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Conventional wisdom vs data: the seventh game and the importance of serving first

Is it true that whoever wins the seventh game at 3-3 ends up winning the set? And that he who will serve first in a decider has an edge? Let’s take a look at the last ten years of Grand Slam matches’ data to see if there’s some validity to these truisms.

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It is a commonly held opinion that tennis is one of the sports in which the psychological component weighs the most during matches. Proof of that is, for example, that Timothy Gallwey, one of the fathers of Business and Life Coaching, was inspired by his experience as a tennis coach in writing his best seller “The inner game of tennis”, published in 1974 and in some ways still very relevant today. In more recent times, even Agassi and Panatta have insisted a lot on this aspect in their autobiographies, with the italian using this concept in the title of his book, stating boldly that “tennis was invented by the devil”.

 

This close connection between what happens on the court and what happens in the mind of the players often leads to proverbial statements that, it can be said, are viewed as conventional wisdom. For example, it is believed that, precisely for psychological reasons, the seventh game, in a set tied at 3-3, is particularly important because it breaks the balance just when the set enters its bottom half. Or, again, it is commonly believed that, particularly in a match that goes to the fifth set, the first player serving has an advantage in the decisive set, thus causing in the opponent the unpleasant feeling of chasing at a time when the match is about to end.

The growing availability of structured data related to ATP matches allows us to put these claims to the test, and to verify their veracity. For this purpose, we will consider all of the men’s singles matches in Grand Slam tournaments of the last decade, from 2011 to 2021. Considering this huge database, let’s start by asking ourselves the first question: does the one player who wins the seventh game on a 3-3 tied set win the set in the end?

THE 7TH GAME

Figure 1. Percentage of cases in which whoever wins the seventh game at 3-3 wins the set, 2011-2021 Grand Slam tournaments

At a first glance, it would be tempting to answer in the affirmative. In fact, in 54.3% of cases whoever goes 4-3 by winning the seventh game ends up winning the set. But to attest to the validity of this first superficial observation it might seems appropriate to ask ourselves, more specifically, whether gaining the advantage at that particular moment is more significant or helpful than doing it slightly earlier, or slightly later. In other words: does winning the seventh game at 3-3 carry more weight than winning the ninth game at 4-4, or the fifth game at 2-2?


Figure 2. Percentage of cases in which whoever wins the ninth game at 4-4 wins the set, 2011-2021 Grand Slam tournaments

The set is won by whoever wins the ninth game after a 4-all in 53.6% of cases. Comparable, but slightly lower than the 54.3% recorded for the seventh-game-case in a tied set. Considering that the ninth game is closer to the ending of the set, winning a game in that situation should have a bigger impact. Therefore it would be tempting to identify a correlation, albeit not particularly strong, between the vin in the seventh game at 3-3 and winning the set. Before getting to any conclusion, however, let’s repeat the analysis, this time examining the fifth game at 2-2.

Figure 3. Percentage of cases in which whoever wins the fifth game at 2-2 wins the set, 2011-2021 Grand Slam tournaments

Perhaps a little surprisingly, we find that, at 2-2, the set is won in 56.7% of cases by whoever wins the fifth game. Although this game takes place further away from the end of the set, it seems to have a greater effect on the final outcome of the set. Although this fact alone is not proof in debunking the myth of the seventh game, this simple analysis has perhaps the merit of generating some doubts and some more curiosity, bringing to the forefront a hypothesis that comes from experience in more direct touch with the data. Let’s try to apply this logic to another statement as well: it’s better to serve first in the final set.

SERVING FIRST IN THE DECIDER

Figure 4. Percentage of cases in which whoever serves first in the fifth set wins the game, 2011-2021 Grand Slam tournaments

Let’s focus on the 728 Grand Slam matches that have reached the fifth set over the last ten years. Indeed, the percentage of cases in which whoever served first in these 728 occasions won the set (and, consequently, the match) is greater than 50%: to be precise, the count is 380 cases (52.2% of the total). Looking back, we can consider that, if such an advantage really exists, it is reasonable to expect it to be greater in the case of the Australian Open, Roland Garros and Wimbledon, which, for a large part of the period considered, did not provide have final set tie-breaks or super tie-breaks, with (possible) prolongation of the psychological pressure on whoever is serving second.

