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87-406: The tournament uses a unique format not seen in other ATP Tour events, where the singles players and doubles teams are separated into two groups of four, within which they each play three round-robin matches. After the round-robin stage, the top two performers from each group play in knock-out semifinals and a final to determine the champion(s). The tournament was first held in 1970, shortly after

174-463: A bye . The schedule can therefore be computed as though the dummy were an ordinary player, either fixed or rotating. Instead of rotating one position, any number relatively prime to ( n − 1 ) {\displaystyle (n-1)} will generate a complete schedule. The upper and lower rows can indicate home/away in sports, white/black in chess , etc.; to ensure fairness, this must alternate between rounds since competitor 1

261-464: A bye. If the number is even, an added player (ω) becomes the opponent. For an even number n {\displaystyle n} or an odd number n − 1 {\displaystyle n-1} of competitors, Schurig builds a table with n / 2 {\displaystyle n/2} vertical rows and n − 1 {\displaystyle n-1} horizontal rows. Then he populates it starting from

348-489: A certain number of wins or losses. The term round-robin is derived from the French term ruban ('ribbon'). Over time, the term became idiomized to robin . In a single round-robin schedule, each participant plays every other participant once. If each participant plays all others twice, this is frequently called a double round-robin . The term is rarely used when all participants play one another more than twice, and

435-527: A clay court. In Britain, where En-Tout-Cas is based, most red clay courts have a surface dressing of burnt shale (with or without brick) for improving drainage. However, shale courts are now comparatively rare, having been steadily replaced in many clubs by all-weather synthetic surfaces (including artificial clay). The few courts that remain tend to be found in industrial areas such as central Scotland and Lancashire , as shale – known as blaes in Scotland –

522-411: A competitor to play the strongest opponents in a round robin in quick succession while others play them intermittently with weaker opposition. This asymmetry means that playing the same opponents is not necessarily completely equitable. There is also no scheduled showcase final match unless (by coincidence) two competitors meet in the last match of the tournament, with the result of that match determining

609-477: A competitor's chance of ultimate victory. Final records of participants are more accurate, in the sense that they represent the results over a longer period against the same opposition. The system is also better for ranking all participants, not just determining the winner. This is helpful to determine the final rank of all competitors, from strongest to weakest, for purposes of qualification for another stage or competition as well as for prize money. In team sports,

696-493: A hard court variant, which has prompted calls from some players (such as Rafael Nadal ) to feature a greater variety of surfaces, including clay courts . For many years, the doubles event was held as a separate tournament staged the week after the singles competition, but more recently both events have been held together during the same week and in the same venue. In 2020, amid the COVID-19 pandemic and in an effort to reduce

783-489: A lower-placed qualifier is perceived to be easier than for a higher-placed one). Four pairs in the 2012 Olympics Women's doubles badminton , having qualified for the next round, were ejected from the competition for attempting to lose in the round robin stage to avoid compatriots and better ranked opponents. The round robin stage at the Olympics was a new introduction, and these potential problems were readily known prior to

870-701: A new jointly-owned event called the "Tennis Masters Cup". As with the Masters Grand Prix and the ATP Tour World Championships, the Tennis Masters Cup was contested by eight players and teams. However, the player or team ranked number eight in the ATP Race world rankings was not guaranteed a spot: if a player or team won one of the year's majors and finished the year ranked from ninth to twentieth, they were included in

957-535: A player to deliver an unreturnable shot. Points are usually longer as there are fewer winners . Clay courts favor baseliners who are consistent and have a strong defensive game, leading to players such as Rafael Nadal , Björn Borg , Chris Evert , and Justine Henin finding success at the French Open. Players who excel on clay courts but struggle to replicate the same form on fast courts are known as clay-court specialists . Clay-court players generally play in

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1044-621: A product, and by the 1920s the company was responsible for laying clay courts for the Davis Cup and at the French , British and Canadian Championships. During the following decade the American engineer H. A. Robinson went still further, creating a surface based on classic clay augmented with green piled metabasalt rock, which he hoped would help deliver a more consistent bounce. This became known as Har-Tru, derived from Robinson's initials and

