Author: Peter Kappler
Date: 13:27:58 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 > >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. > >Those that claim your rating can be inflated by choosing opponents are not aware >of how the math works. Just the opposite. We understand the math very well. See below. 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] But you don't need to be 100% certain to make a good decision. Consider this scenario: I play 10 games against Player X at a 3 0 time control, and get smashed, 9-1. Then I play 10 more games at a slower time control like 5 3, and break even. If I want to save rating points in the future, I will simply decline any 3 0 challenges from this guy. Even though I made my decision based on a relatively small sample size, it's probably the correct decision. Playing another 100 games against "just to be sure" is sub-optimal if the goal is to maintain a high rating. If you spend enough time on ICC, you'll see this stuff happen *all* the time. --Peter
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