John Smith wrote:
> Thanks for the responses guys.
>
> The ELO system does indeed give reasonably accurate estimates of the
> probability of winning. A simple logit model based on the difference
> in ELO rating will give a reasonable estimate of the probabilities of
> players winning.
>
> I suppose what I am asking, in a sense, is could this prediction be
> improved by somehow accounting for the head-to-head record of the two
> participants in addition to the ELO rating difference.
>
> A corollorary to that is obviously whether the head-to-head effect is
> significant of itself.
>
> I am not a statistician (I'm an engineer) but I am numerate and am
> prepared to study the appropriate area. However I don't know what that
> area is!
>
> What would a suitable null hypothesis be?
If you are numerate as you say, you shoudl be able to the effect you
are trying to demonstrate in some sort of equation or model, with
one or more unknown parameters that need to be estimated. I take a
stab at a simple model for your case, given that I don't think I
completely understand what you are trying to show, simply to
illustrate what is involved:
Prob of winning = (ELO Prediction) + p * (head-to-head adjustment)
+ error
If this is a reasonable model, then you want to test whether or not
the parameter p is equal to zero (Null hypothesis), or if it is a
positive number (alternative hypothesis). How you perform such a
test depends on what assumptions you want to make about the errors
and the rest of the data.
However you are closer to the problem and so it may be that you can
write down a better model. If you do so, then the parameter of the
model that you are interested in will be clear, and the hypotheses
should also be clear
--
Paige Miller
Eastman Kodak Company
paige dot miller at kodak dot com
http://www.kodak.com
"It's nothing until I call it!" -- Bill Klem, NL Umpire
"When you get the choice to sit it out or dance, I hope you dance"
-- Lee Ann Womack
.
.
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