## Wednesday, May 07, 2008

### Back-to-back NBA games and home field advantage

Do NBA teams suffer if they've played a game the day before? Apparently they do.

In a study in
JQAS, called "The Role of Rest in the NBA Home-Court Advantage," authors Oliver A. Entine and Dylan S. Small run a straightforward regression on 2,415 NBA games – two season's worth. They use dummy variables for each of the two teams, another variable for home-court advantage, and three more dummy variables for days of rest. They find that, compared to three or more days of rest, teams playing the second of back-to-back games suffer a disadvantage of 1.77 points (split somehow between offense and defense).

That finding was statistically significant at p=.03.

Teams playing with one day of rest or two days of rest showed little difference in performance – the entire effect was in the "zero days of rest" case.

In terms of wins, rather than points, the findings were consistent – an odds ratio of 0.75 for the second of back-to-back games. If I understand that right, that's a winning percentage of .429 (4/7). At 30 points per game, that works out to 2.13 points, close enough to the 1.77 the authors found.

What does days of rest have to do with home-court advantage? Well, the authors note that road teams play a lot more back-to-back games that home teams: 33%, as opposed to 15%. The difference translates into a larger apparent visiting-court disadvantage. It works out that 0.3 points of home field advantage, out of 3.24 total, comes from the fact that home teams are likely to be more rested.

The authors also checked whether the length of a road trip has any effect on winning percentage. They find that teams in the second game of the road swing play significantly different than in the first game, 1.04 points worse (p=0.07). However, there is no effect for the third game or beyond, which suggests that this finding could just be random.

One more test by the authors checks whether the back-to-back effect is different for the home team as opposed to the visiting team. They say, no, the effect is roughly the same. Unfortunately, they don't give us any coefficients or significance levels for the estimates. They just tell us that the fit is not significantly better for the home/road regression (in terms of residual sums of squares), which still leaves us wondering whether the effect might be different in basketball terms.

Perhaps the authors chose to do it this way because the home and road coefficients, taken separately, would not be statistically significant. (The combined coefficient (1.77 points, as described above) is 2.14 standard errors, so the home/road coefficients, if also equal to 1.77, would be about 1.5 standard errors each.) Still, it would be nice to have seen how different the effects are.

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At Wednesday, May 07, 2008 12:59:00 AM,  JavaGeek said...

It shouldn't be a huge surprise. The leagues know this and that's why there are more back-2-back games played on the road (theory is the fans will be happier if teams win when they go to the game)

Those numbers are quite close to what I've seen in the NHL.

NHL this season:
home team 0 days rest vs. away team > 0 days: 41W - 83 GP (should be around 46 W)
home team 0 days rest vs. away team > 0 days: 112W - 258 GP (should be around 116 W)
not actually significant per se, but it's a small sample size without adjustments for team skill (although it should average out.)

Home advantage is 53% this season without any back-2-back games (441W in 830 games)

At Wednesday, May 07, 2008 1:05:00 AM,  Phil Birnbaum said...

I didn't know the leagues did that on purpose ... although it's an easy way to generate HFA, I guess. And it makes sense, thinking about it ... you'd expect B2B games to be mostly home teams, because they don't have to travel. If it's the other way around, it must be specifically engineered that way.

Interesting that home teams on 0 days rest (vs. away teams > 0) are actually almost exactly .500 ... HFA and B2B are about equal, it would seem.

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