Chess rating system

 I don't believe so.  I think I am WAAAAY overrated on here.  I haven't played any live organized event before but cannot imagine I am better than a 1400 and am 1700+ on chess.com for many of the reasons stated (winning on time and withdrawals from tourneys, for example).

No way.

Your wrong. queen is 9. And you forgot king. King = unlimited

dude, I just gained 325 points by winning one game.   Inflated.

(Maybe this is covering old ground I don't know.)

I just got to 1398 in live chess (long), and am in a moral quandary.  Its been a goalpost of mine to get to 1400 for some time, and at this point it would be a simple matter to go find someone rate  200 points lower than me, automatically pick up 4 points or so, and say, "there - I'm a  1400 player now." 

Really, if someone wanted to, they could always only play people rated much lower than them and continually increase their score indefinitely.  That, to me is an inherent flaw in the rating system.  So when I got to 1396 about three weeks ago, I thought,  "If I'm a 1400 player I should be able to beat 1400 players." But then I went into a slide and its taken me this long to regain all the lost ground (playing high 1200 to mid 1300 players primarily.)

But anyway, here's an observation - whatever your rating is, to determine if thats a true reflection of your ability you should be able to win 50% of  games played against opponents rated the same as you. This self-evident fact led me to start devising an alternate rating system a while back.  (It has some flaws in it as well I wasn't able to fully sort out, so I set it aside.)

To state the above principle another way, if by chance you have won exactly 50% of all your games, then your true rating is equal to the average rating of the opponents you have played.  However what is your true rating if you have not won exactly 50% of your games?

Let d = wins-losses

rating system 1:
if d is positive, then remove the d lowest ranked opponents who you beat and recompute average rating of all opponents.
if d is negative, then remove the d highest ranked opponents who you lost to and recompute average rating of all opponents.

rating system 2:
if d is positive, then remove your d earliest wins and recompute average rating of all opponents.
if d is negative, then remove your d earliest losses and recompute average rating of all opponents.

Your true rating would be the average of rating 1 and 2.

There is a slight problem when you first start,  if you have 0 wins or losses.  There's a simple fix but can't remember what it was.  (Also draws were not accounted for but that shouldn't be a big problem.)

A more serious problem is the following.  To implement the above as a global rating system for all players simultaneously, would require that every person be assigned a random rating when first starting,  not 1200.  (Actually the distribution of random rating assignments should adhere to the Bell Curve.)  Also, I think you would always have to be paired with random opponents, not opponents of ratings of your own choosing.

But anyway, I got as far as I could with this.  Don't really have further interest in advocating for it - just something I  came up with (or maybe even someone else I don't know).

Eberulf:

As an alternative to starting everyone with a random rating, you could assign ratings based on win/loss record. Decide on a maximum and minimum rating, say 0 to 3000. Sort all the players by win/loss record, using win/loss record of their opponent's as a tie breaker. For people who haven't played many games, add some draws to their record to account for the uncertainty in their score. Then assign ratings based on this order. Give the top guy 3000 and the bottom guy 0, and use linear interpolation based on rank for everyone else. That gives you an initial rating r_0. Then apply your method to get their base rating r_1.

Here's the trick: if this system works at all, r_1 is a better estimation of a player's rating than r_0 is. So you could apply the system again using r_1 to calculate averages rather than r_0, and get an improved rating estimate r_2. Do you then use r_2 to calculate averages to get r_3?

This is something I've always wondered about rating systems. They use very little information. Elo uses three (the result and the two ratings) while glicko uses five (the result, two ratings, and two rating deviations). But any rating system has at it's disposal far more information than that, because it has the full playing history of everyone in the system. Why not make use of that information? In some sense they do, because some of that information was used to calculate the ratings and the rating deviations.

But say Adam plays Bob, and then Adam goes on to play Charles while Bob goes on to play Dan. Does Bob's game against Dan give us information that could be used in refining our estimate of Adam's rating? Glicko and elo say no. Your system combined with my suggestions says yes. It's easier to answer the question when games are discrete events. Adam plays Bob, then Bob plays Dan. That's the way it is with OTB. We could say Bob's result against Dan reflects changes in Bob's skill, so it is not relevant to Adam's rating. But with online chess, Bob could be playing Adam and Dan at the same time, and just finish his game with Adam first. And how much does Bob learn (or forget) between two games anyway?

ichabod801 wrote:

As an alternative to starting everyone with a random rating, you could assign ratings based on win/loss record. Decide on a maximum and minimum rating, say 0 to 3000. Sort all the players by win/loss record, using win/loss record of their opponent's as a tie breaker. For people who haven't played many games, add some draws to their record to account for the uncertainty in their score.

Still going through the rest of your post, but the whole point of assigning a random rating to someone is that they haven't played anyone yet (and have no won loss record).  If everyone is assigned 1200 to start then no one's score will ever change from 1200 in my system (thus the flaw).  But yes, the random rating would be in some specified range (not potentially infinite).   But some of your subsequent comments are a little over my head ( not being a professional statistician) so still going through them.

edit:

I do understand what you're saying for the most part.  As is always observed "The devil's in the details."  Whatever system it is, it should be simple - something complicated and with a lot of kludges and afterthoughts  is probably wrong.  (Not referring to your ideas or mine though.)   But anyway, thanks for the input.

