Tennis Note #29

Set Scores: Stories Untold

Some sets might be closer than you think…

In “How to Chart a Match…” I made the claim that “A 6-0 set can actually last longer than a 6-4 set, with more points played and longer rallies.” The statement is easy to defend because the math is straightforward: a 6–0 set with every game reaching deuce is at minimum 48 points; a 6–4 set with all “love” games is 40 points.

I thought it would be interesting to explore the assertion by diving into data made available by the Match Charting Project for ~1,800 (and counting) professional matches. But first, a brief review of the theoretical case…

Game Trees. Left: Love Games; Right: Many Paths to Deuce

In the images above, Game Trees are used to depict point progressions. In a “Love game’ there are only two four-point paths. In games that reach deuce, no matter the path, there will always be a minimum of eight points.

Here is a visual comparison of a theoretical 6–4 set composed of love games totaling 40 points next to a theoretical 6–0 set composed of deuce games with a total of 48 points. In the accompanying Game Tree the point progressions for both sets are depicted:

Theoretical Point Progressions: Left: Game Tree; Right: Points-to-Set. 40 points vs. 48 points.

A 6–0 set does not need to reach deuce in every game to stretch beyond the theoretical 6–4 set with only 40 points. Here is a “Game Fish” depiction of game between Williams and Azarenka in Cincinnati in 2013:

Game Fish: Azarenka d. Williams (2013 Cincinnati). 12 deuces. 29 points.

With that game in a 6–0 set, only 11 more points (less than three games) need to be played to stretch beyond the theoretical minimum for a 6–4 set; that’s well below the 20 additional points that will be played.

The theoretical case I am defending is an eight point difference, but how realistic is it? Of the 4783 sets currently in the Match Charting Project (MCP) data, here is a graphic of the range of points played per set:

Depicts total points-per-set for 4783 sets. Click to be redirected to interactive version.

It is immediately obvious from the whiskers on the box plots that indeed the longest 6–0 set has more total points than the shortest 6–4 set. But let’s drill down a bit more and make a visual comparison between these sets…

(There is an interactive version of this chart at TennisVisuals.com, where it is possible to see the point distributions for specific players as well.)

Gasquet d. Duckworth (2014 Wimbledon)
Nadal d. Sousa (2014 Rio de Janiero)

The shortest 6–0 set in the MCP data is currently 28 points, for an average of approximately 4.7 points-per-game, while the longest is 55 points (9.5 ppg).

The shortest 6–4 set in the MCP data is currently 45 points, for an average of approximately 4.5 points-per-game, while the longest is 98 points (9.8 ppg).

Djokovic d. Dimitrov (2014 Wimbledon), Hernych d. Kamke (2014 Wimbledon)

Points-per-game is another metric worthy of consideration. You can see in the chart below that while 6–0 sets do have the lowest maximum points-per-game, they certainly don’t have the lowest minimum.

“Max PPG” for 6–1 sets jumps out. Returning to the box plot above, it turns out that 6–1 sets can stretch well into the territory of 7–5 sets, and even cross into the range of 7–6 sets.

Here’s a stacked view of the sets that prove the theoretical position I put forward in last week’s article.

Nadal played the longest 6–0 set and Djokovic played the shortest 6–4 set, at least in the matches available for study in MCP data.

In this initial review of the MCP data I have focused only on points. Next week I will dig into Rally Lengths (a unique feature of the MCP data) to see what they may have to say about the stories that can’t be told by set scores alone…


Don’t forget to recommend, comment, share, and follow! Also check on the Tennis Data Storytelling Challenge by clicking the image.

All data is from Tennis Abstract’s amazing database available on GitHub. I talked about it previously. Special thanks to those who took the time to chart the matches. If you enjoy reading these tennis notes, make sure to follow the publication, ‘Recommend’ and share! Check us out on Facebook! Made a cool observation? Interested in certain topics and writing? Are you a tennis photographer? Comment, add notes, and check out the submission guideline. Cheers!