## 591Re: [APBR_analysis] Re: nice methods

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• Feb 5, 2002
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On Wed, 6 Feb 2002, HoopStudies wrote:

> >
> > Non-linearity. Individual won-loss records can be a fine way of
> > measuring players' production, but the jump from those individual
> won-loss
> > records to the team's actual won-loss record is not a simple one.

[...]

> despite my hopes nearly 15 years ago. I have actually come close to
> proving that it is theoretically impossible to have a simple number

If "simple" includes "linear" yes, models that are that simple will not
work.

> that allows you to predict a team's win-loss record with that player
> in place of another. Even the net points stuff I have, which comes
> closer. It is practically impossible to remove context. Your 69-13
> Laker team is a good example, I think, reflecting how context is
> important in making predictions. Or consider a team that wins by 10
> ppg. Replace a player who contributes net 1 ppg with one who
> contributes net 6 ppg is very unlikely to make that team win by 15
> ppg because the team doesn't need the extra 5 ppg to win. Very
> context sensitive.

Yes, diminishing marginal returns, and other non-linearities abound.

> Anyway, we can find reasons to discard EVERY single number we
> calculate here. Individual win-loss records are simple scans of

I hope I made it clear that I was not criticizing the individual won-loss
records as measures of player quality, nor as measures of marginal
contributions to wins.

> contribution that do sum to the team total, giving them a reality
> check that linear weights do not have. I like that conceptually. I

This is the part that is troublesome. It's nice that they sum to the team
total, but on the whole I think that doesn't really tell us much about the
validity of the model. With suitable normalization, most or at any
rate many rating schemes could be made to have sums which come close to
adding up to the team's win total.

> don't claim it's predictive (why I pointed out the Brand conundrum),

I suspect it's part of the data-fitting problem in statistics. When we
have a set of data, it's pretty easy to come up with a model that fits
that data set really well. But such models usually perform poorly when
used to make actual predictions on out-of-sample data (i.e. real world
predictions).

Good predictive models are very hard to create. Just ask any economist to
try to predict when the next recession will come. Or any geologist when
the next big earthquake will hit Los Angeles.

> but no one is putting forth any way to make those predictions.
> Unfortunately.

Yes, part of the Holy Grail again: how do individual players' qualities
(and statistics measuring those qualities) combine into determining the
team's outcome? A problem that is difficult enough in baseball and harder