By John Ezekowitz
Basketball coaches do not universally agree on much, but I think there are two things they would all agree on: if given the choice, they would rather play at home, and would rather play with more rest.
Home court advantage has been discussed and empirically studied ad nauseam (most recently in an interesting SI piece by Jon Wertheim and Tobias Moskowitz). In basketball, Vegas oddsmakers, whose job it is to know, give home teams a 3-4 point advantage. Additionally, there has been some very good empirical analysis of the effect that rest days have on NBA efficiency. That research found that defensive efficiency goes down when teams play games on back-to-back days. But before now, these two effects have, to my knowledge, never been studied together in a college basketball framework. I decided to change that.
Luckily for me, the league in which Harvard plays provided a very good natural experiment. The Ivy League is the only league in the country in which conference play is exclusively scheduled to minimize class time missed. The majority of Ivy League play happens on consecutive Fridays and Saturdays. Because each of the eight schools plays the other seven schools twice, home and away, each team has three road trips in which they play road games on back-to-back days. Conventional wisdom would hold that teams who had to play on the road on two straight nights would do worse than expected on that second night. I set out to find out how much worse they would do. But a funny thing happened on the way to the forum. Join me after the jump for details.
To determine how well teams were expected to perform, I used adjusted efficiency ratings from Ken Pomeroy’s invaluable website and calculated expected pythagorean winning percentages (as first detailed by Bill James, and as adapted to basketball by Dean Oliver), with the exponent 11.5 used (special thanks to Michael James for helping me with this calculation). This calculation accounted for the fact that the team was on the road, but not that the team was playing its second road game in as many nights. Ivy League play has 24 games each year where a team is playing on the road for the second night in a row on the road. Since Ken has data from 2004 onward, I had 168 games to work with– not an enormous sample size, but a big enough one from which to draw conclusions.
Once I had the expected win odds for each game and the actual outcomes, I used the same framework as I did in the momentum in overtime study to test the hypothesis that road teams playing on the second night of back to backs did significantly worse than expected. I created a binomial distribution with the expected win odds and the actual results, and summed both variables. The 168 road teams were expected to win 65 games for a winning percentage of 0.385. They actually won 66 games for a winning percentage of 0.391. A z-test of proportions with conservative variance (p(1-p)=.25) rejected the null hypothesis that Ivy road teams played worse than expected on the second night of road back-to-backs.
The gambling numbers told the same story: the “tired” road teams covered exactly 50 percent of the time. This result at least made some sense: if betting markets are efficient, any extra effects of road back-to-backs should be accounted for by oddsmakers and the line moves caused by the betting public. Interestingly, the average difference between the pythagorean expectation game margin and the line was 0.45 points. This implies that on average, gamblers add about half a point to the lines of “tired” road teams.
I was very surprised by this negative result. I thought that the numbers might be thrown off by games played in the last week of the season, after the Ivy League title has been determined and there is far less to play for, but excluding those games made very little difference (expected winning % of .382 compared to actual of .371; still an insignificant difference). From this (admittedly limited dataset), I’m forced to conclude on the first pass that Ivy League road teams do not play significantly worse on the second night of back to backs. Perhaps this is the case because both teams have played two nights in a row. The data seems to suggest that the fatigue factor evens out, and simply accounting for one team being on the road is enough. A tired team is a tired team, no matter if it has been on a bus all night.
There is still more work to be done, however. One thought I had was that perhaps the second game in two days produces more variance in outcomes than other games. Teams may either come out very flat or surprisingly sharp, leading to a wide range of outcomes that even out over the dataset. Additionally, there is the problem of autocorrelation: teams’ results are likely correlated over the three games they play in this situation each year. This threatens any independence assumptions that are made. I find it hard to believe, however, that autocorrelation alone would produce such a profoundly negative result.
While it would seem intuitive that the effects of fatigue of playing multiple games on consecutive and of being on the road for two straight games would combine to make teams perform significantly worse than expected, the data from the last seven seasons of the Ivy League show this not to be the case.