1131-437: A round in which players meets each other. For example, player 7 plays against player 11 in round 4. If a player meets itself, then this shows a bye or a game against player n. All games in a round constitutes a diagonal in the table. The above schedule can also be represented by a graph, as shown below: Both the graph and the schedule were reported by Édouard Lucas in as a recreational mathematics puzzle. Lucas, who describes

1218-497: A round, a non-leftmost position (not including 1 {\displaystyle 1} ) can only be taken by competitors of a fixed distance. In round 1 {\displaystyle 1} of the example, in the second position competitor 2 {\displaystyle 2} plays against 13 {\displaystyle 13} , their distance is 2 {\displaystyle 2} . In round 2 {\displaystyle 2} , this position

1305-540: A schedule where player 14 has a fixed position, and all other players are rotated counterclockwise n 2 {\displaystyle {\frac {n}{2}}} positions. This schedule is easily generated manually. To construct the next round, the last player, number 8 in the first round, moves to the head of the table, followed by player 9 against player 7, player 10 against 6, until player 1 against player 2. Arithmetically, this equates to adding n 2 {\displaystyle {\frac {n}{2}}} to

1392-405: A semicircle about 1.5 to 3 metres (5 to 10 feet) behind the baseline. Clay courts favor the "full western grip " for more topspin . Clay court players use topspins to throw off their opponents. Movement on the loose surface is very different from movement on any other surface, often involving sliding toward the incoming ball while preparing for the return stroke. Clay courts are unique in that

1479-619: A straight knockout system. The top one, two, or occasionally three teams in these groups then proceed to a straight knockout stage for the remainder of the tournament. In the circle of death it is possible that no champion emerges from a round-robin tournament, even if there is no draw, but most sports have tie-breaker systems which resolve this. Round-robins can suffer from being too long compared to other tournament types, and with later scheduled games potentially not having any substantial meaning. They may also require tie-breaking procedures. Swiss system tournaments attempt to combine elements of

1566-403: A string of successes on other surfaces—including completing a Double Career Grand Slam and a Career Golden Slam —led to a broadening of his reputation. 2016 French Open winner Garbiñe Muguruza reached the 2015 Wimbledon final and won the 2017 Wimbledon title. The professional clay court season comprises many more tournaments than the brief grass court season, but is still shorter than

1653-526: A table. In France this is called the Carousel -Berger system (Système Rutch-Berger). The schedule can also be used for "asynchronous" round-robin tournaments where all games take place at different times (for example, because there is only one venue). The games are played from left to right in each round, and from the first round to the last. When the number of competitors is even, this schedule performs well with respect to quality and fairness measures such as

1740-782: A thin layer of fine clay particles on top. Clay courts are more common in Continental Europe and Latin America than in North America, Asia-Pacific or Britain. The only Grand Slam tournament that uses clay courts is the French Open . Clay courts come in the more common red clay , which is actually crushed brick , and the slightly harder green clay , also known as "rubico", which is actually crushed metabasalt . Although slightly less expensive to construct than other types of tennis courts, clay requires much maintenance:

1827-416: A tournament of 16 teams can be completed in just 4 rounds (i.e. 15 matches) in a knockout format; a double elimination tournament format requires 30 (or 31) matches, but a round-robin would require 15 rounds (i.e. 120 matches) to finish if each competitor faces each other once. Other issues stem from the difference between the theoretical fairness of the round robin format and practice in a real event. Since

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1914-571: A variety of tiebreaker criteria. Frequently, pool stages within a wider tournament are conducted on a round-robin basis. Examples with single round-robin scheduling include the FIFA World Cup , UEFA European Football Championship , and UEFA Cup (2004–2009) in football, Super Rugby ( rugby union ) in the Southern Hemisphere during its past iterations as Super 12 and Super 14 (but not in its later 15- and 18-team formats),

2001-503: Is a constituent element of colliery waste and thus can be easily and cheaply sourced in such locations. Shale courts tend to be a lighter shade of red than European clay courts. Aside from crushed brick and shale, other surfaces have also been used as a substitute for natural red clay. In Queensland and New South Wales , courts made from crushed ant hill mounds (known as "ant bed" or "dirt" courts) can occasionally be found; these are similar in appearance to standard red clay courts, as

