Author: Raymond Stefani
California State University, Long Beach
25032 Via Del Rio
Lake Forest, CA 92630
Dr. Raymond Stefani is a professor emeritus at the California State University, Long Beach with 170 publications covering rating systems, individual Olympic sports, team sports, home advantage, and sports history
A longitudinal analysis of the differential performances of seeded male and female Grand Slam tennis players
Purpose: This paper evaluates Grand Slam tennis at the most fundamental level, the match-by-match competition between established players and their challengers. The competitive balance of men and women therefore is evaluated in this paper, as measured by the success of lower-seeded or un-seeded competitors at winning matches. Methods: A 14-season database was tabulated, covering 56 Grand Slams for men and 56 for women contested from 2006 through 2019, including nearly 5,000 matches for men and 5000 for women, each involving at least one seeded player. Results and Discussion: Overall, higher seeded players were upset in 25% of women’s matches and in 21% of men’s matches. As an average season progressed, women were involved in more upset matches than men by 28% at the season opening Australian open on hard court, by 15% on red clay at the French Open, by 14% on grass at Wimbledon (where the most upsets happened for both men and women) ending with 11% on hard court at the US Open. Lower-seeded or un-seeded men became consistently more competitive as each season progressed, while women remained at the same highly competitive level. On a year-by-year basis, competitive balance (upsets) have increased somewhat, that is, the predictability of higher-seeded players has decreased over time. Conclusions: The cumulative effect of the upset differential is that spectators watched the progress of the strongest men’s seeds, wondering how they would do against the three dominant men’s players, Nadal, Djokovic, and Federer, who won 48 of the men’s 56 Grand Slams over the 14-year period. In contrast, dynamic new young female players emerged, winning by upset until some became higher seeds and even Grand Slam champions themselves, only to be upset and replaced as champion by a new wave of enthusiastic and compelling competitors, exemplified by the fact that 24 women won their 56 Grand Slams. Applications to Sport: The marketing, advertising, and psychological/physical player preparation should consider the fundamental spectator’s eye views that differentially define men and women’s Grand Slam tennis.
Key Words: Predictive success, competitive balance, Grand Slam tennis, gender differences
Each season, the tennis world and television audience focus attention on the four Grand Slam tournaments. Since the COVID pandemic has interrupted the normal pattern of tournaments for the 2020 season, as well as inducing many top players to not play, this paper uses that pause to examine past results to gain insight into the fundamental nature of Grand Slam competition. The first competition of the season is the Australian Open contested on a hard court. Next in order are the French Open contested on red clay, Wimbledon contested on grass and finally the US Open contested on a hard court as was true in the season opener.
A statisticians-eye view has sought to explain the progression of points, games, sets, and matches won. In singles competition, the focus of this paper, 128 women, and 128 men compete. The women compete on a best-of-three set basis, the winner having a record of 2-0 or 2-1 sets won. Men compete on a best-of-five set basis, the winner having a record of 3-0, 3-1, or 3-2 sets won. Fanshawe (1) pointed out that the most observed result for both genders at Wimbledon was a straight set win, which was generally consistent with an independent, fixed probability of winning a set. Kovalchik (3) demonstrated that more upsets should be expected for women playing on a best of three set basis than for men playing on a best-of-five set basis, generally assuming independence of probabilities. Newton and Aslam (5) related the probability of winning a point to that of winning a game, a set and winning a match. They referred to their work as “Monte Carlo Tennis”, with independent probabilities. Pollard (7) showed that a player can increase the probability of winning certain important points, which agreed with some anomalies noted by Fanshawe, somewhat contradicting the assumption of total independences.