Figure 5. Percentage of cases in which whoever serves first in the fifth set wins the game,,
Australian Open, Roland Garros and Wimbledon 2011-2021

Indeed, 310 of the 576 matches of the Australian Open, Roland Garros and Wimbledon of the last 10 years in the fifth set were won by the player who served first: 53.8% of the total. A higher percentage, therefore, than the one observed also considering the US Open’ s data. We can therefore say that, in this case, at least for this analysis’ sake, there seems to be a correspondence between conventional wisdom and actual data.

Let’s now move on to the critical analysis of a third consideration, common indeed, but not necessarily supported by the data: in a hard-fought match, whoever wins the most games who go to deuce will win the match in the end.

DEUCE GAMES

Figure 7. Box-plot representing the percentage of game per advantage won by the winners of men’s singles matches in Grand Slam tournaments in the period 2011-2021

To analyse this statement, and to measure its coherence with the trend of men’s singles matches in Grand Slam tournaments over the last ten years, let’s first focus on the matches with at least ten games that went to 40-40. This will allow us to focus on the statistically more significant data. Winning ten deuce games out of ten (100% of them), for example, has a different weight than winning the only one who went the distance.

Preparing the dataset for analysis, we can see that in the last ten years 2,050 men’s singles matches have been characterized by at least ten hard-fought games. To evaluate whether, starting from this subset of games, the victory of the games with advantage points is significantly linked to match wins, let’s try to use a different graphic representation: the box-plot.

The box plot represents the statistical distribution of a variable, in this case the percentage of deuce games won by the winner of the match for the 2,050 matches considered. A commonly used concept, in the analysis of statistical distributions, is that of the percentile. Let’s imagine we order the hard-fought-game percentages won by the winners of the 2,050 matches considered in ascending order. Match number 205 of this ordered list would be classified as the to the 10th percentile of the distribution (given that 205/2050 = 0.1 = 10%). In the box plot, we see a thin yellow bar to identify the fiftieth percentile, also called the median of the distribution. If the percentage of deuce games won was particularly significant, we would expect a median value, for the winners of the matches, greater than 50% – but this is not the case.

Not just that: the green colored area of ​​the box-plot defines the range within which the “central” 50% of the distribution is found. That is, the lower end of the green colored area coincides with the twenty-fifth percentile of the distribution, the upper end with the seventy-fifth. We observe that the central band of the distribution has the same excursion towards the lower extreme (50% -36.4% = 13.6%) than the upper one (63.6% -50% = 13.6%).

As a further check, let’s ask the data the same question once again, using a different survey tool: the ROC curve.

Figure 8. ROC curve that correlates the percentage of games won to the advantages with the victory of the match, based on the men’s singles matches played in Grand Slam tournaments in the period 2011-2021

We will ask ourselves, this time, if there are thresholds (not necessarily 50%) of 40-40 games that can become decisive for the match win. Once again, for the reasons already mentioned, we will focus on matches with at least ten hard-fought games. To conduct this type of analysis, we can use the ROC curve.

To trace it, we will proceed as follows:

  1. every possible threshold value is considered in terms of percentage of deuce games won, starting from 0% up to 100%
  2. for each of these values ​​(let’s take 10% for example) we ask ourselves: how accurate would it be to say that whoever wins more than 10% of the game at the advantages wins the match?
  3. the answer to this question is analysed using two components: sensitivity (i.e. the percentage of correctly identified victories) and specificity (i.e. the percentage of correctly identified losses)
  4. each threshold can therefore be represented as a point, drawn in a chart in which the vertical axis is represented by the wording “Sensitivity” and the horizontal axis represented by “Specificity”
  5. by connecting these points, a curve can be drawn, called ROC curve (Receiver Operating Curve)
  6. it can be shown that the area included under this curve, called AUC (Area Under the Curve) equals to the probability that, given a pair of matches (match 1 and match 2), the percentage of deuce games won by the winner of match 1 is greater than the percentage of deuce games won by the loser of match 2.

