# Back to Back Blues? The Effect of Road Trips in the Ivy League

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.

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• Matt says:

Love the analysis. Somebody has to look at these things and you guys are doing a great job.

• DRDR says:

Isn’t your null hypothesis that the effect is zero, and your test stat isn’t large enough to reject this null?

The first check I might try is to also control for distance. The Columbia-Cornell trip is by far the longest, so I suspect if there’s an effect anywhere, it’s there.

• jezekowitz says:

DRDR:

Thanks for the comment. Yes, that could be the null (that is the orthodox way). I chose to reverse it for the sake of clarity.

As for distance, I controlled for that and that actually was not significant factor at all. I was surprised by that, as well. Sample size may be a bigger issue there (only 44 Columbia-Cornell road trips).

• DRDR says:

Thanks for looking into that.

You might also consider looking into these kind of effects for hockey, since the ECAC hockey schedule is just like the Ivy basketball. Robin Lock has 15 years of rating estimates here: http://it.stlawu.edu/~chodr/current.html

• Brack says:

DRDR- I would think the Dartmouth/Harvard trip would be up there as well.

Excellent break down. There is 1 other league that keeps to the same kind schedule. I know no one else does back to back, however, the pac-10 keeps to the same state teams and plays on Thursday Night/Sat/Sun. Would be interesting to see how their #’s would come out to be.

Keep up the great work. Always love the gambling stories.

• DRDR says:

Harvard-Dartmouth is much closer to Brown-Yale than Columbia-Cornell. You can do Harvard-Dartmouth in under 2.5 hours. Brown-Yale is a shade under 2 hours.

Columbia-Cornell is about 4 hours best case, plus the potential for a 1-hour heavy traffic delay getting in/out of Manhattan is far greater than for any other Ivy location.

• Brack says:

Yes, distance wise for sure DR. I was thinking more about the weather of getting stuck in NH. I think one of the other things to look @ is who Princeton/Penn do when they play each other. Its always on a separate lone day.

Also, a friend of mine, who played on the Penn team back in the 90’s, wounder what the stats where on the back to back of the Princeton/Penn trip. Now, this is when they were both the Top 2 teams, however he said they used to crush teams on the 2nd night.