Clearly, much has been learned about the probabilities of winning points, games, sets, and then matches. An overarching reality is that the sport is driven by the spectators-eye view. Those spectators fill stadia, enabling large payouts to the winners, inducing young players to take up the game and incentivizing television networks to broadcast the competition, sponsored by large advertising fees. As each match begins, a spectator cannot help but know the relative seeding of both players, which are prominently displayed in the schedule, in newspaper accounts and during TV coverage. Of the 128 male and 128 female singles players, the best players of each gender are ranked (seeded) from first to 32nd, based on their ranking positions by the men’s Association of Tennis Professionals (ATP) and by the Women’s Tennis Association (WTA). The ranking systems assign points for each tournament dependent on position achieved and on tournament importance (usually measured by money at stake), with the four Grand Slam tournaments having the highest point values. Points are accumulated over the most recent 52-week period. At a fundamental level, the spectator will categorize a match as between two players who are both seeded (having past success), who are both un-seeded (and wanting to move upward) or where one is seeded and one is not seeded (making for an interesting contrast).
To understand the fundamental nature of Grand Slam tennis, as observed from the spectator’s-eye view, we want to know if they see differences between how often higher-seeded men and women win. Do spectators see differences in competitive balance among the types of surfaces used for the four Grand Slams? Is there an observable trend in the sequence of the four Grand Slams played each year? What have been the year-by-year variations for the four Grand Slams? How many consistently successful male winners will spectators see, compared to their female counterparts?
The answers to those questions are obtained using a 14-season database, tabulated in real time, tournament-by-tournament, for all four Grand Slams from 2006 through 2019, including nearly 5,000 men’s matches and nearly 5,000 women’s matches. Understanding the trends is useful for marketing the sport, for teaching young players what to expect upon entering a tennis career and for advising established players on maintaining their ranking positions.
RESULTS AND DISCUSSION
Table 1 includes averages of the percentages of matches won by higher-seeded men and women in singles from 2006-2019, inclusive. Averages are organized by gender for each Grand Slam (for 14 competitions each) and overall (for 56 Grand Slams each). Since each Grand Slam begins with 128 players, 127 matches are needed to eliminate all but the winner. Since only 32 of the 128 players are seeded, in the first round of 64 matches, the 32 seeded players are each paired with an un-seeded player while the other 32 matches involve pairing un-seeded players, meaning that a maximum of 95 of the 127 matches could involve at least one seeded player. In Table 1, one or two seeded men played in 87 matches per Grand Slam, while one or two seeded women played in 86.
Table 1: Success of Higher Seeds and Upset Ratio over 14 Seasons of Grand Slam Tennis (2006-2019)
|Matches||Higher Seed Won||Matches||Higher Seed Won||Higher Seed Won||Upset Ratio|
Higher-seeded women won 75.3% of the matches, meaning that spectators enjoyed the surprise of an upset 24.7% of the time. Overall, higher-seeded men averaged 78.9% success (21.1% upsets). The differences between the average success of higher-seeded men-women and the ratio of upsets for women/men both formed a within-season pattern. The upset ratio is a good measure of the spectator-eye experience. Women began the season on hard court at the Australian open, in which lower-seeded women competed in 28.8% more upset matches than men (the higher-seed success difference for men-women was 80.9% – 75.4% = 5.5%, while the upset ratio for women/men was 24.6/19.1 = 128.8%). That 28.28% percent value for more upset matches by women dropped monotonically for the next three Opens: to 15.2 % on red clay at the French Open, to 13.6% on grass at Wimbledon, ending with 10.8% on hard court at the US Open. Since the 14 seasons began and ended on the same surface, the progression of values was clearly caused by within-season activity. Lower-seeded or un-seeded men became consistently more competitive through the seasonal sequence of four Grand Slams while lower-seeded and un-seeded women remained close to 25% upsets for each Grand Slam.
The lesson for men moving into Grand Slam competition is that improving a skill set as a season progresses and better understanding the opponent pool pays off. Spectators can count on a steady level of competition from lower-seeded or un-seeded women, making the matches exciting and unpredictable. Young women entering the Grand Slam arena of competition should be incentivized by the fact that 25% of lower-seeded or un-seeded players win consistently. The grass surface is the biggest equalizer, in that the most upsets for both men and women were on that surface at Wimbledon. That suggests a need for strategic practice time for the higher seeds and an opportunity of the lower-seeded and un-seeded players to win.
