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Re: Winning streak / team strength question

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  • HoopStudies
    ... numbers ... random ... certainly show ... they ... combining ... accordance ... the ... No, I think smoothing is OK and that the spiking is random. I just
    Message 1 of 12 , Jan 16, 2002
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      --- In APBR_analysis@y..., "Michael K. Tamada" <tamada@o...> wrote:
      > Ah, the disadvantage of using purely empirical numbers. They're
      numbers
      > from the real world, but such numbers are always contaminated with
      random
      > errors, hence spikes. The theoretical numbers would almost
      certainly show
      > a smooth pattern. If our theories are good enough (I don't know if
      they
      > are in this case) then the best result is usually obtained by
      combining
      > theory and data: start with the raw data but then smooth it in
      accordance
      > with theory.
      >
      > But if we don't have a good theoretical reason for smoothing (maybe
      the
      > real NBA percentages really are supposed to show a spike) then we
      > shouldn't.
      >

      No, I think smoothing is OK and that the spiking is random. I just
      haven't done the smoothing. One way we could get a sense for whether
      the spiking is random is to have DeanL generate the curve for a
      different set of bins and see if the spikes move. That would also
      give us a fair way to smooth, rather than my arbitrary hand.


      > > numbers don't add up because of rounding (though I'll double
      check
      > > later). The win% makes sense to me. If a win streak of 1G leads
      to
      > > an expected win% of just over 0.500 (the average of the prior),
      every
      > > longer streak goes a little higher. This doesn't seem out of
      norm.
      >
      > We may be using different definitions of win streaks. I'm thinking
      > that if I'm told that a team had a 15 game winning streak, that
      means
      > that that was the LONGEST winning streak that the team achieved.
      And if,
      > over an 82-game season, I am told that a team's longest winning
      streak was
      > 1 game, then I'd expect that that was a very very bad team,
      not .500 one.
      > Even the Bulls this year have had a 2-game winning streak (Dec 29
      and Dec
      > 31).
      >

      We're going at the same thing, but the method has to be used
      different ways to get at the answers we're looking for. I wouldn't
      use the method to test what a 1G winning streak means. I would look
      at the team's longest losing streak and plug that in. If a team's
      longest winning streak is 5 G and its longest losing streak is 5G,
      that generally brackets its likely win% pretty well. If a team's
      longest winning streak is 5G, but its longest losing streak is 10G, I
      use the 10G streak to ascertain that the team is likely a 27 win
      team. But I'd also assume that they are independent events and
      multiply probabilities together. That would suggest that the most
      likely range of winning %'s is 35-40%, which is a little better than
      a 27 win season. (This assumes that the tables I gave you can be
      flipped to work with losing streaks, which, strictly, they cannot. I
      would strictly have to smooth the distribution so that its
      symmetric. I'm lazy.)

      >
      > I suppose you might be using a definition of a win streak something
      like
      > this: if we're told that a team had a 15 game winning streak, then
      we
      > know that it had at least one streak of at least 15 games. That
      seems to
      > me to be lead to harder probability calculations. If nothing else,
      the
      > number contains less information now. That 15G team could for all
      we know
      > also have had a 33 game winning streak that same season. Whereas
      if we
      > know that 15G was their longest winning streak, we've got a much
      better
      > idea of what sort of team it's likely to be.

      The longest streak has the most info.

      DeanO
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