Single-elimination tournament

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Example of a single-elimination tournament bracket Mitbat-2007-bracket-large.png
Example of a single-elimination tournament bracket
The tournament has been completed until the semifinals, the winner of Lisa-Ernie match and Andrew-Robert match will play in the final. SixteenPlayerSingleEliminationTournamentBracket.svg
The tournament has been completed until the semifinals, the winner of Lisa-Ernie match and Andrew-Robert match will play in the final.

A single-elimination, knockout, or sudden death tournament is a type of elimination tournament where the loser of each match-up is immediately eliminated from the tournament. Each winner will play another in the next round, until the final match-up, whose winner becomes the tournament champion. Each match-up may be a single match or several, for example two-legged ties in European football or best-of series in American pro sports. Defeated competitors may play no further part after losing, or may participate in "consolation" or "classification" matches against other losers to determine the lower final rankings; for example, a third place playoff between losing semi-finalists. In a shootout poker tournament, there are more than two players competing at each table, and sometimes more than one progressing to the next round. Some competitions are held with a pure single-elimination tournament system. Others have many phases, with the last being a single-elimination final stage, often called playoffs.

In sports, a two-legged tie is a contest between two teams which comprises two matches or "legs", with each team as the home team in one leg. The winning team is usually determined by aggregate score, the sum of the scores of the two legs. For example, if the scores of the two legs are:

A third place playoff, match/game for third place, bronze medal game or consolation game is a single match that is included in many sporting knockout tournaments to decide which competitor or team will be credited with finishing third and fourth. The teams that compete in the third place playoff game are usually the two losing semi-finalists in a particular knockout tournament.

Poker tournament

A poker tournament is a tournament where players compete by playing poker. It can feature as few as two players playing on a single table, and as many as tens of thousands of players playing on thousands of tables. The winner of the tournament is usually the person who wins every poker chip in the game and the others are awarded places based on the time of their elimination. To facilitate this, in most tournaments, blinds rise over the duration of the tournament. Unlike in a ring game, a player's chips in a tournament cannot be cashed out for money and serve only to determine the player's placing.



In English, the round in which only eight competitors remain is generally called (with or without hyphenation) the quarter-final round; this is followed by the semi-final round, in which only four are left, the two winners of which then meet in the final or championship round.

English language West Germanic language

English is a West Germanic language that was first spoken in early medieval England and eventually became a global lingua franca. It is named after the Angles, one of the Germanic tribes that migrated to the area of Great Britain that later took their name, as England. Both names derive from Anglia, a peninsula in the Baltic Sea. The language is closely related to Frisian and Low Saxon, and its vocabulary has been significantly influenced by other Germanic languages, particularly Norse, and to a greater extent by Latin and French.

The round before the quarterfinals has multiple designations. Often it's called the round of sixteen, last sixteen, or (in South Asia) pre quarter-finals. In many other languages the term for these eight matches translates to eighth-final (e.g., in these seven European languages: "huitième de finale" in French, ' "octavos de final" in Spanish, "achtelfinale" in German, "ottavi di finale" in Italian, "osmifinále" in Czech, "osemfinále" in Slovak, and "osmina finala" in Serbian), though this term is rare in English itself.

French language Romance language

French is a Romance language of the Indo-European family. It descended from the Vulgar Latin of the Roman Empire, as did all Romance languages. French evolved from Gallo-Romance, the spoken Latin in Gaul, and more specifically in Northern Gaul. Its closest relatives are the other langues d'oïl—languages historically spoken in northern France and in southern Belgium, which French (Francien) has largely supplanted. French was also influenced by native Celtic languages of Northern Roman Gaul like Gallia Belgica and by the (Germanic) Frankish language of the post-Roman Frankish invaders. Today, owing to France's past overseas expansion, there are numerous French-based creole languages, most notably Haitian Creole. A French-speaking person or nation may be referred to as Francophone in both English and French.