FIGURE 1: Percent of Matches Won by the Higher-Seeded Player, Averaged Yearly for the Four Grand Slams (2006-2019)
Figure 1 plots the 14 yearly men and women’s higher-seeded players’ success averages, calculated including all four Grand Slams for each year. Women and men proceeded in lockstep in 2006, 2007 and 2008. After 2008, the plots for women and men separated with lower-seeded or un-seeded women producing more upsets than their male counterparts do, for example do, by a differential of 6.3% in 2009, 6.8% in 2016, and 7.0% in 2017. The upset gap narrowed in 2018 and 2019. We would have been able to see if that trend was to continue in 2020, had it not been for COVID. A downward trend in predictability is visible in Figure 1, indicating an increase in competitive balance.
Figures 2-5, respectively, display the 14 yearly percentages of matches from 2006 thorough 2019, won by the higher-seeded men and women at each Grand Slam, following the seasonal order of Table 1. Figures 2-5 demonstrate decreasing differences between men and women, as we would expect from Table 1.
FIGURE 2: Percent of Matches Won by the Higher-Seeded Player, Australian Open (2006-2019)
The 14 seasons each opened on hardcourt at the Australian Open as shown in Figure 2. There were more upsets for women in 13 of the 14 years, including a remarkable differential of 22% in 2016.
FIGURE 3: Percent of Matches Won by the Higher-Seeded Player, French Open (2006-2019)
FIGURE 4: Percent of Matches Won by the Higher-Seeded Player, Wimbledon (2006-2019)
As plotted in Figure 3, the yearly competitions next moved to red clay at the French Open. Women had fewer upsets for the first three years, including a differential of 9.9% fewer in 2007. The lower-seeded women went on to achieve more upsets than men do in nine of 14 years, including a differential of 10.3% more upsets in 2019. The third Grand Slams were played on grass at Wimbledon. In Figure 4, women achieved a differential of 10.3% more upsets in 2017. Women had consistently more upsets at Wimbledon, doing so in 12 of the 14 years. From 2009 through 2019, Figures 3 and 4 show nearly parallel curves for men and women.
FIGURE 5: Percent of Matches Won by the Higher-Seeded Player, US Open (2006-2019)
The Grand Slams then returned to a hard court at the season-ending US Open. In Figure 5, the two curves were so close to each other that women had more upsets in just seven of the 14 years, with a differential of 15.6% more upsets in 2015 and with 8.4% fewer upsets in 2019.
Figures 1-5 show a downward trend for the higher-seed successes for both men and women after 2009, indicating increasingly more upsets and more excitement for the spectators, who knew not to assume the outcome was locked in by pre-match seedings. Instead, spectators enjoyed fresh young faces holding their own against established players, especially for the women’s competition.
Over the 14-season span from 2006-2019, inclusive, higher-seeded women lost in 24.7% of their 5000 matches compared to 21.1% for men in a similar number of matches. The spectators at women’s matches were treated to an upset in 17% more matches than for men overall. As the average season progressed over the four Grand Slams, the upset gap between women and men narrowed from playing in 28.8% more upsets in the Australian Open on hard court, to 15.2% more at the French Open on red clay, to 13.6% more at Wimbledon on grass (with the most upsets for men and women of any Grand Slam), ending with 10.8% more upsets at the US Open on hard court, the same surface as at the opening Grand Slam.
That upset gap is amplified in the list of champions. Three men won 48 of the men’s 56 Grand Slams (4): Rafael Nadal (18 wins), Novak Djokovic (16 wins) and Roger Federer (14 wins). The remaining 8 Grand Slams were won by four other men. The two most successful women in their 56 Grand Slams were Serena Williams with 16 wins and Maria Sharapova with four wins, while 22 other women won from one to three each of the other 36 trophies (8).