2088-613: Is a simple algorithm to create a schedule for a round-robin tournament. All competitors are assigned to numbers, and then paired in the first round: Next, one of the competitors in the first or last column of the table is fixed (number one in this example) and the others rotated clockwise one position: This is repeated until when the next iteration would lead back to the initial pairings: With an even number n {\displaystyle n} of competitors this algorithm realizes every possible combination of them (equivalently, that all pairs realized are pairwise different). First,

2175-458: Is a tennis player who excels on clay courts, more than on any other surface. Due in part to advances in racquet technology, current clay-court specialists are known for employing long, winding groundstrokes that generate heavy topspin; such strokes are less effective on faster surfaces on which the balls do not bounce as high. Clay-court specialists tend to slide more effectively on clay than other players. Many of them are also very adept at hitting

2262-435: Is always on the first row. If, say, competitors 3 and 8 were unable to fulfil their fixture in the third round, it would need to be rescheduled outside the other rounds, since both competitors would already be facing other opponents in those rounds. More complex scheduling constraints may require more complex algorithms. This schedule is applied in chess and draughts tournaments of rapid games, where players physically move round

2349-691: Is even, then in each of ( n − 1 ) {\displaystyle (n-1)} rounds, n 2 {\displaystyle {\begin{matrix}{\frac {n}{2}}\end{matrix}}} games can be run concurrently, provided there exist sufficient resources (e.g. courts for a tennis tournament). If n {\displaystyle n} is odd, there will be n {\displaystyle n} rounds, each with n − 1 2 {\displaystyle {\begin{matrix}{\frac {n-1}{2}}\end{matrix}}} games, and one competitor having no game in that round. The circle method

2436-1054: Is held by competitors 14 {\displaystyle 14} and 12 {\displaystyle 12} , also having distance 2 {\displaystyle 2} , etc. Similarly, the next position ( 3 {\displaystyle 3} against 12 {\displaystyle 12} in round 1 {\displaystyle 1} , 2 {\displaystyle 2} against 11 {\displaystyle 11} in round 2 {\displaystyle 2} , etc.) can only hold distance- 4 {\displaystyle 4} competitors. For every k < n 2 {\displaystyle k<{\frac {n}{2}}} , there are exactly n − 1 {\displaystyle n-1} pairs of distance k {\displaystyle k} . There are n − 1 {\displaystyle n-1} rounds and they all realize one distance- k {\displaystyle k} pair at

2523-504: Is never used when one participant plays others an unequal number of times, as is the case in almost all of the major North American professional sports leagues. In the United Kingdom , a round-robin tournament has been called an American tournament in sports such as tennis or billiards which usually have single-elimination (or "knockout") tournaments, although this is now rarely done. A round-robin tournament with four players

2610-513: Is packed to make the court, with the top most layers consisting of finely crushed loose particles. Such courts are most common in Europe and Latin America. The exact color of the surface varies with the composition of the bricks used, and can appear from a light yellow to a deep red. Natural clay courts are rare because this type of surface does not absorb water easily and takes two to three days to dry. A good example of natural red clay can be seen at

2697-413: Is sometimes called "quad" or "foursome". In sports with a large number of competitive matches per season, double round-robins are common. Most association football leagues in the world are organized on a double round-robin basis, in which every team plays all others in its league once at home and once away. This system is also used in qualification for major tournaments such as the FIFA World Cup and

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2784-408: Is the fairest way to determine the champion from among a known and fixed number of contestants. Each contestant, whether player or team, has equal chances against all other opponents because there is no prior seeding of contestants that will preclude a match between any given pair. The element of luck is seen to be reduced as compared to a knockout system since one or two bad performances need not ruin

2871-548: Is the long spring clay season that starts in the Americas and Morocco before moving to mainland Europe and finishing with the French Open. It is usually played over two months between April and June, after the Miami Open . Unlike the other two clay seasons, this swing does not share the majority of its time with simultaneous hard court tournaments. The third is the brief summer clay season that takes place after Wimbledon. It

