--- In APBR_analysis@y..., "Michael K. Tamada" <tamada@o...> wrote:

>

>

> 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

got the formula from Dallas Adams. I asked him once about a citation

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

Journal of Basketball Studies