John Smith <[EMAIL PROTECTED]> wrote:
> The problem concerns finishing position at the end of round-robin
> chess competition.
> If competitor A has probability Pa of finishing in the top half of the
> league table, and competitor B has Pb, what is the probability that A
> finishes higher than B ?
> Likewise, if competitor A has probability Pa of winning a match (any
> match - so I suppose this would be some notional 'average' opponent),
> and B has probability Pb, what is the probability that A would win a
> match against B?
Perhaps you should read Elo _The rating of chess players past and present_,
or Google on Elo ratings.
The original Elo system (apparently the US uses a Bradley-Terry model)
would give:
Performance Rating = (mean rating of opponents) + C*qnorm(score)
Pr(A beats B) = 1/C * pnorm(Rating.A-Rating.B)
Where pnorm and qnorm are the distribution function and quantiles of the normal.
So, if this model of ability holds and A and B have played against the
same opponents, and I'm doing this right :) then eg
score so far
A B Pr(A beats B)
.5 .5 .5
0 .4 .0
.05 .45 .06
.1 .5 .1
.2 .6 .13
.3 .7 .15
--
| David Duffy. ,-_|\
| email: [EMAIL PROTECTED] ph: INT+61+7+3362-0217 fax: -0101 / *
| Epidemiology Unit, The Queensland Institute of Medical Research \_,-._/
| 300 Herston Rd, Brisbane, Queensland 4029, Australia v
.
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