## Monday, November 05, 2007

### Evidence that NBA teams play better when rested

Do NBA teams play better if they've had more days of rest? Conventional wisdom says they do, and so does a study by Oliver Entine and Dylan Small.

(The study was presented at NESSIS, the New England Symposium on Statistics In Sports. Thanks to Paul Wendt of SABR, who pointed out that presentation slides from several studies are
online. This particular study can be found here (.pdf).)

The subject of Entine and Small's study was actually home field advantage (HFA), but the results on rest are more interesting, so I'll start with them.

The authors ran a regression on points scored minus points allowed (UPDATE: this used to just say "points scored"), using indicator variables for team, visting team, which team was at home, and four additional indicators for each team – whether they were playing on 0 days rest (back-to-back games), 1 day, or 2 days, or 3+ days.

It turns out that the more rest, the better the performance:

3+ days' rest is 0.58 points better than 2 days
3+ days' rest is 1.09 points better than 1 day
3+ days' rest is 2.26 points better than 0 days

Only the 2.26 figure is statistically significant (at exactly .05). Only one season's worth of data was used. It would be nice to re-run this using a decade or so (for hockey and baseball too).

2.26 points doesn't seem like a lot, but it is. Home field advantage was only 3.62 points, and resulted in a home winning percentage of .608. This is about 60% of that.

The study re-ran a (logistic) regression for wins, rather than points, and got similar results. The odds of winning are only .62 as big in back-to-back games as after 3+ days' rest. So a team that's .500 after 3+ days' rest would be 1 win per 1 loss; but on 0 days' rest, it would be 0.62 wins per loss. That works out to only a .383 winning percentage. (Again, that result is only barely statistically significant.)

Where HFA comes in is that the authors noted that the way the NBA schedule was constructed, teams on the road played on fewer days' rest than home teams (see slide 5 for the numbers). They wondered whether that could account for the home team's advantage. They found that it only accounted for "9%" of the HFA.

Entine and Small downplay this result, but I find it quite significant a finding – explaining even 9% of home field advantage is more than I've seen anywhere.

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At Monday, November 05, 2007 10:53:00 AM,  Brian Burke said...

Slightly off-topic: I've read that the most "honest" research results are found in the variables that are not the primary focus of the study, just like the "rest" factor here. There are just too many ways for researchers to be biased, consciously or otherwise.

For example, in a study focusing on the effects of second hand smoke, the results of the controlling variables for obesity, diet, or family history, etc. are likely to be more honest than when those factors are studied directly.

Besides all the advocacy research out there, the impulse to dig deeper to find significance in primary variables is profound. After all, who wants to do a study just to say "never mind?"

At Monday, November 05, 2007 10:55:00 AM,  Phil Birnbaum said...

I love "Overcoming Bias." It sometimes depresses me, though ... Eliezer Yudkowski is so much smarter than me that I don't think I'll ever fully understand what he's talking about.

At Monday, November 05, 2007 11:15:00 AM,  dfobare said...

I can run this for a lot longer than one season. More than twenty seasons actually. What would you like to know?

At Monday, November 05, 2007 11:18:00 AM,  Phil Birnbaum said...

dfobare: would like to know the regression results, basically. After adjusting for home/road and team, do days of rest matter the same way as in the study?

If the regression option isn't available, then: what's the winning percentage for home teams on 0, 1, 2, 3+ days of rest, and what is it for road teams on 0, 1, 2, 3 days of rest?

Would be awesome if you can post results!

At Tuesday, November 06, 2007 9:43:00 PM,  Phil Birnbaum said...

Ed Kupfer did a similar regression here:

http://sonicscentral.com/apbrmetrics/viewtopic.php?p=172#172

I haven't looked too closely, but it looks like it confirms the results here: more days off = better performance.

(Ed had trouble commenting, so I'm doing it for him.)

At Wednesday, November 07, 2007 7:42:00 PM,  John D said...

Over 5 seasons Mark Cuban quanitifed the impact of back to backs as well as 4 games in 5 days-- http://www.blogmaverick.com/2005/12/21/back-to-backs-in-the-nba

(I have a completely gratuitious point to make also. The resulsts of the logistic regression-- 62% of games won-- match, as they should, how pythagorean win expectation translates a 2.6 pt edge.)

At Monday, April 20, 2009 4:09:00 AM,  cvxv said...