The more the AUC approaches to the value of 1, the more the element considered (in this case the percentage of deuce games won) is relevant compared to the target (the match win). We observe that, in this case, the AUC is equal to 0.504, just above 50%. The lack of relevance of deuce games supremacy therefore seems to be confirmed.

Let’s now try to ask ourselves if, indeed, as is often supposed, the victory of the first set is often decisive, especially for the underdog player.

THE FIRST SET IS KEY, ESPECIALLY FOR THE WEAKER PLAYER

Figure 9. Distribution of 2011-2021 Grand Slam matches with respect to the question: who wins the first set wins the match?

The matches in which the winner of the first set has a better ATP ranking at the end of the season is represented by the green bars of the histogram, the other matches are represented by the red bars. So let’s ask ourselves if, especially in a Grand Slam tournament, considering the men’s singles matches only and therefore a three out of five set match, the victory in the first set is relevant and, more specifically, let’s try to understand if this consideration is more valid for players who face an opponent of greater clout, or with a better ATP ranking.

First of all, we observe that 2,271 of the 2,902 matches considered ended with the victory of the player who won the first set: in other words, in 78.2% of cases whoever won the first set also won the match. This is by far the strongest pattern explored in this article. For example, if we consider the effect of ranking on the outcome of the match, we observe that in 2,238 cases out of 2,902 (i.e. in 77.1% of cases) the match is won by that player who, at the end of the season, will occupy a better position in the ATP ranking. In other words, the victory of the first set seems to “weigh” even more (albeit slightly) than the ranking in the outcome of the match.

And, as conventional wisdom teaches, the combination of the two factors is even more predictive of the name of the match winner. In fact, if the first set is won by the lower ranked player, the opponent will manage to get away with it in 30% of cases (196 matches out of 664). If, on the other hand, the better-ranked player takes the first set, then his opponent seems to have less than a 20% chance of reversing the situation (435 cases out of 2238).

This is what the data tell us, which, as always, we try to approach with a critical eye. That is, always keeping in mind Henri Poincarè, according to whom “science is made of data as a house is made of stones. But a mass of data is no more science than a pile of stones is a real house.”

Article by Damiano Verda; translated by Michele Brusadelli; edited by Tommaso Villa

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Wimbledon Daily Preview: Compelling Matchups Scheduled All Around the Grounds on Thursday

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A look at the grounds of The All-England Club (twitter.com/wimbledon)

Day 4 play is headlined by top names such as Rafael Nadal, Iga Swiatek, Coco Gauff, and Stefanos Tsitsipas.  Those names are all considerable favorites in their second round matches, so other matchups on Thursday’s schedule may be more compelling and competitive.  And with many of those encounters scheduled at the same time, multiple screens are recommended.

 

Throughout the tournament, this preview will analyze the day’s five most prominent matches, while highlighting the other notable matches on the schedule.  Thursday’s play begins at 11:00am local time.


Filip Krajinovic (26) vs. Nick Kyrgios – Second on No.2 Court

Despite his usual poor behavior, Kyrgios survived in five on Tuesday against British wild card Paul Jubb, who is ranked outside the top 200 in the world.  But Nick is in strong form this month, with an 8-3 record on grass, having reached the semifinals of both Stuttgart and Halle.  Krajinovic is also in the midst of a strong grass court season, coming off a run to the final of Queen’s Club.  Like Kyrgios, he also required five sets to advance in the first round.  That was actually Filip’s first-ever win at SW19, as he was 0-4 prior to this fortnight.  Krygios leads their head-to-head 3-0 at all levels, though they haven’t played since 2015.  On grass, Nick’s formidable firepower should be plenty to prevail again over Filip, as long as he can maintain his composure.


