# The “bye week” fallacy

The saying goes that if you have more time than your opponent to rest then you have a competitive advantage, especially in a sport like American football, where the physical contact can drain the players’ energy.  Is that the case though or is it another one of the sports myths that are not supported by data? For example, in short time-scales (e.g., within a game), prolonged periods of inactivity can lead a player to get “cold”, impacting his/her performance in a negative way.  Is then one week enough to lead a team lose its form or does it work in a “healing” manner?

In order to examine this I used data from the last 7 NFL seasons and in particular I calculated the probability of a team winning, losing and tieing coming off of a bye week.

As it is evident the probability that a team coming from a bye week will win is 51.9%.  The corresponding 95% confidence interval for the probability of win is [0.45, 0.58], i.e., one cannot reject the null hypothesis that the two teams have a 50-50 chance of winning!

The above is a straightforward way to estimate the probability from data, but let’s try to see whether we can reach a similar conclusion by using simple regression models to control for other factors and in particular for the opponent’s strength as well as home field advantage.  In particular, using the game data for the 7 seasons we run a logistic regression model, where each data point corresponds to one game for a specific team.  The input parameters are whether the team plays at home or away, what is the differentail in the current standings between the team and the opponent and whether the team is coming from a bye.  The output is binary and is 1 if the team won and 0 if it lost.  The corresponding logistic regression coefficients are:

It is clear that while the difference in standings between the two teams is a strong predictor of the winning team (and fairly moderate predictor is also the home field advantage), the bye week is not significant in predicting the outcome of a game.  So next time your are at your favorite sports bar, watching your team coming from a bye week impress your friends by telling them not to be “tricked” – the bye week has not impact.

Of course if the bye week gave Ben (I guess now you know why 412!) the ability to recover from an injury then this can have an impact.  However, quantifying it will require detailed roster analysis and the dataset on bye week data and roster changes will be sparse to obtain any meaninful result – it might be worth trying though.

Footnotes
Computing confidence interval for a proportion. Assume that you used N data points to estimate a proportion as p.  The corresponding 95% confidence interval for this proportion is given by: $p\pm 1.96\sqrt{\dfrac{p\cdot(1-p)}{N}}$, where 1.96 is the $Z_{.95}$.