The human side of those facts is that spectators watched the rising young men’s stars, wondering how they would do against the three dominant men’s players, Nadal, Djokovic and Federer, while dynamic new young female players emerged, winning by upset until some became higher seeds and even Grand Slam champions themselves, only to be upset and replaced as champion by a new wave of enthusiastic and compelling competitors.
An excellent example of the women’s dynamic is the story of Naomi Osaka and Coco Gauff. On 31 August 2019, as defending 2018 champion, at the 2019 US Open, 21-year old Osaka defeated 15-year old Gauff (6). With compassion, young Osaka gently persuaded even younger Gauff to share the microphone for the traditional winner’s interview. Osaka remembered, from her own early years, how much it hurt to lose. In a tearful and heartfelt interview, Osaka told Gauff what an amazing competitor Gauff was, which certainly also described Osaka’s own recent rise to prominence. In the next Grand Slam, while trying to defend her 1999 Australian Open title on 24 January 2020, Osaka was defeated by Gauff, making Gauff the youngest to defeat a defending Grand Slam champion (2). Gauff then delivered her own winner’s interview, having been mentored by Osaka one Grand Slam earlier. Stories like that are why women’s tennis is such a compelling and dynamic competition, always renewing itself to remain current.
The marketing, advertising, and psychological/physical player preparation can consider the dominant spectator’s eye views that differentially define men and women’s Grand Slam tennis.
APPLICATIONS IN SPORT
Understanding the trends above is useful for marketing the sport, for teaching young players what to expect upon entering a tennis career and for advising established players on maintaining their ranking positions. The lesson for men moving into Grand Slam competition is that improving a skill set as a season progresses and better understanding the opponent pool pays off. Spectators can count on a steady level of competition from lower-seeded or un-seeded women, making the matches exciting and unpredictable.
Young women entering the Grand Slam arena of competition should be incentivized by the fact that 25% of lower-seeded or un-seeded players win consistently. That is, women in tennis have greater competitive balance then their male counterparts. It appears that the process by which women choose a career in tennis, train for that career and then compete creates a tighter distribution of skilled athletes than for men as evidenced by only one woman won more than four of the 56 women’s Grand Slam titles in this study while 3 men won 48 of their 56.
The grass surface is the biggest equalizer, in that the most upsets for both men and women were on that surface at Wimbledon. That suggests a need for strategic practice time for the higher seeds and an opportunity of the lower-seeded and un-seeded players to win.
- Fanshawe, T. (2013, 9 August). The elusive final set: are tennis finals always close run contests? https://www.significancemagazine.com/sports/57-the-elusive-final-set-are-tennis-finals-always-close-run-contests
- Baum, G. (2020, 25 January). Teenager startles the tennis world with win over defending champ. https://www.theage.com.au/sport/tennis/teenager-startles-the-tennis-world-with-win-over-defending-champ-20200124-p53ulv.html
- Kovalchik, S. (2015). Grand Slams are short‐changing women’s tennis. Significance, 12(5), 12-17.
- List of Grand Slam men’s singles champions. (2020, 29 August). In Wikipedia. https://en.wikipedia.org/wiki/List_of_Grand_Slam_men%27s_singles_champions
- Newton, P and Aslam, K. (2006) Monte Carlo Tennis, SIAM, 48(4), 722-742.
- Russo, A. (2019, 1 September). Coco Gauff And Naomi Osaka’s Post-Match Interview Will Bring Tears To Your Eyes, https://www.huffpost.com/entry/coco-gauff-naomi-osaka-us-open-post-match-interview_n_5d6bf144e4b0cdfe0571c179
- Pollard, G (2004) Can a Tennis Player Increase the Probability of Winning a Point when it is More Important? Proceedings of the Seventh Australasian Conference on Mathematics and Computers in Sport, Massey University, 30 August to 1 September 2004.
- List of Grand Slam women’s singles champions. (2020, 27 August). In Wikipedia. https://en.wikipedia.org/wiki/List_of_Grand_Slam_women%27s_singles_champions