Spanish or Castilian, is a Romance language that originated in the Iberian Peninsula and today has over 450 million native speakers in Spain and the Americas. It is a global language and the world's second-most spoken native language, after Mandarin Chinese.

German language West Germanic language

German is a West Germanic language that is mainly spoken in Central Europe. It is the most widely spoken and official or co-official language in Germany, Austria, Switzerland, South Tyrol in Italy, the German-speaking Community of Belgium and Liechtenstein. It is one of the three official languages of Luxembourg and a co-official language in the Opole Voivodeship in Poland. The languages that are most similar to the German are the other members of the West Germanic language branch, including Afrikaans, Dutch, English, the Frisian languages, Low German/Low Saxon, Luxembourgish, and Yiddish. There are strong similarities in vocabulary with Danish, Norwegian and Swedish, although those belong to the North Germanic group. German is the second most widely spoken Germanic language, after English.

The round before the round of sixteen is sometimes called round of thirty-two in English. Terms for this in other languages generally translate as "sixteenth final".

Earlier rounds are typically numbered counting forwards from the first round, or by the number of remaining competitors. If some competitors get a bye, the round at which they enter may be named the first round, with the earlier matches called a preliminary round, qualifying round, or the play-in games".

Examples of the diverse names given to concurrent rounds in various select disciplines:

By competitorsFraction of final Grand Slam tennis [1] FA Cup football Coupe de France [2] NCAA Men's Basketball North American Debating Ch'ship
Round of 2 Final Final Final FinalNational ChampionshipFinal
Round of 4SemifinalsSemifinalsSemi-finalsSemifinals Final Four
(National semifinals) [t 1]
Round of 8QuarterfinalsQuarterfinalsquarter-finals [t 2] Quarterfinals Elite Eight
(Regional finals) [t 3]
Round of 16Eighth-finals4th round (Wimbledon [4] )
Round of 16 (US Open [5] )
5th round [t 4] 8th-finalsSweet Sixteen
(Regional semifinals) [t 5]
Round of 3216th-finals3rd round4th round [t 4] 16th-finals3rd/2nd round [t 6] [t 7] Double-octofinals or Decimosexto-finals
Round of 6432nd-finals2nd round3rd round [t 4] 32nd-finals2nd/1st round [t 6] [t 7] Triple-octofinals
Round of 12864th-finals1st round2nd round [t 8] [t 4] 8th qualifying round [t 9] First Four [t 6] Quad-octofinals [t 10]


  1. The NCAA also uses the "Final Four" terminology in the Division I women's tournament, as well as the Division III tournaments for both men and women. In Division II for both sexes, this round is called the "semifinals"; both championship events in that division consist of eight teams instead of four.
  2. The quarter-finals were called the "sixth round" until 2016–17, the first in which replays were discontinued for this round. [3]
  3. In the Division II men's and women's tournaments, the Elite Eight is the championship event, with all qualifying teams participating at a single site. The NCAA does not use "Elite Eight" in Division III, simply calling this round the "regional finals".
  4. 1 2 3 4 The first to fifth rounds are often called the "first/second/etc. round proper", to distinguish them from the "first/second/etc. qualifying round".
  5. The NCAA only uses the term "Sweet Sixteen" in the Division I tournaments.
  6. 1 2 3 Starting in 2011, 68 teams played in the Championship, with four play-in games, nicknamed the First Four, before the top 60 teams enter at the round of 64. (From 2001 to 2010, there was a single "Opening Round" game before the round of 64.) The NCAA originally called the First Four the first round, making the rounds of 64 and 32 the second and third rounds respectively; in 2014 it announced that from 2016 it would revert to calling the rounds of 64 and 32 the first and second rounds. [6]
  7. 1 2 Since the NCAA Division I women's tournament expanded beyond 32 teams in 1986, the round of 32 has always been called the "second round", and the preceding round the "first round". The women's tournament has involved 64 teams since 1994, but has never expanded beyond that number.
  8. The FA Cup 2nd round involves 40 teams, of which 20 qualify for the 3rd round, to which the top 44 teams will have received byes.
  9. The 8th qualifying round involves 88 teams, of which 44 qualify for the 32nd-finals, to which the top 20 teams will have received byes.
  10. The number of eligible teams is typically less than 128, but more than 64, so not all teams play this round.