2958-486: Is the men's premier indoor event of the season, only in three editions it was played outdoors; 1974, 2003 and 2004. The 2024 ATP Finals has a total prize money pool of $ 15,250,000, an increase of 1.67% compared to 2023 and the same total as the WTA Finals for the first time since 2015. The tournament rewards the following points and prize money, per victory (Doubles' prize money is per team): Additional prizes include

3045-533: The 2024 title, Sinner earned a record $ 4,881,100, the highest payout for a tournament winner in tennis. In 2022 , Rajeev Ram and Joe Salisbury claimed $ 930,300, the highest payout in doubles history. The ATP Finals is the fifth iteration of a championship which began in 1970. It was originally known as the Masters Grand Prix and was part of the Grand Prix tennis circuit . It was organised by

3132-574: The 2025 ICC Champions Trophy . In a more extreme example, the KBO League in baseball plays a 16-fold round robin, with each of the 10 teams playing each other 16 times for a total of 144 games per team. LIDOM (Baseball Winter League in the Dominican Republic) plays an 18-fold round robin as a semi final tournament between four classified teams. Group tournaments rankings usually go by number of matches won and drawn, with any of

3219-656: The Cricket World Cup along with Indian Premier League , major Twenty-20 Cricket tournament, and many American football college conferences , such as the Conference USA (which currently has 9 members). The group phases of the UEFA club competitions and Copa Libertadores are contested as a double round-robin, as are most basketball leagues outside the United States, including the regular season of

3306-536: The EuroLeague (as well as its former Top 16 phase); the United Football League has used a double round-robin for both its 2009 and 2010 seasons. Season ending tennis tournaments also use a round robin format prior to the semi on stages. The champion in a round-robin tournament is the contestant that wins the most games, except when draws are possible. In theory, a round-robin tournament

3393-932: The drop shot , which can be effective because rallies on clay courts often leave players pushed far beyond the baseline. Additionally, the slow, long rallies require a great degree of mental focus and physical stamina. The definition of "clay-court specialist" has varied. Anthony Wilding, Sergi Bruguera , Albert Costa and Gastón Gaudio were French Open champions who won all or nearly all of their career titles on clay. Andrés Gimeno , Adriano Panatta , Manuel Orantes , Yannick Noah , Michael Chang , Thomas Muster, Gustavo Kuerten , Carlos Moyá and Juan Carlos Ferrero won major titles only on clay, but won lower tournaments, including Masters Series events, on other surfaces. Among female players, there have been few whose best results were confined exclusively to clay. Virginia Ruzici , Anastasia Myskina , Iva Majoli , Sue Barker , Ana Ivanovic , Francesca Schiavone and Jeļena Ostapenko are

3480-645: The 'true' nature of the bounce experienced on the court. First used in Hagerstown, Maryland , in 1932, green Har-Tru clay soon became the preferred surface for American clay court tournaments. In later years, the Har-Tru company would go on to develop all-weather clay surfaces at its factory in Charlottesville, Virginia , that could be played on throughout the entire year. Almost all red clay courts are now made not of natural clay but of crushed brick that

3567-606: The ATP Finals trophy and the ATP year-end No. 1 trophy, all made by London-based silversmiths Thomas Lyte . Note: Titles, won by a team of players from same country , count as one title, not two. Round-robin tournament A round-robin tournament or all-play-all tournament is a competition format in which each contestant meets every other participant, usually in turn. A round-robin contrasts with an elimination tournament , wherein participants are eliminated after

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3654-470: The French Open (1976–78), to participate in World Team Tennis . She also has the highest career win percentage on clay courts (94.55%) during the open era. The most successful currently active female player on clay is Iga Świątek , who won the French Open in 2020 , 2022 , 2023 , and 2024 . In 2022 and 2024, Świątek won three titles and lost only one match on clay. A clay-court specialist

