## 607Re: nice methods

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• Feb 8, 2002
>
>
> On Wed, 6 Feb 2002, Michael K. Tamada wrote:
>
> > Two examples: odds ratios are what's behind the log5 method for
> > predicting win probabilties that some mathematician friend
introduced Bill
> > James to.
>
> I deleted the email, but I think someone asked about Bill
James' "log5
> method". That's simply his name for his formula (not as well known
but
> much cleverer than his Pythagorean formula) for calculating the
expected
> win probability when, say, a 75% win-probability team plays a 25%
> win-probability team. I don't know where the log or the 5 comes
from, but
> the formula can be derived from standard probability formulas, I
think
> with a small assumption about functional form thrown in.
>
> The really fantastic more general version of the formula is for
situations
> which are not inherently 50-50 balanced, such as batters'
probability of
> getting a hit against a pitcher. Someone told me that version can
also be
> derived from probability theory, but I haven't been able to do it.
>
> Despite the name, the formulas use odds ratios, not logarithms.
Actually
> come to think of it I don't think Bill James put the formulas in
terms of
> odds ratios, he used probabilities. But the formulas are much
simpler
> and cleaner when cast in odds terms.
>

Things are coming together for me. I didn't know the method was
called log5. I called them matchup probabilities and use them a lot
myself. I can't say that I could quite derive the formula either (it
always seemed that the league average had to be some sort of prior
probability, if you framed it in a Bayes perspective). James said he
and he didn't give me a specific one, so I spent some time looking
for it in math/stat journals and couldn't find it there.

>
> --MKT
>
>
> P.S. For those who are interested, the formulas.
>

Or I've got them documented at

http://www.rawbw.com/~deano/methdesc.html#matchup

Dean Oliver