Elena Rybakina (17) vs. Bianca Andreescu – Second on Court 12

On Tuesday, Andreescu achieved her first career victory at The Championships.  Bianca had only played five tour-level matches on grass ahead of this year, though she’s now 5-2 on grass this month.  Rybakina reached the fourth round of Wimbledon a year ago, but lost two of her three grass court matches coming into this event.  In their first career meeting, I give the slight edge to Andreescu based on recent form.  And while Elena has accumulated 22 wins this season, only four of them have come at Majors, and none of those four against a top player like Bianca.


Barbora Krejcikova (13) vs. Viktorija Golubic – Second on Court 18

This is only Krejickova’s fourth singles match since February due to an elbow injury.  Her opening round victory was her first since returning to the tour.  Golubic was a surprise quarterfinalist here a year ago, when she defeated both Danielle Collins and Madison Keys.  Yet she has not been able to follow-up on that result, as she has a losing record since that run.  They have split four previous meetings at all levels.  Their most recent clash occurred two years ago in Dubai, with Barbora prevailing 6-1, 6-2.  But her lack of match play, along with Viktorija’s grass prowess, make Krejcikova an underdog on this day.  While results on other surfaces have not followed, Golubic is now 13-7 on grass since last season, which includes a semifinal appearance earlier this month in Nottingham.


Karolina Pliskova (6) vs. Katie Boulter (WC) – 1:30pm on Centre Court

Pliskova was the runner-up a year ago, losing the championship match to Ash Barty 6-3 in the third.  Unfortunately a hand injury forced her to miss the first two months of 2022, and she’s only 9-10 this season as a result.  Boulter is a 25-year-old Brit who pushed Aryna Sabalenka to three sets at last year’s event, and is 8-3 on grass at all levels this season.  And just like week, Boulter beat Pliskova on grass in Eastbourne 6-4 in the third.  Now can Katie repeat that result on her country’s most prestigious court?  She’ll certainly have the full support of the Centre Court audience, and her experience last year on this court could prove extremely valuable.  Considering Pliskova has only twice won back-to-back matches this year, an upset on Thursday feels entirely possible.


Alex de Minaur (19) vs. Jack Draper – Third on No.1 Court

This could easily become the most competitive show court match of the day.  And the British crowd will be vociferously behind Draper, especially late in the day on the tournament’s second biggest court.  Jack is a 20-year-old Brit who last year took a set off Novak Djokovic on Centre Court.  And he’s collected 31 match wins at all levels this season, which includes four Challenger titles as well as a semifinal run just last week in Eastbourne.  But de Minaur is also having a strong season.  The Australian has 25 wins, all at tour level, and was also a semifinalist in Eastbourne.  Both players won their first round matches in straight sets, so they’re surely feeling fresh and confident.  While Alex’s defensive skills will force Jack to strike some extra balls, Draper’s offensive weapons will be rewarded on this surface.  And the crowd’s encouragement may be the x-factor Draper needs to prevail.


Other Notable Matches on Thursday:

Stefanos Tsitsipas (4) vs. Jordan Thompson – Tsitsipas prevailed in four sets on Tuesday, bringing his Wimbledon record to just 4-4.  He’s 1-0 against Thompson, who is only 8-12 this season at tour level.

Rafael Nadal (2) vs. Ricardas Berankis – Nadal is now 31-3 on the year, and seemed rather unbothered by his chronic foot injury in the opening round.  Earlier this season in Australia, he defeated Berankis in straight sets.

Iga Swiatek (1) vs. Lesley Pattinama Kerkhove (LL) – A victory for Swiatek on Thursday would be her 37th consecutive win, tying her with Martina Hingis for the longest women’s singles win streak across the past three decades.  Lesley is a 30-year-old ranked 138th in the world who at last year’s Wimbledon earned for first-ever main draw win at a Major by defeating Svetlana Kuznetsova.

