How is a player rated who has similar results against a wide range of players?

Question

There is a player I know, whom I would guess to be somewhere between 1600-1800 in strength (call it 1700) who has an unusual profile.

He's a defensive player who's good enough to beat players 1500 and under most of the time. But he stops beating players as they approach the 1600 level, even though he seldom loses to them. Against players in the 1600-1800 range, he wins 10%-15% of the time, loses 10%-15% of the time, and draws the remaining 70% Against players in the 1800-2000 level his stats are slightly worse, about 15% wins, 25% losses, and 60% draws. His loss rate rises as he plays opponents above 2000. But basically, he gets similar results against people in a (wide) range of 1600-2000.

What are the dynamics of this player's rating? Will he get points for beating 1500 players more often than other 1700 players? Will his ability to draw against players up to 2000 also pull up his rating above 1700? Or will his lack of wins hold down his rating?

Answer 1

The Elo system treats every player as if his expected score against for example -200 -100 0 100 200 points stronger players would be 24 36 50 64 76 percent. If your real expected score deviates from this assumed distribution it just means that the Elo rating doesn't describe your strength very well.

In a way that is actually the norm and the culprit is the huge drawing range in chess. Stronger players on average slightly underperform against weaker opposition afaik, because drawing with white is just a little too easy.

In your special case the players rating would fluctuate depending on his opposition without his actual strength changing all that much. If he manages to get a steady diet of 1800-2000 opponents his rating would rise above 1800, if his opponents are between 1600 and 1700, his rating would stay in that range.

This doesn't actually mean much and it isn't particularly unusual. It's only relevant in team matches or if you need to maximise your rating to be eligible for titles or something.

Answer 2

I'm not completely sure what your exact question is, but this may help clarify things for you.

Keep in mind that an Elo rating only makes sense within a given population of players, and the difference between the ratings of two players serves to predict the result of a competition between those two players. Also, remember that the ratings of your friend's opponents are not static - just as your friend's rating changes over time as a result of his play, so do his opponents' ratings. There's no such thing as a "2000 player", per se - there are only players who are rated 2000 as a result of play within a given population of players. The Elo rating isn't like a "skill level" or anything, like, "if you have this rating, then you have X, Y, and Z skills".

When your friend plays an opponent, the difference between their ratings is a predictor of the eventual result. So if your friend is rated 1600, and plays 6 games against an opponent also rated 1600, then your friend's expected result would be 3.0 - which could come as 3 wins and 3 losses, all 6 games drawn, or some other combination. If the result is different than that - say, your friend scores 4.0, a better than expected result - then as far as the rating system is concerned, either your friend's rating is too low, or his opponent's rating is too high, or both. So the rating system adjusts both players' ratings - your friend's rating goes up, and his opponent's rating goes down. The amount by which the players' ratings change depends on how different the actual result is from the expected result - and the expected result depends on the difference between your friend's rating, and his opponent's rating. If your friend does better than expected against someone whose rating isn't too different than his, then his rating will go up by a little bit, by a small portion of the K value (and the opponent's rating will go down a little bit, by a small portion of the K value). If your friend does better than expected against someone whose rating is much higher, than your friend's rating will go up by a much larger portion of the K value. Depending on exactly what rating system you're using, and the ratings of the players involved, the K value for each player might be different, so your friend may not gain the same number of rating points as his opponent loses. And of course, if your friend does worse than expected against an opponent, he'll lose some number of rating points, and his opponent will gain rating points, depending of the K value, and exactly how different the actual result is from what the rating system would predict.

But, in either case, the ratings of your friend's opponents are not some fixed, static thing - they're changing too, as a result of actual play.

Does that help answer your question?