## Re: Winning streak / team strength question

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• ... 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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> 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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