## 811Re: Assigning Credit to Players

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• Mar 29, 2002
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--- In APBR_analysis@y..., "dlirag" <dlirag@h...> wrote:
> >
> > One of the things I remember hearing about Dominique Wilkins and
> have
> > heard about Allen Iverson is that their shots are more often
> > rebounded by their own team because their teammates know that
they
> > are going to shoot the ball. We already have put forth evidence
(I
> > think, I know I did the work) showing that Iverson's presence
does
> > help the Philly offense even though the boy sometimes can't hit
the
> > side of a barn with his shot.
>
> A shot can be seen as a pass that results in one of the following
> things happening: 2 or 3 points are immediately scored (45%
chance),
> the ball ends up in a teammate's hands (16% chance), or the ball
goes
> to the opposing team (39% chance).

This gets at what Gary Skoog did in one of James' abstracts, where
they assessed the expected runs for every given state and assigned
credit/blame for transitions between those states.

At the point before a shot, every possession is worth about 1 pt.
After the shot, it could go to 2 pts with a made shot and end of
possession, 3 pts with a made shot and end of possession, rare cases
of >3 pts with or without continued possession, 0 pts with the
probability of an offensive rebound (expected value of 1 pt after
OR), 0 pts with probability of opponent getting the ball (expected
value of 0 after DR). In the 0 pts with offensive rebound, you
diminish the value of the missed shot by about 2/3 (assuming 1/3
chance of OR), so, using relative to the mean credit (as Skoog did),
the credit is -2/3 to the shooter who missed (bring expected points
from 1 to 1/3), 2/3 to the offensive rebounder (who brought it back
to 1), then 1 to the scorer (for going from 1 to 2). If this
methodology is carried out in detail, you could modify the shooter-
specific OR%, so that rather than diminishing Iverson's misses by
2/3, you diminish them by 1/2 if you think that half of his misses
are rebounded by the offense.

Though in this case the rebounder and scorer are the same, note that
there is more relative credit to the scorer (+1) than to the
rebounder (+2/3). This may be in conflict with what the offensive
rebound studies we did earlier here said, but I'd need to check.

Dean Oliver
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