- Jun 2, 2004Replies to DanR and DeanO

Dean Oliver wrote:

> I was curious to see how you handled the early games of the season,

I'm sorry I didn't make it clear. For the second analysis (on the 03-04

> especially the times where one team was undefeated. It looks like you

> used Pythagorean projections, rather than real records anyway. That

> helps. But 0-0 usually requires some other assumption, like a

> Bayesian prior that carries through the first few games.

regular season results) I didn;t use Pythagorean records. I instead used

each team's record to date. Two teams facing each other on the first game of

the season each had a 0.5 chance of winning that game, since they had

identical 0-0 records.

The results don't deviate much from my first analysis, which used season's

end Pythagorean Win%. I supposed this is because after the first part of the

season, each team's Pyth is relatively stable. I must admit to being a

little surprised by this, though.

> Not sure what to make of that weakening of the Days. What was the R2

r = 0.06 for 00-01, r = 0.03 for this season.

> of the previous version?

> We may have to improve the prior matchup P

Games 2-20: r = 0.048 (p = 0.261)

> to get back a reasonable estimate of the value of Days. If you just

> look at games beyond the first 20 in the season, does r2 get better

> and does Days become more significant?

>

Games 21-82: r = 0.024 (p = 0.314

dan_t_rosenbaum wrote:

> Interesting results. Here are a couple of suggestions.

Okay, I tried this. The regression outputs follow. I'm afraid that I don't

>

> I would leave out the MatchupP variable, since it is a lot like the

> dependent variable. Including it probably increases R-squared a

> lot, but probably doesn't do much else. (All in all, it probably is

> pretty harmless, since it unlikely to be correlated with your

> independent variables.)

>

> Another option with your day variable is to enter it as a series of

> dummy variables.

>

> DAY0 - equals 1 if 0 days of rest, 0 otherwise

> DAY1 - equals 1 if 1 day of rest , 0 otherwise

> DAY2 - equals 1 if 2 days of rest, 0 otherwise

> DAY3 - equals 1 if 3 days of rest, 0 otherwise

> DAY4+ - equals 1 if 4 days or more of rest, 0 otherwise

>

> Then run the regression leaving one of those variables out.

>

> If, for example, you left DAY0 out of the regression, the DAY1

> coefficient would give you the effect of playing on one day's rest

> versus playing in a back-to-back.

>

> The DAY2 coefficent would give you the effect of playing on two

> days' rest versus playing in a back-to-back.

>

> The DAY3 coefficent would give you the effect of playing on three

> days' rest versus playing in a back-to-back.

>

> The DAY4+ coefficent would give you the effect of playing on four or

> more days' rest versus playing in a back-to-back.

>

know how to interpret the results -- very few of the coefficients are

significant. (Note that I use Day1 to mean 1 day between games, ie back to

back -- the 1 does not mean "rest days.")

Ommitting Days1

Predictor Coef SE Coef T P

Constant -3.8515 0.5971 -6.45 0.000

Home 7.1257 0.5267 13.53 0.000

Distance -0.0000105 0.0003920 -0.03 0.979

Days2 0.5837 0.6157 0.95 0.343

Days3 0.3022 0.7996 0.38 0.706

Days4 -2.363 1.394 -1.70 0.090

Days5+ 0.935 1.801 0.52 0.604

Omitting Days2

Predictor Coef SE Coef T P

Constant -3.2678 0.5624 -5.81 0.000

Home 7.1257 0.5267 13.53 0.000

Distance -0.0000105 0.0003920 -0.03 0.979

Days1 -0.5837 0.6157 -0.95 0.343

Days3 -0.2815 0.6981 -0.40 0.687

Days4 -2.947 1.338 -2.20 0.028

Days5+ 0.351 1.758 0.20 0.842

Omitting Days3

Predictor Coef SE Coef T P

Constant -3.5494 0.7833 -4.53 0.000

Home 7.1257 0.5267 13.53 0.000

Distance -0.0000105 0.0003920 -0.03 0.979

Days1 -0.3022 0.7996 -0.38 0.706

Days2 0.2815 0.6981 0.40 0.687

Days4 -2.665 1.426 -1.87 0.062

Days5+ 0.633 1.824 0.35 0.729

Omitting Days4

Predictor Coef SE Coef T P

Constant -6.215 1.385 -4.49 0.000

Home 7.1257 0.5267 13.53 0.000

Distance -0.0000105 0.0003920 -0.03 0.979

Days1 2.363 1.394 1.70 0.090

Days2 2.947 1.338 2.20 0.028

Days3 2.665 1.426 1.87 0.062

Days5+ 3.298 2.152 1.53 0.126

Omitting Days5+

Predictor Coef SE Coef T P

Constant -2.917 1.799 -1.62 0.105

Home 7.1257 0.5267 13.53 0.000

Distance -0.0000105 0.0003920 -0.03 0.979

Days1 -0.935 1.801 -0.52 0.604

Days2 -0.351 1.758 -0.20 0.842

Days3 -0.633 1.824 -0.35 0.729

Days4 -3.298 2.152 -1.53 0.126

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