Should teams fight for this half-time advantage?
Updated: Jul 18, 2021
A well-covered analysis suggested that being slightly behind at halftime leads to an increase in winning percentage. The explanation is psychological, and the authors argue that teams get an extra-motivation from going into half-time while slightly behind.
One statistical method is particularly appropriate to investigate this question and find the causal effect of behind behind at half-time: a regression-discontinuity (RD) design. We obviously cannot randomly assign teams to being ahead or behind of halftime, which would be the gold standard in trying to address this question. A RD design assumes that teams that go into halftime with a slight advantage are not systematically different from teams that go into the half with a slight deficit. Being up by 2 points or being down by 2 points going into the half is considered as-random: both teams try to be ahead, but also know that a second half is about to be played. Therefore, all the differences one could imagine systematically exist between a team that wins a game by 2 points and a team that loses that game (the quality of the coaching, how ‘clutch’ or experienced the players are for example) do not matter that much at halftime.
I use play-by-play data scraped from ESPN for WNBA games played between 2002 and 2020. I separate regular season games from playoffs games into two separate analyses. I add the winning percentages of both teams at tip-off as covariates in order to improve the precision of the result. The plots below show the difference between the home and away teams score at halftime (home teams are winning on the right side of the 0) on the X axis, and the percentage of games won by the home team on the Y axis. If the ‘losing leading to winning theory’ was true, we would see a ‘jump’ around the 0 line: the percentage of winning would drop for teams who are right ahead at the half compared to teams that are right behind. The jumps can be seen below, but they are not statistically significant. The coefficient for the regular season games (-0.037) is much smaller than the one found by the authors for the NBA, and not significant (95% CI: [-0.123:0.048]). The small number of playoff games limit the statistical power of the analysis, and the 95% CI for the Confidence Interval is [-0.417:0.227].
There does not appear to have any significant effect of being ahead or trailing going into the half on the game outcome. These results confirm the findings of a 2020 study that ran a similar analysis on four different sports (including a larger sample of NBA games than were including in the original study) and find no significant result. As the authors point out, our lack of results in the WNBA could be driven by power issues: we don't have enough games to work with. It is hard to know if the null result is driven by a 'real' null effect (going into the half behind really does not matter), as opposed to a lack of power. The coefficients from the RD analysis go in the 'right' direction to back up the 'losing lead to winning' theory, but they are not significant. The fact that analyses from more highly-powered league such as the NBA also lead to null results provide some evidence that the 'losing lead to winning' theory might not hold up well to empirical data and a causal inference approach.