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Chess Ratings - How They Work

  • erik
  • | Aug 23, 2007
  • | 148525 views
  • | 489 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 days ago

    mitto

    thanx for replying to our chess cares ! important  article

  • 4 weeks ago

    CharlesRoberson

    For those of you that think it is not bad, ask yourselves why the inventor has publically stated that it is flawed and he went on to invent two or more new systems to replace it. Just look it up. It is all documented online.

  • 6 weeks ago

    spradip

    I think glicko system is not bad its more efficient

  • 6 weeks ago

    spradip

    I think glicko system is not bad its more efficient

  • 6 weeks ago

    spradip

    I think glicko system is not bad its more efficient

  • 6 weeks ago

    spradip

    I think glicko system is not bad its more efficient

  • 6 weeks ago

    spradip

    I think glicko system is not bad its more efficient

  • 7 weeks ago

    Punky81

    Charles,

    I don't think that effect really matters after the first handful of games are played. I always have the same number of points on the line for each game I play, so I would in fact start and end with the same rating in your example. This is because the points on the line for each game seem to be rounded to an integer value, so small RD changes are truncated.

  • 8 weeks ago

    CharlesRoberson

     The biggest problem with the first Glickman system which is used here is that is automatically deflationary. Deflationary systems are bad. 

      Here is the proof.

    In a normal system: Lets say you play a person 200 points below you. You are expected to win 3 of 4. You lose the first game and win the next 3. With a normal system, you will end up with the same rating that you started with. 

      With the first Glickman system (used here), the RD value drops with each game and you end up with a rating below your starting rating. Thus, the rating system used here is deflationary which means all ratings of participants that are holding steady in their playing strength will drop over time.

      I don't know why Chess.com and Freechess.org continue to use this system when it is clearly bad and has been abandoned by its author. Mr. Glickman has created newer versions of his sytem that solve that problem and admits that in his first system he forgot to include the concept of "practice makes perfect". He only included "practice makes you consistent" which means the more you play the more your rating should stay the same.

      This is not how people actually perform. There is lots of data on the net showing that people start getting consistent then gain a noticable strentgh boost and become inconsistent again. Then, the process repeats. Thus, real life is practically the opposite of the first Glickman system.

  • 8 weeks ago

    CharlesRoberson

    Jimmy, 

      How you lose doesn't matter to the rating system. It only cares if you win, lose or draw.

  • 8 weeks ago

    jimmyschlitz

    i cant be bothered going into the details, i play chess and watch youtube at the same time, i am complete amateur...but, please, tell me just one thing about ratings: is it better to resign when i am sure to lose, or play to the bitter end? will my rating go down faster if i am check mated more often, or will it go down faster if i resign more often?

  • 4 months ago

    Mariodude99

    my rd is 34

  • 4 months ago

    peppapig4

    hmm

  • 4 months ago

    Salvatore_Perciante

    Really a nice article!

  • 5 months ago

    immune_2_karma

    "theoretical" pat for this "theoretical" articleCool

  • 5 months ago

    Punky81

    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.

  • 5 months 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.
  • 5 months 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 months ago

    Punky81

    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 months ago

    ChessGodExtreme

    Good stuff !

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