Are there More Upsets in the ATP or WTA?

I’ve been a pretty serious tennis fan since high school. Back then, Andre Agassi and Pete Sampras were still battling it out, along with Justine Henin-Hardenne (now Justine Henin) and Kim Clijsters. It was great fun to watch.

Nowadays, I still follow tennis throughout the season, but I mainly just watch the four major tournaments. For the last number of years it has seemed to me that the men’s tennis matches (ATP Tour) were generally pretty unsurprising: The top-ranked player in the duel was usually the winner. However, on the women’s side (WTA Tour) it seems to me that no single player (or set of players) can remain atop the rankings chart and win out consistently against a variety of opponents (Serena Williams is the notable exception here).

So, this post is all about figuring out if there are more “upsets” (i.e., the lower-ranked player wins) on the WTA Tour compared to the ATP Tour. My suspicion is that there should be more upsets on the WTA Tour.

Approach

My approach to this problem is simple: Look at historical matches and calculate the fraction of matches in a given year that are upsets, where an upset is defined as the winner’s ATP/WTA ranking being at least some value below the loser’s ranking. For example, one might define an upset as any time the lower-ranked player wins (i.e., the difference between the winner’s rank and loser’s rank is at least 1). Alternatively—and perhaps more accurately—one could define an upset as any time the difference between the winner’s rank and loser’s rank is at least 5. In this example, if the 3rd-ranked player beat the 1st-ranked player, that would not be upset; however, if the 6th-ranked player beat the 1st-ranked player, that would be an upset.

Note that, by definition, a “higher-ranked” player should have a lower ranking value. That is, the best player in the world has a #1 ranking, whereas the 25th-best player in the world has a #25 ranking.

We will take a look at the fraction of matches in a given year that result in an upset, and we’ll compare the ATP Tour and the WTA Tour side-by-side so that we can observe any clear differences. We will also break out these data by surface type, to see if any particular surface (clay, grass, or hard) generally results in more upsets (I’ve ignored carpet here, as not many tournaments are played on carpet). My thinking here is that on grass courts, for instance, big servers typically have an advantage. For the past decade or so, we haven’t seen any of the really big servers on the men’s side reach the #1 world ranking; but, on grass courts these big servers may have enough advantage to consistently beat higher-ranked players. Conversely, clay courts tend to neutralize big serves, and I would therefore expect that big servers may consistently lose to lower-ranked players in clay-court matches.

Finally, the data have been filtered for this analysis according to the following:

• Tournament types include Master’s Series and Grand Slams only.
• Only matches for which the winner’s world ranking and loser’s world ranking are provided are used.
• Only matches played on clay, grass, or hard courts are used.

Data

Thankfully, a guy by the name of Jeff Sackmann has collected data on professional tennis matches dating back to 1968! The data files—one file per year—are freely available on his GitHub repositories: tennis_atp and tennis_wta.

The annual data files contain everything we need for this analysis:

• ATP (men’s) or WTA (women’s) Tour
• Date of the match (from 1968 up to May 2018)
• Court surface the match was played on
• Winner and loser world rankings

Results

To generate the results for this post I used the Matplotlib library in Python 3. The full analysis, including creation of the plots, was completed in a Jupyter notebook. An interactive version of the notebook can be viewed here (created using Binder), but I provide a discussion of the key results below.

Quickly, here are some notes on using the interactive notebook:

• Once you click the link, the notebook may take a few seconds to load.
• If you have never used a Jupyter notebook before, click “Run” on the top menu bar and then “Run all cells.”
• The cells will take a minute or so to load, mainly because of the data collection step.
• The interactive plots will be displayed at the very bottom of the notebook if all cells have been run.

When originally looking at the results, the year-by-year data showed quite a bit of variance. Therefore, I went ahead and used a moving average of three years for plotting the fraction of matches resulting in an upset. (Note that the time frame for the moving average can be adjusted in the notebook’s interactive plot.) A three-year moving average kept some of the variance, but allowed for a clearer look into the trends in upsets.

The plot below shows the fraction of matches resulting in an upset by year and tour, for all surface types. In this case, the definition of an upset is that the winner’s rank was at least five ranks lower than the loser’s rank, which seems like a reasonable default definition.

The two sets of plots below show the same data, except that the fraction of matches resulting in an upset are now broken out by surface type as well, and the definition of an upset is different in each set of plots:

1. The winner’s rank was at least five ranks lower than the loser’s rank.
2. The winner’s rank was at least 25 ranks lower than the loser’s rank. Again, you are able to change the definition of an upset in the interactive plot. However, looking here at a difference in rankings of five and 25 allows us to see the general effect of changing the definition of an upset.

The data start a bit later for the WTA in these plots due to not having all the required data for the earlier years (e.g., not having rankings for both players). As expected, the fraction of matches resulting in an upset decreases as the required difference in rankings for an upset increases. But, there are quite a few unexpected findings here for me:

1. On average, the ATP Tour actually had more matches resulting in upset than the WTA Tour until about 2013. Since then, the WTA Tour has experienced more upsets, but the Tour trends in upsets are converging again in the last year or two.
2. The fraction of matches resulting in an upset is roughly equivalent for all surfaces over time.
3. I never expected that at least 20% of matches would result in the winner being ranked at least five spots below the loser. (I thought the fraction would be much lower, especially for the ATP Tour.)
4. About 15% of matches result in an upset where the winner is ranked at least 25 spots below the loser. In this case, grass appears to result in slightly more upsets than the other surfaces for the ATP Tour.
5. The fraction of upsets appeared to have peaked around the year 2000 for the ATP Tour, and has been in decline since (other than the past year or two). Conversely, the fraction of matches resulting in an upset on the WTA Tour has been rising over the time period of these data. This may explain why, anecdotally, I thought that more WTA matches resulted in upsets.

Conclusions

According to this analysis, the answer to this post’s motivating question is: Neither the ATP Tour nor the WTA Tour appear to have significantly more upsets at the Master’s Series and Grand Slam level at this time. However, the ATP Tour actually had more upsets than the WTA Tour until about 2013. Furthermore, it would appear that the number of upsets is trending upward for the WTA, whereas the trend has been generally downward since the year 2000 for the ATP Tour. Hopefully, Mr. Sackmann will continue aggregating tennis data, and this can be revisited in a couple years to see if anything has changed.

Again, the interactive analysis notebook is published and available for your perusal.