What Were the Odds of an All-American Women's SF at the US Open?

For the first time in 36 years, the US Open women’s singles event will have an all-American semifinal. What were the odds of this historic outcome?

While many have grumbled that the men’s draw at the 2017 US Open has been humdrum at best, the women’s draw hasn’t disappointed. Among the highs, for US fans, the moment when Madison Keys converted her second match point in the last of the women’s quarterfinals and assured an all-American semifinal had to be a standout.

On Day 11, Americans Venus Williams, Sloane Stephens, CoCo Vandeweghe, and Madison Keys will duke it out for spots in the US Open finals. It is the first time since 1981 that the US Open will see the American flag along side all the semifinalists names. And with 3 of the 4 semifinalists having no slam title in her trophy case, there is a good chance that Saturday will see a new US woman added to the list of US Open champions.

Breaking the 1981 record couldn’t just happen by chance. The knockout structure of the 128-draw required strong US competitors in every quarter in order for American players to outlast the rest of the draw after five rounds of competition. A draw peppered with American talent would seem a necessary condition for this to happen.

There were 23 total US competitors in the women’s draw this year. For tennis, an increasingly diversified sport, that is a big share for any single nation to have at a Major. But only in the new millennium of the sport.

As the trends in US Open women competitors show below, it was quite common in the 1980s to have 50% or more of the women’s draw filled with American players. The representation of the USA has dropped precipitously since then. In the past decade, in fact, the number of American players in the women’s event has been under 20 in most years.

This makes the all-American women’s semifinal that much more impressive in contrast to 1981, when the composition of the draw was so much more heavily in the US’s favour. 23 pales in comparison to the 78 American competitors in 1981, but is is important to note that 23 is a high in a rising trend of US competitors at the US open since 2010. This is another measure of the depth of the American women’s game that helped produce the 2017 semifinal.

Undoubtedly, the 2017 US Open women’s draw is special in a number of ways. But is it special statistically? How fortunate are US fans in getting a US-only women’s semifinal?

We can get some idea of the odds of this record-breaking year by simulating the most probable outcomes of the 2017 women’s draw based on player Elo ratings. Out of 100,000 simulations, an all-American women’s semifinal occurred just 27 times. In other words, a roughly 1 in 4,000 chance. And, in 14 of the 27 cases, just more than 50%, the semifinalists were the 4 competitors for Day 11.

American tennis fans enjoying the finals weekend at the US Open have two more reasons to feel lucky.

The code and data for this post can be found here.

Stephanie Kovalchik avatar
About Stephanie Kovalchik
Tennis Data Scientist at the Game Insight Group at Tennis Australia and researcher at the Institute of Sport Exercise and Active Living at Victoria University.
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