Impact of Game Number of Chance to Break

Hi folks!

## The Question

Watching Khachanov-Shelton last night got me thinking about the often discussed importance of the 7th game as a potential for elevated chance to break. Conventional wisdom/tennis folklore often suggests that, because it is the final game with the original balls, this is the best chance for a returner to score a break. I was curious if it was really true!

## The Data

I used [this awesome dataset by Jeff Sackmann](https://github.com/JeffSackmann/tennis_pointbypoint/tree/master) because it had a really robust set up for point by point results. Unfortunately, that means the data is restricted to a window between 2011 and 2015. If anyone knows of a similarly complete data set that's more recent, I'd love to redo this! This dataset also included a number of sets that went beyond 12 games plus a tiebreak. I excluded those for simplicity.

## The Results Some overall results stand out right away. + During this window, the baseline break rate across the ATP was 20.7%. So breaking about 1 in 5 games. + Break rate absolutely plummets as the set nears the end, suggesting that returners prioritize getting themselves into a tie breaker instead. + The percentages don't *look* all that different by game—you can see them rising and falling by 1–2% in any given game spot.

However, these small differences can actually be really meaningful. For example, if we look a little deeper, we can see that: + Odd nubmered games have a higher chance to break across the board, suggesting that serving first is actually NOT as advantageous as we typically assume. + The 7th game *does* have the highest break rate, at 22%. This is 1.3% above the baseline break rate. + A delta break rate of 1.3% is actually a *proportional* increase of 6.1%. In other words, a returner is six percent more likely to break in the 7th game than they are any game at random.

Anyway...nothing super ground breaking here. I was just having fun on a lazy Friday and got excited when I found a dataset that could help me answer the question. If anyone knows of a way to get more modern day, I'd love to rerun and also break down by surface!