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607Re: nice methods

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  • HoopStudies
    Feb 8, 2002
      --- 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
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