Author: Robert Hyatt
Date: 11:19:31 10/27/99
Go up one level in this thread
On October 27, 1999 at 13:50:46, Dann Corbit wrote: >On October 27, 1999 at 11:47:14, Robert Hyatt wrote: >[snip] >>If you play someone that far under you, you had better win every game, or else >>your rating _only_ can go down. > >But if they are really that far under you, you will win the expected number on >average, and your number will stay the same. >Consider the following table: >Win expectency for a difference of 0 points is 0.5 >Win expectency for a difference of 100 points is 0.359935 >Win expectency for a difference of 200 points is 0.240253 >Win expectency for a difference of 300 points is 0.15098 >Win expectency for a difference of 400 points is 0.0909091 >Win expectency for a difference of 500 points is 0.0532402 >Win expectency for a difference of 600 points is 0.0306534 >Win expectency for a difference of 700 points is 0.0174721 >Win expectency for a difference of 800 points is 0.00990099 >[snip] >Win expectency for a difference of 2000 points is 9.9999e-006 That is all correct. But it doesn't apply to ICC and the other servers. Ratings are stored as ints... which means that once you can only win less than one point, you can only win zero. That makes a _huge_ difference in your calculations... > >If you play someone one hundred points lower than you, they will get 36% of the >points and you will get 64% and your rating will stay the same. >If you play someone 200 points lower, you will get 76% of the points and they >will get 24% and your rating will stay the same. If you play someone 300 points >lower, you will get 85% of the points. If you play someone 400 points lower you >will get 91% of the points. At a 500 point difference, you will win 95% of the >points. At a 600 point difference, you will get 97% of the points. At a 2000 >point difference, you will win 99.99% of the points. In all cases, your rating >will stay the same. Playing lower rated players should not (in theory) change >your rating at all. The very rare draw or extremely rare loss to a low-rated >player will be balanced out by a bazillion wins. On the other hand, games >against players hundreds of points beneath you are not really very exciting >[imo]. Who would gather around to watch Kasparov play me? If he played Anand >or Adams or some highly skilled player, that would be something people want to >watch. The reason is that I have basically no chance of winning so the outcome >is pretty well known even before we start. So from a point of interest, I don't >think it makes a lot of sense to play opponents that are miles beneath. I set my 'floor' for that reason. Given the choice of playing (a) GM players, (b) computers and (c) lower-rated non-GM/IM players, I want (a) first. And then (b). I don't learn much from 30 consecutive wins vs lower rated players. I do a couple of people I know play crafty (non-rated). One of them is an ICC 2000-rated player that has played a huge number of games with no wins or draws at all. I try to cull those, and if I know the player it is easy. But for others it is harder and they also displace stronger players from getting in as well. > >Those that claim your rating can be inflated by choosing opponents are not aware >of how the math works. And (let's suppose) that you have played someone ten >times and lost them all. You might think that -noplay would be good for you. >But look at all the recent SSDF contests where one program had a big lead and >suddenly lost it. Without a huge number of games, there is really no way to >know what the win expectancy would be, and once we know it accurately, then it >will only reflect upon our true rating. >[snip] just don't forget the 'int' problem. that hurts.
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