Of all the quirks introduced to college basketball this season, playing back-to-back games might be one of the strangest. Yeah, NBA teams play back-to-back sometimes, but against different opponents. Also, yes, the Ivy League plays back-to-back road games, but also against different opponents. Now try bussing up on a Saturday morning to play the same team twice.
It is unclear what the expected effect of this type of back-to-back is on team performance. One could think that the road team could feel the impact of fatigue more and play worse in the second game. The winning team may have an advantage if it is difficult for the other team to refocus on the task at hand. Indeed, even the losing team may have an advantage if they can quickly learn from their mistakes.
In the NBA, there is some evidence that road teams perform worse in back-to-backs, losing 17.7 percentage points more often compared to road games with rest. Tiredness is a factor: net rating for the road team decreases by 2.2 points from game to game. However, on a road trip of at least two games, teams have a win percentage higher than the road league average. This result is interesting and somewhat counter-intuitive. In the Ivy League, some work has found that road teams performed no worse than expected in the second game of a back-to-back and that the tiredness factor impacts both teams equally.
In a recent NBN podcast, Bailey Eichner, center for the Tribe Women, said, on the topic of playing after losing the day before, that she felt there is a real advantage going into that second game. The team reviews film the next morning to learn from mistakes and develop a new game plan to counter what they saw from their opponent. On the other side, the winning team may have less to review and might be slow to react to adaptations from our Tribe women.
Based on the above table, teams that lost the first game had a general win rate of 39.2% in the second game. From this, one would think that the losing teams are at a major disadvantage. However, many of the teams losing the first game are likely to be weaker than their opponents and would therefore be expected to lose again. To know if teams are under- or over-performing, you need to compare pre-game win probabilities with observed win rates.
Pre-game win probability is only corrected for home-court advantage, not fatigue or other impacts from back-to-backs. Therefore, any difference in the observed win probabilities between games 1 and 2 should be due to effects related to back-to-backs. The first figure above presents a calibration plot for the win probability for the first game of a back-to-back series. Calibration plots compare the predicted win probabilities (binned in 10% groups) with the actual outcomes; for example, teams with an estimated probability in the 30% category (between 25% and 34%) won 33% of their games, just above what the model would have predicted. The more above or below the dotted line, the more a group of teams over- or under-performed relative to expectations. A good model would perfectly predict outcomes, and all dots would be along the dotted line. The blue line estimates the trend line to fill the gaps between the dots. If the blue line is significantly above the dotted line, teams with the corresponding estimated win probability are out-performing. The grey area represents a confidence interval.
For the first game, win probabilities are well-calibrated and seem to accurately reflect outcomes; the blue line is on top of the dotted line. The calibration plot of the subsequent games shows the blue line significantly above the dotted line for estimated win probabilities <50%. In other words, weaker teams are out-performing expectations in the second game, perhaps due to the advantage Bailey describes.
To compare to the analyses done on the NBA and the Ivy League, the next set of calibration plots compare win probabilities for home and visiting teams in the first and second games. The dotted and blue lines are nearly identical for the first game, indicating that the road team might not perform any worse (after correcting for home-court advantage), similar to the conclusions of the Ivy League analysis. In the second games, surprisingly, weaker home teams only get a small boost from the theoretical second-day advantage relative to visiting teams. Perhaps the home court advantage wanes after the first game? Does time spent traveling limit game preparation?
Extending this to the teams that initially lost, the difference between expected and actual win probabilities indicates the losing teams come back stronger and outperform expectations. These teams win 6.7% more than KYUSAG predicts, a statistically significant result.
So it seems that teams that lose the first game have an advantage in the second. Indeed, it is hard to beat a team twice in any season, let alone one where you have to play them twice in a weekend. The losing team, if well-coached, can identify things they can work on and watch film, like Bailey described. Winning the first game may give a false sense of security. We have seen these effects at play first and foremost in Bailey and her teammates’ dominant performance against Drexel last Sunday. On the men’s side, the Sunday games against Hofstra and Drexel were much more competitive than the first iterations. The calibration plot below shows that this effect is consistent across the entire spectrum of predicted win probabilities; teams who lost the first game, no matter how good they are, outperform the model expectations in the second.
To finish, I can extend this analysis by introducing it into the regression model KYUSAG uses to predict games. Regressing the win indicator on the unadjusted predicted score differential and an indicator for winning the previous game indicates that winning the first game is correlated with a 5.5% decline in win probability for the second game. This result is significant at the 1% significance level. Running a similar linear regression with the score differential from the second game shows that the score differential is expected to tighten by 1.72 points.
With all that, I think these results are pretty interesting! Visiting teams and teams that lost in the first game experience clear advantages that cannot be explained by the team’s previous performance or typical home-court advantage. It remains to be seen if this sort of trend plays in William and Mary’s favor though.