3741-539: The Frick Park Clay Courts in Pittsburgh , a public facility of six red clay courts that has been in continual use since 1930. Sports surface providers such as En-Tout-Cas still offer red clay surfaces with a coarser top layer to improve drainage. These courts are particularly popular in southern Australian states such as Victoria , where the phrase 'En-Tout-Cas' is a common generic shorthand for

3828-696: The International Lawn Tennis Federation ( ILTF ) and ran alongside the competing WCT Finals from 1971 to 1989. The Masters was a year-end showpiece event between the best players on the men's tour, but did not count for any world ranking points. In 1990, the Association of Tennis Professionals (ATP) took over the running of the men's tour and replaced the Masters with the "ATP Tour World Championships". World ranking points were now at stake, with an undefeated champion earning

3915-459: The Tennis Masters Cup instead. If two outside the top eight won majors, the higher-ranked of the two in the world rankings took the final spot. This accommodation for major champions continues in the event's current form. In 2009 , the championship was renamed the "ATP World Tour Finals" and was held at The O2 Arena in London. The contract ran through 2013, but was extended multiple times until it

4002-715: The US Open in 1977 while it was held on clay. Thomas Muster is also considered a successful clay court player; although he also only won the French Open once, 40 out of his 44 career singles titles were won on clay. Other notable players who had significant success on clay include Ivan Lendl and Björn Borg - the former winning the French Open in 1984, 1986, and 1987, while the latter won it 6 times. While often overshadowed by Nadal's clay successes due to being contemporaries, Roger Federer and Novak Djokovic also were known for being extremely formidable on clay courts throughout their careers and had significant successes. Federer made

4089-532: The Vallauris terracotta pots, as the factory could not keep up with this eruption in demand. Courts covered in a top layer of brick dust thereafter became the norm in many Mediterranean and South American countries, as they were not only durable in summer but did not need to be tended and mowed, as grass courts did (although they did require regular maintenance involving rolling, "dragging", and occasional watering). Yet further improvements were still imperative, as

4176-446: The algorithm obviously realizes every pair of competitors if one of them equals 1 {\displaystyle 1} (the non-moving competitor). Next, for pairs of non- 1 {\displaystyle 1} competitors, let their distance be the number k < n 2 {\displaystyle k<{\frac {n}{2}}} of times the rotation has to be carried out in order that one competitor arrives at

4263-540: The amount of rest between games. On the other hand, when the number of competitors is odd, it does not perform so well and a different schedule is superior with respect to these measures. Alternatively Berger tables, named after the Austrian chess master Johann Berger , are widely used in the planning of tournaments. Berger published the pairing tables in his two Schach-Jahrbücher (Chess Annals), with due reference to its inventor Richard Schurig. This constitutes

4350-493: The ant hill "loam" or grit is pinky-brown in color. Top Australian competitors such as Mal Anderson , Roy Emerson and Rod Laver , who all grew up in Queensland, practiced on ant bed courts when they were young. Green clay, also known by brand names such as Har-Tru and Rubico, is made of crushed metabasalt rather than brick, making the surface slightly harder and faster than red clay. These courts are located primarily in

4437-428: The ball bounce leaves an impression in the ground, which can help determine whether a shot was in or out. Furthermore, clay courts are still playable in light rain because the courts are meant to be slightly wet when played on and the surface absorbs water better than hard courts and grass courts. This is opposed to hard courts and grass courts where play is usually suspended almost immediately during even light rain. In

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4524-477: The beginning of the Open Era . Novak Djokovic holds the record for the most singles titles with seven, while Peter Fleming and John McEnroe jointly hold the record for the most doubles titles with seven (all won consecutively as a team). In the tournament's current format, the champion can earn a maximum of 1,500 ranking points, if they win the event after going undefeated in the round-robin stage. By winning

4611-462: The bounce on these courts was often irregular, the surface dried slowly after rain had fallen, and the courts could not be used in winter months for fear of damage. In 1909, the newly-established Leicestershire firm En-Tout-Cas (translated roughly into English as "in all conditions") came up with a prototype court made from crushed brick and burnt shale that could drain much more quickly than standard clay courts. These proved very popular once offered as

