# REPLICATION: Losing is NOT the Key to Winning

[Excerpts are taken from the article “Does Losing Lead to Winning? An Empirical Analysis for Four Sports” by Bouke Klein Teeselink, Martijn J. van den Assem, and Dennie van Dolder, forthcoming in Management Science.]

“In an influential paper, Berger and Pope (2011, henceforth BP) argue that lagging behind halfway through a competition does not necessarily imply a lower likelihood of winning, and that being slightly behind can actually increase the chance of coming out on top.”

“To test this hypothesis, BP analyze more than sixty thousand professional and collegiate basketball matches. Their main analyses focus on the score difference at half-time because the relatively long break allows players to reflect on their position relative to their opponent.”

“BP find that  National Basketball Association (NBA) teams that are slightly behind are between 5.8 and 8.0 percentage points more likely to win the match than those that are slightly ahead.”

“The present paper…extends the analysis of BP to large samples of Australian football, American football, and rugby matches, and then revisits the analysis of basketball.”

“In our main analyses, the running variable is the score difference at half-time and the cutoff value is zero. We estimate the following regression model:”

“where Yi is an indicator variable that takes the value of 1 if team i wins the match, and Xi is the half-time score difference between team i and the opposing team.”

“The treatment variable Ti takes the value of 1 if team i is behind at half-time. The coefficient τ represents the discontinuity in the winning probability at a zero score difference. This coefficient is positive under the hypothesis that being slightly behind improves performance. The interaction term Ti × Xi allows for different slopes above and below the cutoff.”

“If the assumption of a piecewise linear relationship between the winning probability and the half-time score difference is violated, then the regression model will generate a biased estimate of the treatment effect. Hahn et al. (2001) propose the use of local-linear regression to solve this problem.”

“Even if the true relationship is non-linear, a linear specification can provide a close approximation within a limited bandwidth around the cutoff. A downside of this solution is that it reduces the effective number of observations and therefore the precision of the estimate.”

“To strike the appropriate balance between bias and precision, we use the local-linear method proposed by Calonico et al. (2014). This method selects the bandwidth that minimizes the mean squared error, corrects the estimated treatment effect for any remaining non-linearities within the bandwidth, and linearly downweights observations that are farther away from the cutoff.”

“We find no supporting evidence for [BP’s result that marginally trailing improves the odds of winning in Australian football, American football, and rugby]: the estimated effects are sometimes positive and sometimes negative, and statistically always insignificant.”

“We then also revisit the phenomenon for basketball. We replicate the  finding that half-time trailing improves the chances of winning in NBA matches from the period analyzed in BP, but consistently  find null results for NBA matches from outside this period, for the sample of NCAA matches analyzed in BP, for more recent NCAA matches, and for WNBA matches.”

“Moreover, our high-powered meta-analyses across the different sports and competitions cannot reject the hypothesis of no effect of marginally trailing on winning, and the confidence intervals suggest that the true effect, if existent at all, is likely relatively small.”

“In our view, the performance-enhancing effect documented in BP is most likely a chance occurrence.”