Chess Ratings - How They Work

  • erik
  • | Aug 23, 2007
  • | 243599 views
  • | 516 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

    Scarbrow

    The About .com link is broken.

    The Glicko system link redirects to http://www.glicko.net/glicko.html

    Please update the links

  • 4 weeks ago

    pranavkeshav

    Thanks, totally get it!

  • 3 months ago

    pikachu11

    Thank you,erik!

  • 3 months ago

    notabjoe

    so what is a high number

    mine says 56

  • 4 months ago

    jimmyschlitz

    why is everybody starting with 1200? is that average rating on this web site? what is the average chess rating among general population….if,  by any chance, it is possible to know this cause not everyone plays chess ….but, anyways, is 1200 average rating on this web site? is this why everyone starts with 1200?

  • 4 months ago

    jimmyschlitz

    cusanusnicolas wrote:

    Still don't know if my rating tells how smart I am. Or stupid! Probably better off not knowing! haha

    i think that one can't be good chess player if his/her IQ is low, but nevertheless you can have the high IQ and be the bad player (if your thinking patterns are not in tune with chess).

  • 4 months ago

    Collin1965

    Rating... Tell me. If I step out of a tournement, coz decided to play less matches, does it make me a worser player than before? If I lose a game, does it make me a worser player than before? So why is it that I drop in rating? I think rating sucks, and does not say anything about how good a player is in chess. I met a lot of players on line of who I think are better than their rating, and the other way around. And that is a pitty. Especially when you want to play tournements.

  • 4 months ago

    LegoPirateSenior

    @cyadvert -- with the amount of games played here, analyzing their quality would be prohibitively expensinve, even with cheapest computing time that could be bought in bulk from Amazon.

  • 4 months ago

    cyadvert

    Am I understanding correctly, that the rating calculation bases only on qty of games and rating of the opponent?

    Shouldn't there be any analysis of the game played?

    What if I won an opponent 200+ rating higher than mine only because he blundered? Or I beat a guy regardless of his rating, but the game I played had no mistakes, all brilliant moves (I wish )?

    Should't the game quality affect rating?

  • 5 months ago

    jimmyschlitz

    why is everybody starting with 1200? is that average rating on this web site? what is the average chess rating among general population….if,  by any chance, it is possible to know this cause not everyone plays chess ….but, anyways, is 1200 average rating on this web site? is this why everyone starts with 1200?

  • 6 months ago

    WeRfriends

    cannot find the resign button. Any idea?

  • 6 months ago

    bravegrape

    play games

  • 6 months ago

    soldierjoe3446

    i want to be rated not unrated,how do i do that?

  • 7 months ago

    SpankYoHiney

    btw, wouldn't it be appropriate to have displayed the formula?

  • 7 months ago

    SpankYoHiney

    LeenvdBijl makes a good point.  many games are lost by only a few seconds even though you were spanking hiney!  This is very relevant to me because I'm older and my hand won't keep up with my brain sometimes.  Also, many of us have shaky internet quality, which contributes mostly to our loses.  So, if you have bad internet quality like I currently do, you can be comforted that your actual rating is a bit higher! (lol, i'm being more humorous than serious btw)

  • 8 months ago

    sober10

    How do I avoid playing "unratted" players?

  • 9 months ago

    Poemander

    When two people play chess with each other, one factor concerning their relative strength alone can be measured . Probability? Two gents over six months play every day and one wins two games per loss. A real rating, mathematically derived, would cause ratings to converg over time such that a rating difference implies a probability. The hyperbolic tangent curve, translated and scaled, should represent the relationship between a rating difference and a probability. What more is needed. The asymptotic nature of the curve, at exponential rate, truly depicts the impossibility of greatly mismatched players causing an upset. ELO ratings are linear, not logarithmic, and therefore create inconsistent results. Statistical bandaides do not heal shaky foundations. FIDE seems to have hoped for 10 years that a better theory may emerge. The real mathematics will be derived directly from a consideration of probabilities and the hyperbolic tangent curve. This hypothesis can be contested in practice using a derived theorem:

       If A wins m points per loss against B, and B wins n points per loss against C, then A wins mxn games per loss against C.

     Note that this may be taken as hypothesis and the hyperbolic tangent then derived, but it well explains the novice's chances against the World Champion!

  • 9 months ago

    LeenvdBijl

    I have a problem with higher rated opponents timing out. My rating goes up even though I was losing. Why does chess.com not simply adapt ratings according to the standing of the game at the point of time out??

  • 10 months ago

    bluefirex24

    Is there a site/artical on the statiscitcs on the players average elo on chess.com? How many people on chess.com have a Elo of 900, or how many players out there have 2400 elo? I currently have an Elo 1360 in "Standard" and I want to know where I stand in this ratio.

  • 11 months ago

    MarcoBR444

    I found a very interesting site:

    See the new thread I created below

     

    Find your REAL ELO rating: ELOMETER.NET then post here the results

    http://www.chess.com/forum/view/general/find-your-real-elo-rating-elometernet-then-post-here-the-results

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