You say to use won-loss record to assign initial rating.  But won loss record against who?  If you don't know the skill level of the player's opponents then his won-loss record tells you nothing.

OK I definitely have the solution now (ahem):  If players were always paired against random opponents on this site (as opposed to being able to choose their opponents themselves)  then their mere won-loss record would be a perfect reflection of their ability relative to other players on this site.  Any sort of additional "rating" number would be pointless. 

So evidently the complicating factor for rating purposes is that people can choose who they play, e.g. they can choose to only play people they can beat up on, or alternatively only play people who are way better than them (out of possibly some inflated sense of their "true" ability)  and thus lose often.  If opponents are assigned randomly the rating problem goes away.  And since people play 100's of 1000's of games here, random opponent assignment would mean they were truly getting a cross-section of players and their won-loss record would be reflective of their ability.

edit:

A simple weighting formula could give precedence to more recent won-loss results.

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edit 2:

Suppose 2 people came on this site and only played each other (being the best of friends or whatever).  One of them always wins and the other always loses. So one is ranked 3000 and the other 0.  What do those ratings tell you about their ability relative to the other players on this site - absolutely nothing. 

However, no one's selection of opponents is random. Without random opponent assignment, any player's ranking  is not telling you  about their ability relative to players on this site in general - only their ability relative to the people they happened to have played - which most certainly will not be a representative or random sample of players on this site.

hohohehehaha

If a player hasn't played yet, why would he need a rating? Any rating you give him is just going to be a stab in the dark anyway.

And win loss record does give you information about skill. It is not perfect, which is why you start with it and refine it using your method of average opponent's rating. Which is really what glicko and elo are doing, they're just coming at it from different perspectives with different methods. But starting with win loss is better than starting with random numbers, IMHO. Both introduce error, but the error would seem to be greater with the random numbers.

Just noticed a problem with your idea Eberulf: If someone has a perfect record (all wins or all losses), you end up removing everyone they played against, and you have no one to judge their rating by.

ichabod801:

Just noticed a problem with your idea Eberulf: If someone has a perfect record (all wins or all losses), you end up removing everyone they played against, and you have no one to judge their rating by.

from my original post:

There is a slight problem when you first start,  if you have 0 wins or losses.  There's a simple fix but can't remember what it was.

 You would keep one remaining game and use that as your rating.  So if you were 20 and 0 you would remove 19 wins against your 19 weakest opponents, leaving the rating of your one strongest opponent as your rating.  Conversely if you were 0 and 20,  you would remove the 19 losses against your 19 strongest opponents leaving the rating of your weakest opponent as your rating.

You wrote:

If a player hasn't played yet, why would he need a rating? Any rating you give him is just going to be a stab in the dark anyway.

Well, the main impetus was that if you're just assigning everyone 1200 to start, then no one's rating would ever change from 1200 in my system, as your rating is based on the average of your opponents.  My thinking was that a random intial rating would inject some variability into the system that might magically sort it self out to reflect ability accurately as everyone was playing opponents randomly.  That aspect of it sounds kind of suspect now.  Anyway, it wouldn't hurt me to actually review the two existing rating systems you mentioned before devising a new one.   But as I said above in 401, the main problem seems to be that opponents are not randomly selected.  Better minds than mine have devoted themselves to this issue, no doubt. 

But the fact that in chess.com the average rating of your opponents is listed right below your own rating indicates I guess that its understood the two figures have to be considered together to accurately understand a player's ability.  It seems there should be some formula for combining the the two (your rating and your opponents' average rating).  This is arm chair statistics to some extent.

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Actually, it lists rating, followed by your opponent's average rating, followed by your won-loss record.  So all three are necessary to understand your ability.  Therefore all three should somehow be combined into one value, according to some formula.

In some sense, it's in the rating already. Your rating adjustment is determined using your rating, your opponent's rating, and the score of the game (and the rating deviations). So all of your opponent's ratings and all of your results are in your rating, in an a finer sense than just the average and the overall results.

starting with win loss is better than starting with random numbers, IMHO. Both introduce error, but the error would seem to be greater with the random numbers.

I just wasn't clear exactly on how the two systems would be integrated. Any initial rating can't be based on win-loss record.

ichabod801 wrote:

Give the top guy 3000 and the bottom guy 0, and use linear interpolation based on rank for everyone else. That gives you an initial rating r_0. Then apply your method to get their base rating r_1. Here's the trick: if this system works at all, r_1 is a better estimation of a player's rating than r_0 is. So you could apply the system again using r_1 to calculate averages rather than r_0, and get an improved rating estimate r_2. Do you then use r_2 to calculate averages to get r_3?

OK to restate the above, one could use your rating system, or for that matter, the existing one, and then as a second step apply mine. (Although my step wouldn't make sense until a player had played a number of games.)  I think I'm on the same page with you now.

As far as the recursion aspect (r_3, etc.) I would say no.  Only applying an additional method completely independent of the other two would make sense.

imagine if for your first game you beat pelger on time. how cool would that be!

That would a nice feeling , I admit.

Hey does the rating start with 1200?