Simona Halep (16) vs. Kirsten Flipkens – Halep is on an eight-match win streak at Wimbledon, dating back to her title run in 2019.  36-year-old Flipkens has said this will be her last-ever singles tournament.  She was a semifinalist here in 2013. 

Coco Gauff (11) vs. Mihaela Buzarnescu – Gauff scarcely survived the first round, overcoming Elena-Gabriela Ruse 7-5 in the third.  But Coco should be able to settle into the tournament from here, especially against Buzarnescu.  She’s currently 127th in the world, and on Tuesday won her first WTA-level match in nearly a year.


Thursday’s full Order of Play is here.

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Roland Garros Daily Preview: The Second Major of 2022 Begins on Sunday

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A shot from the grounds of the French Open (twitter.com/rolandgarros)

The second Major of the year is upon us, with its unique Sunday start.  Roland Garros is the only Grand Slam event where first round singles play is spread across three days. 

 

The men’s draw is headlined by 13-time champion Rafael Nadal, defending champion Novak Djokovic, 2021 runner-up Stefanos Tsitsipas, and the ATP’s breakout star of the last 12 months, Carlos Alcaraz.  The 19-year-old Spaniard will play his opening match on Sunday, as will top ATP names like Dominic Thiem and Sascha Zverev.

The women’s draw features 12 Major singles champions, five of whom have won this event: Iga Swiatek, Barbora Krejicikova, Simona Halep, Jelena Ostapenko, and Garbine Muguruza.  The 28-year-old Spaniard plays perpetual draw-buster Kaia Kanepi on Sunday.  The Order of Play also includes the red-hot Ons Jabeur and US Open finalist Leylah Fernandez, who faces France’s Kiki Mladenovic.

Throughout the tournament, this preview will analyze the day’s two most prominent matches, while highlighting the other notable matches on the schedule.  Sunday’s play begins at 11:00am local time.


Ons Jabeur (6) vs. Magda Linette – 11:00am on Court Philippe Chatrier

Outside of Iga Swiatek, Jabeur is the WTA player with the most momentum heading into Paris.  Before losing to Swiatek in the final of Rome, Ons was on an 11-match win streak, coming off her title run in Madrid.  She’s now 17-3 on clay this season, and has reached the fourth round of this tournament the last two years.  She’ll be a considerable favorite against Linette on Sunday, though Magda could easily test the sixth seed.  The 30-year-old from Poland was a quarterfinalist this year at clay events in Charleston and Strasbourg, and she owns victories over some top names at Majors, including Ash Barty and Elina Svitolina.  They’ve met twice before on clay, with both matches going to Jabeur.  That includes a three-set encounter at this event a year ago.  I expect a similar result on Sunday.


Hugo Dellien vs. Dominic Thiem (PR) – 11:00am on Court Simonne Mathieu

Thiem is a two-time French Open finalist, but he is still fighting for his first win in over a year.  Since coming back from his wrist injury, he is 0-6 at all levels, with all those matches occurring on clay.  Earning that elusive win in the best-of-five format may prove challenging for an out-of-form player.  This will be Thiem’s first match against Dellien, a 28-year-old from Bolivia who has played 43 matches on clay this season at all levels.  He’s accumulated 30 wins, and advanced to two Challenger finals.  However, Hugo is yet to defeat a top 40 player this year.  While Dominic is not currently a member of that group, and is not performing at that level, taking out a Major champion at a Grand Slam event remains a daunting task.  At a tournament where Thiem has fond memories of success, I expect Dominic is earn his first win since last May.


