close game at end of 3rd quarter ==> big 4th quarter minutes for Yao

blowout game at end of 3rd quarter ==> small 4th quarter minutes for Yao

I took the absolute value of the 3rd quarter lead/deficit, and regressed Yao's 4th quarter minutes against that. Even with only 13 observations, the regression statistics support the conventional hypothesis (indeed, as Ed points out, simply eyeballing the numbers, this jumps out at you).

The regression equation is

4th qtr mins = 10.55 - .38*abs(lead)

i.e. for every point by which Houston's lead or deficit grows, Yao's minutes diminish by .38 minutes. With a 28 point lead or deficit, we'd expect Yao to play 0 minutes (and lo and behold, in Game 3 Houston had a 29 point deficit and Yao sat).

The t-statistic on the estimated coefficient of -.38 is -3.31, with a significance level of p = 0.7%, i.e. significant at better than the 1% level. Pretty good for a sample size of 13. The adjusted r-squared from the regression is .45.

This regression benefits from what might be aguably a statistical outlier, that 29-point Game 3 blowout. If we leave that out of the regression, the coefficient estimate stays at around the same value, -.43, but the adjusted r-squared falls to .16 and the t-statistic is -1.77, significant at only the p = 10.7% level.

So Game 3 probably makes these results look overly conclusive. On the other hand, it is almost certainly too drastic to literally throw out Game 3, a baby-with-the-bathwater move. Game 3 does provide support for the notion that big leads cause small minutes for Yao, so to totally ignore Game 3 is not a wise course.

The regression might be further strengthened by correcting for censoring; it's physically impossible for Yao to play more than 12 minutes in the 4th quarter, and the data around the regression line thus hit a ceiling and flatten out at 12 minutes, making the estimated regression line probably flatter than it should be. And thus our estimates will be a little too low and seemingly lacking in significance.

Of course, none of this explains the original question, about why Yao's total minutes are so low. Many other superstars probably get similar 4th quarter treatment (sit during a blowout, play during a close game); why do their minutes per game exceed Yao's by so much?

--MKT

-----Original Message-----

From: igor eduardo küpfer [mailto:edkupfer@...]

Sent: Friday, February 06, 2004 1:35 PM

I began a study of this a couple of months ago, but didn't get far. Here's

what I have:

| YAO'S MINUTES | ROCKET's LEAD

GAME | 1 2 3 4 OT | 1 2 3 4 OT

-----|---------------------------------------------------

1 | 9 5 3 3 | 2 6 12 17

2 | 8 12 8 8 | -9 -1 5 -8

3 | 8 10 11 0 | -7 -20 -29 -32

4 | 9 10 9 8 | 1 -7 -5 11

5 | 10 7 12 5 | 3 6 6 10

6 | 12 3 7 10 | 0 7 9 20

7 | 12 5 9 5 | -2 -6 -10 -11

8 | 9 6 12 9 | 3 -6 -1 5

9 | 8 10 9 12 10 | -8 -3 2 0 -4

10 | 7 12 7 12 | 3 10 10 8

11 | 7 7 9 12 | 3 4 -1 2

12 | 8 10 9 10 | 11 -3 -7 -7

13 | 10 7 10 4 | 4 14 7 15

AVG 9.0 8.0 8.8 7.5 0.3 0.1 -0.2 2.3

The numbers in the Yao's Minutes columns represent the number of minutes he

played in each quarter. The Rockets Lead numbers are their lead at the end

of each quarter (a negative number would be a Rockets deficit).

There's not much to look at there, but you can see that in games where the

score difference is 5 or less points, Yao plays about 10 minutes in the 4th.

When the lead is more than 5, he plays 6 minutes in the 4th.

ed

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