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.