Originally posted by jvanhineThe winning expectancy formula from the FAQ is actually the same formula that the USCF uses. See the formula in Section 2.3 (page 8) of the following Glickman paper -
the more i play the more i can guess whats going to be gained/lost, although there is a way to see that automatically...
heres the part from the FAQ that loses me-
"Win Expectancy = 1 / (10^(-200/400)+1) = 0.76"
http://math.bu.edu/people/mg/ratings/rating.system.pdf
Also, here's another Glickman paper that has "approximating formulas" for USCF ratings. But the nice thing about this paper is that it also includes an example calculation for the winning expectancy in Column 2 of page 2.
http://math.bu.edu/people/mg/ratings/approx.pdf
In simple terms, the difference between two players' ratings is designed to predict the chance that one player will beat the other. As shown above, a rating difference of 200 points is about a 75% chance that the higher-rated player will win.
If you win at the predicted rate, on average your rating won't change. If you're winning more or less than you "should" be, your rating gradually adjusts so your predicted results are closer to your actual results.
Originally posted by jvanhineIts a "probabilty" formula.
the more i play the more i can guess whats going to be gained/lost, although there is a way to see that automatically...
heres the part from the FAQ that loses me-
"Win Expectancy = 1 / (10^(-200/400)+1) = 0.76"
It gives the probability of winning based on the difference in rating.
Satistically it works.
Originally posted by incandenzaJust to be pedantic (a fault of mine, sorry) I will point out that this isn't quite right, even assuming the statistical concept is well founded, because "win expectancy" is actually a bit of a misleading name. It would be better termed "score expectancy", although I admit that's less punchy.
In simple terms, the difference between two players' ratings is designed to predict the chance that one player will beat the other. As shown above, a rating difference of 200 points is about a 75% chance that the higher-rated player will win.
200 points difference implies a "win expectancy" of 75% for the stronger player, as you suggest. This doesn't mean that you should expect the stronger player to win 75% of the time (despite what it says in the FAQ). What it actually means is that the higher player would expect to score, on average, about 75% of the available points against the lower player, on the standard scale of 1 for a win and 0.5 for a draw (not the system used in RHP tourneys, where it is 3 for a win and 1 for a draw). Because of draws, that's not the same thing as winning 75% of the time. It could be achieved that way, of course, if the other 25% were lost, or it could be achieved by winning 50% of the time, drawing 50% of the time and never losing. In practice, it will be somewhere in between. I would guess the draw percentage varies a lot with playing style.
And of course, it's not really a reliable predictor as between any two players anyway, because of all sorts of inevitable inefficiencies in the system. But it's the best system anyone's ever thought of, and considerably better than nothing.
Originally posted by d36366You are correct. However if you consider that a draw is a 50% win and a 50% loss, then the name "win expectancy" is still correct.
Just to be pedantic (a fault of mine, sorry) I will point out that this isn't quite right, even assuming the statistical concept is well founded, because "win expectancy" is actually a bit of a misleading name. It would be better termed "score expectancy", although I admit that's less punchy.
200 points difference implies a "win expectancy" of 75% for the ...[text shortened]... t's the best system anyone's ever thought of, and considerably better than nothing.
Rating Change 0-2099
Difference ___ H D L
0-10__________ 16 0 16
11-32_________ 15 1 17
33-54_________ 14 2 18
55-77_________ 13 3 19
78-100________ 12 4 20
101-124_______ 11 5 21
125-149_______ 10 6 22
150-176_______ 9 7 23
177-205_______ 8 8 24
206-237_______ 7 9 25
238-273_______ 6 10 26
274-314_______ 5 11 27
315-364_______ 4 12 28
365-428_______ 3 13 29
429-523_______ 2 14 30
524-719_______ 1 15 31
720-__________ 0 16 32
H - higher rated player wins
d - draw, higher player losses that number, lower players gains that number
L - lower rated player wins