4698-435: The championship. A notable instance of such an event was the 1950 FIFA World Cup match between Uruguay and Brazil . Further issues arise where a round-robin is used as a qualifying round within a larger tournament. A competitor already qualified for the next stage before its last game may either not try hard (in order to conserve resources for the next phase) or even deliberately lose (if the scheduled next-phase opponent for

4785-542: The competition, his results are considered separately, i.e. the alternate does not inherit the results of the player he is replacing. If an alternate's round-robin results qualify him for the semifinals, then he may continue into the single-elimination rounds. Unlike other events on the ATP Tour , the ATP Finals is not a straightforward single-elimination tournament. The eight players and teams are divided into two groups of four and each play three round-robin matches against

4872-581: The continental tournaments (e.g. UEFA European Championship , CONCACAF Gold Cup , AFC Asian Cup , CONMEBOL Copa América and CAF Cup of Nations ). There are also round-robin cricket , bridge , chess , draughts , go , ice hockey , curling , and Scrabble tournaments. The World Chess Championship decided in 2005 and in 2007 on an eight-player double round-robin tournament where each player faces every other player once as white and once as black. There has been several major international cricket tournaments held in this format including ICC events, including

4959-560: The court should be covered with a fine powder that would protect it from the sun's rays. This powder was sourced from discarded terracotta discovered at a small ceramics factory in Vallauris , near Cannes , where the brothers regularly purchased decorative pots for their garden. Success with the new surface came quickly: after only a year or two, it was reported that 104 clay courts had been built in Cannes alone. Brick powder soon replaced

5046-427: The court surface and the court's illumination. In recent years it has been played on indoor hard courts, however, indoor carpet was used in some previous editions. On one occasion, when Melbourne hosted the event in 1974 , the grass courts of Kooyong Stadium were used; the tournament was staged only 1–2 weeks before the 1975 Australian Open , which was also played on grass. Apart from 1974, all tournaments have been on

5133-405: The final of the French Open every year from 2006 to 2009, finally winning the last one in the sequence, while Djokovic has won the title 3 times (2016, 2021, 2023), beating Nadal en route to the title in 2021. Federer is also notable for ending Nadal's 81 match win streak on clay courts in 2007 at the 2007 Hamburg Masters. On the women's side, Monica Seles , Justine Henin and Iga Swiatek hold

5220-450: The following years: Since 2019, the group standings at the end of the round-robin stage are determined by, in order: If some players are tied, the following tiebreakers are used depending on how many players are tied (two or three): If two players are tied , then: If three players are tied , then the following tiebreakers are used, in order, until all three players are no longer tied OR until only two players are tied, at which point

5307-469: The groups, the eight players and teams are seeded according to rank. The first and second seeds are placed in Group A and Group B, respectively. The remaining seeds are drawn in pairs (third and fourth, fifth and sixth, seventh and eighth); the first of the pair to be drawn goes to Group A and the other to Group B, and so on. The format described above has been in place for all editions of the tournament except

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5394-738: The hard court seasons. There are three distinct clay court seasons during the year. The first is the men's South American clay season. Played primarily in February between the Australian Open and the Indian Wells Masters , the ATP has four tournaments in this swing, although other ATP tournaments played on hardcourt occur the same weeks. The WTA discontinued its participation in Rio de Janeiro after 2016, so there are no clay court women's tournaments during this period. The second

5481-413: The highest-ranked player who has not otherwise qualified for the event. If both alternate spots are available, they are awarded to the two highest-ranked players who did not otherwise qualify for the event. An alternate can replace a player who withdraws before the round-robin stage is over, so long as the player who withdraws still has at least one round-robin match left to play. When an alternate enters

5568-399: The main sponsor for the tournament through 2020. In September 2020, Nitto Denko announced it will extend its title partnership of the ATP Finals for another five years, until 2025. The criteria to qualify for the ATP Finals are as follows: Two alternates also attend the ATP Finals. If the first alternate has already been selected according to (3) mentioned above, then the second alternate is

