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Chess Ratings - How They Work

  • erik
  • | Aug 23, 2007
  • | 136927 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


  • 6 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. 

  • 6 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."

  • 6 months ago

    BlackLeopard-1

    [COMMENT DELETED]
  • 6 months ago

    Punky81

    For Live Chess, ratings adjustments are shown in the chat box at the beginning of the game, for example: "Win +8, Loss -8, Draw 0". For Online Chess (Turn-Based) you have to look under the details tab and click on "show rating adjustment". I have never noticed these numbers changing during the course of a game.

  • 6 months ago

    pfred42

    Thanks.  I guess I am incorrect.

  • 6 months ago

    LegoPirateSenior

    @pfred42: suppose a new player with real rating about 1600 joins the site and starts 10 games against established players with 1200 rating. If I recall correctly, the first win will add some 150 rating points.  If this happened in all games, the new player would be now rated at 1200+10*150 = 2700.

    Hence the reason for always using the rating at the end.

    USCF does the same thing, BTW; the ratings are computed iteratively with pre-tournament ratings being only a starting point, then replaced with new proposed rating, then again, until they converge and change no more. At that point, the final post-tournament result are consistent with each other.

  • 6 months ago

    spanishfly25

    as far as I can tell, points are calculated at the end of the game,  and are base on the difference from your own rating. example above if a player has the same rating as you, you get 7 points for a win.  if he has less ranking than you, you get less points  and if he has better ranking than you,  you get more.  now if you have for example 1500 and you play a player with 1600, you can get 9 or 10 points,  but if the same player lose many games due to time, you may only get one point because his ranking may be down to 1300 by the time he lose with you.

  • 6 months ago

    pfred42

    I guess I would disagree.  I would think at the beginning because that is the basis by which one chooses an opponent.  For most players who have been around awhile the change would be small in the short period of time and same for newcomers as they would not have been likely to complete that many other (online) games in that same interval.  For example, I chose an about-equally rated opponent back in January (online game still in progress) whose rating has dropped because he "timed-out" on several games--didn't really lose competitively.

  • 6 months ago

    LegoPirateSenior

    Ophunky is incorrect.

    Rating at the end is always more reliable than at the beginning.  It would make no sense to use the one at start.

  • 6 months ago

    pfred42

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

  • 6 months ago

    LegoPirateSenior

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

  • 6 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?

  • 6 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. 

  • 6 months ago

    pfred42

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

  • 6 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 ...

  • 6 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.

  • 6 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

  • 6 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)

  • 6 months ago

    spanishfly25

    thanks.

  • 6 months ago

    LegoPirateSenior

    @spanishfly25  - at the end

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