## 3023Re: Well, admittedly the name Amos Tversky didn't ring a bell, so I ...

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• Jan 8, 2004
--- In APBR_analysis@yahoogroups.com, igor eduardo küpfer
<igorkupfer@r...> wrote:
?
>
> ...found one statistically significant instance of a cold streaky
> players: Darryl Dawkins's 80-81 season....> from Gilovich et al.:
>
> Probability of Making a Shot Conditioned on the Outcome of
>Previous Shots

>Dawkins
3ms 2ms 1ms all 1md 2md 3md
.88 .73 .71 .62 .57 .58 .51 -.142**

Ed, I've inserted "column headers" over Dawkins' numbers. I hope I
got them right.

This situation seemed mighty curious to me. Why did Darryl shoot
almost 90% after 3 missed shots?

My source shows that he averaged just over 9 FGA per game, in '81.

9 FGA is a rather finite number; it's also hard to hit 62% of 9
shots.

Let's suppose Darryl's average game is 8 FGA, with 5 made (.625
shooting). That leaves 3 misses per game.

After 1 made shot, he's 4-7 (.571) for the remainder of the sample,
for this game.

After 1 missed shot, he's 5-7 (.714).

These numbers are startlingly close to the above "revelations" about
his inverted hot hand.

Consider a game in which the guy is 2-3. After his miss, there is
0% chance of a miss. After a hit, the chances are 50%.

Dawkins was a high-%, low-volume shooter. As such, he serves the
purpose of refuting the "hot hand"; and then he serves to spoil the
party.

If you evaluate the 3-point-shootout charts (subtracting the miss/
make from the sample totals), you might find a similar self-
contradiction. The samples are bigger, but as expected, the
conclusions are less dramatic.

> The column headers represent each player's FG% in the specified
situations;
> after 3 missed shots, after two misses, etc. Notice that none of
the players
> have a positive r -- showing that these players tended to shoot
_worse_
> after making shots, and better after missing shots, the opposite
of the
> hot-hand theory. Of course, none of those correlations were
statistically
> significant, except for Dawkins.
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