5655-403: The method as simple and ingenious , attributes the solution to Felix Walecki, a teacher at Lycée Condorcet . Lucas also included an alternative solution by means of a sliding puzzle . To easily remember this method, the following mnemonic can be used. Starting from the first round, the next round is constructed: and then, If the number of players is odd, the player in the first venue gets

5742-669: The mid-Atlantic and southern United States. They are also found in Central and Eastern Canada. There is one WTA tournament played on green Har-Tru clay courts, the Charleston Open in Charleston, South Carolina . From 1975 until 1977, the US Open was played on Har-Tru clay courts. The US Men's Clay Court Championships are played on clay that has a maroon color. Not only is this a darker color than other clay courts used in

5829-497: The number of staff on-site, the ATP introduced live electronic line-calling powered by Hawk-Eye Live . Instead of line umpires, the system detects the relevant movements of the player and where the ball bounces on court. A pre-recorded voice announces "Out", "Fault", and "Foot fault". Also, video review was also introduced for suspected double bounces, touches, and other reviewable calls. The tournament has traditionally been sponsored by

5916-399: The only female players to have won major titles at only the French Open since the beginning of the open era. Increasingly, clay courters have attempted to play better on other surfaces, with some success. Ferrero reached the final of the US Open in 2003 , the same year he won the French Open , and also won several hardcourt tournaments. Nadal was considered a clay court specialist until

6003-520: The open era record for the number of consecutive French Open titles won at three (1990–1992 for Seles, 2005–2007 for Henin and 2022–2024 for Swiatek). In the pre-open era this feat was first achieved by Helen Wills Moody (1928–1930) and followed by Hilde Krahwinkel Sperling (1935–1937). Chris Evert holds the record for longest winning streak on clay for either gender in the open era: from August 1973 to May 1979, she won 125 consecutive clay court matches. During this time, Evert skipped three editions of

6090-448: The others in their group. After the round-robin stage, the top two performers in each group advance to the semifinals in a knock-out stage. The two winners of the semifinals play a final to determine the champion. In this format, it is theoretically possible to advance to the semifinals with two round-robin losses, but no player in the history of the singles tournament has won the title after losing more than one round-robin match. To create

6177-496: The position the other had. In the example given ( n = 14 {\displaystyle n=14} ), 2 {\displaystyle 2} has distance 1 {\displaystyle 1} to 3 {\displaystyle 3} and to 14 {\displaystyle 14} and it has distance 6 {\displaystyle 6} to 8 {\displaystyle 8} and to 9 {\displaystyle 9} . In

6264-686: The pre-open era Anthony Wilding is particularly notable for his achievements on clay courts. Starting in May 1910 at the Championship of South Africa and ending in June 1914 at the World Hard Court Championships he registered 120 consecutive clay court match victories. Rafael Nadal, winner of a record 14 French Open men's singles titles , is noted for his success on clay; since his debut in 2005, he has only lost four times at

6351-400: The previous row, with the exception of player n {\displaystyle n} . When the result of the addition is greater than ( n − 1 ) {\displaystyle (n-1)} , then subtract ( n − 1 ) {\displaystyle (n-1)} from the sum. This schedule can also be represented as a (n-1, n-1) table, expressing

6438-407: The professional game, but it is also a type of Har-Tru court, meaning it is actually composed of the same substance (basalt) as green clay courts, and not a type of red clay. Har-Tru market this kind of court as "American red clay". Clay courts are considered "slow" because the balls bounce relatively high and lose much of their initial speed when contacting the surface, making it more difficult for

6525-406: The round-robin and elimination formats, to provide a worthy champion using fewer rounds than a round-robin, while allowing draws and losses. The main disadvantage of a round robin tournament is the time needed to complete it. Unlike a knockout tournament where half of the participants are eliminated after each round, a round robin requires one round less than the number of participants. For instance,

6612-525: The round-robin major league champions are generally regarded as the "best" team in the land, rather than the cup winners, whose tournaments usually follow a single-elimination format. Moreover, in tournaments such as the FIFA or ICC World Cups, a first round stage consisting of a number of mini round robins between groups of 4 teams guards against the possibility of a team travelling possibly thousands of miles only to be eliminated after just one poor performance in

