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Chess Ratings - How They Work

  • erik
  • | Aug 23, 2007
  • | 129213 views
  • | 480 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


  • 35 hours ago

    immune_2_karma

    "theoretical" pat for this "theoretical" articleCool

  • 9 days ago

    ohpunky81

    Proxima-Centaurus,

    Ratings for players are calculated independently (there is no law of conservation of rating points). If you are a newb, your rating is very uncertain, and therefore swings up or down quite drastically until it settles on an accurate figure. Your opponents rating may be more certain, and therefore it only goes up or down a few points at a time. I tend to have about 8 points on the line for each game because I have played a few hundred games and my playing strength is pretty consistent within about a fifty point rating range.

  • 10 days ago

    backtracking

    As I read, the RD quantifies the uncertainty in terms of probability:

    • The interval formed by current rating +/- RD contains your true rating with probability of about 0.67.
    • The interval formed by current rating +/- 2 * RD contains your true rating with probability of about 0.95.
    • The interval formed by current rating +/- 3 * RD contains your true rating with probability of about 0.997.
  • 13 days ago

    proximus-centaurius

    I just played a game and my rating jumped +77, but only took half as much from my opp.  Where did these extra points come from?  The Federal Reserve?  Printed out of thin air?

     

    My other rating was suffering due to the ads, making my slow computer lag even more, so I increased the time to 5 min 15 sec, even tho i'm a yahoo 1 min 5 sec player.

  • 6 weeks ago

    ohpunky81

    If you think you're real rating is higher, then play opponents with the rating you want. If you beat them, your rating will jump dramatically. If you lose to them, then maybe your rating was right to begin with. You will also learn more from tougher opponents.

    Ashesandembers, it's probably based on the last game you played. I see your bullet rating.

  • 7 weeks ago

    ChessGodExtreme

    Good stuff !

  • 8 weeks ago

    ReedSorensen

    A confidence interval isn't a measure of how "confident" or "sure" you should feel. It's the range that has a 95% probability of including your true rating, based on whatever model you're using to estimate people's ratings (Glicko in this case).

  • 3 months ago

    AshesAndEmbers

    If you want to increase your rating quickly, try playing some games you know you can win while your RM is still high. Then be inactive on online chess for a while. (Play live, do tactics, etc.) But stay active in chess in general. After a few months your RM will be high again, and you can boost it with a few good games.

  • 3 months ago

    Gokuthegreat

    Great, i've been willing to now how the points work since i arrived here, i made my account two years ago but just now i started to use it, so i'm new, anyone has an idea of how can i increase my rating fast? Thanks.

  • 3 months ago

    AshesAndEmbers

    Actually, on Chess.com, it seems to me that everyone is somewhat underrated. My rating is only about 1300, but I can form very good strategies and see up to eight moves ahead (on a good day) I actually had to bring my rating up to where it is from about 950 as a result of me losing my first two games (or so) At first the rating system may seem flawed, and it is to an extent, but the more you play, the more you realize that it's not too bad. Sure, if you wanna get your rating to jump up quickly, you have to wait a while between games, but overall it's okay. There's not much more you can do with a computer-generated rating system. (At least it's better than Mariokart)

  • 3 months ago

    bass-to-mouth

    I Have Been Playing chess for around 10 years now. Im new to chess.com. I feel as if this ranking system is flawed. I find it hard to believe that my ranking is so low. 950 right now. I play people inbetween 1000-1500 and have won games in all of them. The definition of someone with a 1000 rank is someone who is just begining to understand how the peices work and cant form any sort of strategy. I assure i can create many strategies and am having trouble understanding how i can be such a low rank when ive been playing for such a long time. 

  • 3 months ago

    AshesAndEmbers

    Is anyone sure how I can change what rating of mine is displayed when someone rolls over my name? I have a bullet rating of 1400 but my blitz is only 1000 (I don't play it much) I've seen other people with their bullet or online chess ratings displayed.

  • 3 months ago

    ohpunky81

    Not everything that matters can be measured, and not everything that can be measured matters.

  • 3 months ago

    pfred42

    Points awarded for win or taken away for a loss are the same whether mate, resign, or time expired.  Also, support person changed their answer so points awarded for wins/losses are based on the players' ratings at the end of a game.

  • 3 months ago

    TheKrypticHeroSpott

    Do you get less points if the person lets the time run out? Or if he/she resigns?

  • 4 months ago

    LegoPirateSenior

    Both ohpunky81 and the support person are mistaken.

    Observations made by spanishfly25 agree with what I have seen and are consistent with the only way of calculating the ratings that makes any sense.

  • 4 months ago

    pfred42

    Interesting!  And not concistent with what their support people say.  I'll run your info past them and see what happens.

  • 4 months ago

    spanishfly25

    I started a game and showed me W+8  L -7 D+1,  I drop rating a little sicne I started the game and the other player increase his rating, the game still going on but now shows W+9 L-6 D+1, so to answer the question when is calculated, is when the game finish. 

  • 4 months ago

    pfred42

    ohpunky81 is correct--ratings change based on the players'  ratings as of the beginning of the game.  From chess.com support, after I queried them: "Glicko [used by chess.com] does it from the beginning."

  • 4 months ago

    BlackLeopard-1

    [COMMENT DELETED]
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