Garbine Muguruza (10) vs. Kaia Kanepi – Second on Court Simonne Mathieu

Muguruza is a two-time Major champion, and won the third-biggest title of her career at November’s WTA Finals in Guadalajara.  But since that title run, Muguruza has struggled mightily, with a record of 7-8 in 2022.  She’s won back-to-back matches only once this season.  And in the opening round, she’s drawn one of the sport’s most dangerous floaters.  Kanepi has made a career out of upsetting top seeds at Majors.  As per Tennis Abstract, she owns nine top 10 wins at Grand Slam events, over the likes of Angelique Kerber, Simona Halep, and most recently at January’s Australian Open, Aryna Sabalenka.  Kaia is a seven-time quarterfinalist at Majors, including two times at Roland Garros.  Her only previous meeting with Muguruza took place eight years ago in Melbourne, when Muguruza prevailed in three sets.  But considering Garbine’s recent form, and Kaia’s history at Majors, this match is definitely deserving of an upset alert.


Carlos Alcaraz (6) vs. Juan Ignacio Londero (Q) – Fourth on Court Philippe Chatrier

Alcaraz has rapidly become one of the ATP’s players.  Carlitos is 28-3 in 2022, with four titles.  He is No.3 in the year-to-date rankings, and is within 200 points of the two players ahead of him (Nadal, Tsitsipas).  The teenager arrives in Paris on a 10-match win streak on clay, having taken back-to-back titles in his home country.  Londero is a former top 50 player who reached the fourth round of this event in 2019.  But he is coming off multiple seasons with a losing record, and hasn’t played a match since early-April.  Alcaraz should not have much trouble dismissing Londero on Sunday, though it is always a treat to see the Spaniard’s formidable skills on display.


Leylah Fernandez (17) vs. Kiki Mladenovic – Fourth on Court Suzanne Lenglen

Fernandez has not immediately been able to follow-up on her thrilling US Open run from last summer.  Despite winning a title in Monterrey, she hasn’t reached a quarterfinal at any other event this year.  But still only 19-years-of-age, Leylah undoubtedly has some big results ahead of her.  Mladenovic was top 10 player in 2017, the same year she was a quarterfinalist at her home Slam.  But the Frenchwoman is 2-4 in Paris since, and only 2-10 this season at all levels.  While Kiki will certainly be motivated by the Parisian crowd, it would be surprising if she could upset Leylah, as the Canadian remains a dogged competitor who thrives on big stages.


Other Notable Matches on Sunday:

Sloane Stephens vs. Jule Niemeier (Q) – Stephens was the 2018 runner-up in Paris, and reached the fourth round a year ago.  But she’s 0-4 on clay in 2022.  Niemeier is a 22-year-old German who won an ITF-level event on clay last month.

Grigor Dimitrov (18) vs. Marcos Giron – Dimitrov is only 12-11 lifetime at Roland Garros, though he was a semifinalist in Monte Carlo this season.  This is a rematch from last year’s French Open, when Giron defeated Dimitrov after Grigor retired during the fourth set.

Felix Auger-Aliassime (9) vs. Juan Pablo Varillas (Q) – Auger-Aliassime is still looking for his first main draw win at Roland Garros.  He is 8-6 on clay this year.  Varillas is a 26-year-old from Peru who has won 19 matches on clay this season at all levels.

Maria Sakkari (4) vs. Clara Burel – Sakkari has some scar tissue to overcome at this event, as in last year’s semifinals, she was one point away from defeating eventual champion Barbora Krejicikova.  Burel is a 20-year-old from France who is a former junior No.1.

Sascha Zverev (3) vs. Sebastian Ofner (Q) – Zverev has reached the second week of this tournament four consecutive times.  Ofner is a 26-year-old from Austria who prevailed at a Challenger event in Prague last month.


Sunday’s full Order of Play is here.

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[VIDEO] Merry Christmas from Ubitennis!

Our CEO Ubaldo Scanagatta sends his greetings to all the readers of ubitennis.net

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From everybody at ubitennis.net, we want to send to our readers our Christmas greetings: thank you for your ever-growing support! Here’s a message from the website’s CEO, Ubaldo Scanagatta:

 

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