6699-540: The same number of points they would earn for winning one of the four Grand Slam events. The ITF, who continued to run the Grand Slam tournaments, created a rival year-end event known as the Grand Slam Cup , which was contested by the 16 players with the best records in the Grand Slam tournaments of the season (1990–99). In December 1999, the ATP and ITF agreed to discontinue the two separate events and create

6786-408: The same position. Clearly, these pairs are pairwise different. The conclusion is that every distance- k {\displaystyle k} pair is realized. This holds for every k {\displaystyle k} , hence, every pair is realized. If there are an odd number of competitors, a dummy competitor can be added, whose scheduled opponent in a given round does not play and has

6873-659: The surface must be watered and rolled regularly to preserve texture and flatness, and brushed carefully before each game. Clay courts, although now commonly associated with continental Europe, were the invention of the English tennis player William Renshaw (a seven times Wimbledon champion) and his twin brother Ernest . The Renshaws had built a grass court at their summer home on the French Riviera , but found it unable to withstand prolonged exposure to heat and sunlight. To remedy this, in 1890 William Renshaw decided that

6960-608: The teams. This famously happened during the 1994 FIFA World Cup Group E , where all four teams finished with a record of one win, one draw, and one loss. This phenomenon is analogous to the Condorcet paradox in voting theory. If n {\displaystyle n} is the number of competitors, a pure round robin tournament requires n 2 ( n − 1 ) {\displaystyle {\begin{matrix}{\frac {n}{2}}\end{matrix}}(n-1)} games. If n {\displaystyle n}

7047-468: The title sponsor of the tour; however, in 1990–2008 the competition was not sponsored, even though the singles portion of the event, as part of the ATP Tour, was sponsored by IBM . In 2009, the tournament gained Barclays PLC as its title sponsor. Barclays confirmed in 2015 that they would not renew their sponsorship deal once it expires in 2016. On 25 May 2017, it was announced that Nitto Denko would be

7134-403: The top left corner by repeating the sequence of numbers from 1 up to n − 1 {\displaystyle n-1} . Here is an example table for 7 or 8 competitors: Clay court A clay court is one of the types of tennis court on which the sport of tennis is played. Clay courts are built on a foundation of crushed stone, brick, shale, and other aggregate , with

7221-492: The tournament – in 2009 , 2015 , 2021 and 2024 . Nadal holds the record for the longest winning streak by any male player on a single surface since the Open Era began in 1968: 81 clay court wins between April 2005 and May 2007. He also holds the record for most clay court titles in the Open Era, with 63. Guillermo Vilas won 49 of his 62 singles titles on clay. He only won a single French Open title, although he also won

7308-435: The tournament; changes were made prior to the next Olympics to prevent a repeat of these events. Another disadvantage, especially in smaller round-robins, is the "circle of death", where teams cannot be separated on a head-to-head record. In a three-team round-robin, where A defeats B, B defeats C, and C defeats A, all three competitors will have a record of one win and one loss, and a tiebreaker will need to be used to separate

7395-416: The two-player tie is broken by the head-to-head round robin result: When calculating tiebreakers, a match that ended in a retirement is counted as a 0–2 sets loss for the retiring player and a 2–0 sets win for their opponent, regardless of the actual score when the retirement occurred. When calculating the "Highest % of games won" tiebreaker, a match that ended in a retirement is disregarded. ATP Finals

7482-451: The victor is gradually arrived at through multiple rounds of play, teams who perform poorly, who might have been quickly eliminated from title contention, are forced to play out their remaining games. Thus games are played late in the competition between competitors with no remaining chance of success. Moreover, some later matches will pair one competitor who has something left to play for against another who does not. It may also be possible for

7569-584: Was last held there in 2020. In 2017 the event was renamed the "ATP Finals ." In April 2019, the ATP announced that Turin would host the ATP Finals from 2021 to 2025. For most of its history, the event has been considered the most important indoor tennis tournament in the world (there were a few exceptions when the event was held outdoors: 1974 in Melbourne & 2003–04 in Houston). The indoor atmosphere allows for controlled conditions of play, both in terms of

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