustrating. every game should have a certain amount of points to win or lose no matter who's your opponent. the more you play the lower gets your rd, that's punishment and NOT fair.

  • 2 years ago

    CharlesRoberson

    there are two Glickman systems. Sounds like chess.com is using the first one which has a flaw. Glickman admits this and created the second system to correct it. The flaw with the first system is that it doesn't incorporate the idea of "practice makes perfect". It uses the idea that practice makes you consistent. Thus, if you play often enough and your RD gets low enough, then you can't raise your rating. The only way to raise your rating is to leave the server for a month and let the RD value raise before you play again.

  • 2 years ago

    GM__Sanand

    Good article.

  • 2 years ago

    hueyann

    Rating does matter.It affect my emotion every time I lose my game.

  • 2 years ago

    MichaelDuggan

    How does one calculate their percentile? My rating is usually around 1600 (although, has collapsed lately).  And how do you stop yourself getting frustrated when you lose (which then triggers a losing streak)?

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