| George John 2005-04-11, 5:59 pm |
| David Kane wrote:
[SNIP]
quote:
> Well you haven't stated exactly what math
> you think should be relevant, but the average opponent
> rating isn't even relevant for determining performance
> rating in the general case. That is an approximation useful
> when the opponents have ratings in the linear portion
> of the winning expectancy curve. The performance
> rating is the rating that predicts the achieved result,
> taking into the actual non-linear winning expectancy
> formula.
>
> Your original assumption that identical performance
> ratings should have the same effect on rating
> (independent of the rating mix of the opponents) is
> unfounded for the reason I gave. What matters
> is the expected vs. actual, so some results don't
> matter
Overall, I agree with this. One minor nit pick is the score (BTW, I
prefer score to winning) expectancy curve is never linear.
WRT performance ratings, I should also mention the online calculator
gets into minor trouble when there is a perfect score since the
expected rating is always less than one. For example, if a player wins
4 games against all 1000 rated players, what is the performance rating?
It really could be anything, say 1400 or higher. The online
calculator comes up with 1400, since 400 is commonly accepted, but
there is no truly satisfactory way to do this, SFAIK. Interestingly,
sometimes the performance rating at 1/2 point less than perfect is
higher than using the 400 number! For example, try 8 opponents with
ratings of 2299. With a score of 8 the PR is 2699; 7.5, 2769.
Best regards,
George John
|