The final three rounds of the 2014 Australian Open – Women's Singles knock-out tournament:

Li Na defeated Dominika Cibulková in the final, 7–6(7–3), 6–0 to win the Women's Singles tennis title at the 2014 Australian Open. Li became the first Asian Australian Open champion and sixth woman to win the title after being match point down.

Quarterfinals Semifinals Final
14 Flag of Serbia.svg Ana Ivanovic 75 2
30 Flag of Canada (Pantone).svg Eugenie Bouchard 5 76
30 Flag of Canada (Pantone).svg Eugenie Bouchard 2 4
4 Flag of the People's Republic of China.svg Li Na 66
4 Flag of the People's Republic of China.svg Li Na 66
28 Flag of Italy.svg Flavia Pennetta 2 2
4 Flag of the People's Republic of China.svg Li Na 776
20 Flag of Slovakia.svg Dominika Cibulková 630
11 Flag of Romania.svg Simona Halep 3 0
20 Flag of Slovakia.svg Dominika Cibulková 66
20 Flag of Slovakia.svg Dominika Cibulková 66
5 Flag of Poland.svg Agnieszka Radwańska 1 2
5 Flag of Poland.svg Agnieszka Radwańska 65 6
2 Flag of Belarus.svg Victoria Azarenka 1 70


When matches are held to determine places or prizes lower than first and second (the loser of the final-round match gaining the latter position), these typically include a match between the losers of the semifinal matches called third place playoffs, the winner therein placing third and the loser fourth. Many Olympic single-elimination tournaments feature the bronze medal match if they do not award bronze medals to both losing semifinalists. The FIFA World Cup has long featured the third place match (since 1934), though the UEFA Euro has not held one since the 1980 edition.

FIFA World Cup Association football competition for mens national teams

The FIFA World Cup, often simply called the World Cup, is an international association football competition contested by the senior men's national teams of the members of the Fédération Internationale de Football Association (FIFA), the sport's global governing body. The championship has been awarded every four years since the inaugural tournament in 1930, except in 1942 and 1946 when it was not held because of the Second World War. The current champion is France, which won its second title at the 2018 tournament in Russia.

1934 FIFA World Cup 1934 edition of the FIFA World Cup

The 1934 FIFA World Cup was the second FIFA World Cup, the world championship for men's national association football teams. It took place in Italy from 27 May to 10 June 1934.

Sometimes, contests are also held among the losers of the quarterfinal matches to determine fifth to eighth places – this is most commonly encountered in the Olympic Games, with the exception of boxing, where both fighters are deemed to be third place. In one scenario, two "consolation semifinal" matches may be conducted, with the winners of these then facing off to determine fifth and sixth places and the losers playing for seventh and eighth; those are used often in qualifying tournaments where only the top five teams advance to the next round; or some method of ranking the four quarterfinal losers might be employed, in which case only one round of additional matches would be held among them, the two highest-ranked therein then playing for fifth and sixth places and the two lowest for seventh and eighth.

Olympic Games Major international sport event

The modern Olympic Games or Olympics are leading international sporting events featuring summer and winter sports competitions in which thousands of athletes from around the world participate in a variety of competitions. The Olympic Games are considered the world's foremost sports competition with more than 200 nations participating. The Olympic Games are held every four years, with the Summer and Winter Games alternating by occurring every four years but two years apart.

Boxing combat sport

Boxing is a combat sport in which two people, usually wearing protective gloves, throw punches at each other for a predetermined amount of time in a boxing ring.

The number of distinct ways of arranging a single-elimination tournament (as an abstract structure, prior to seeding the players into the tournament) is given by the Wedderburn–Etherington numbers. [7] Thus, for instance, there are three different arrangements for five players:

However, the number of arrangements grows quickly for larger numbers of players and not all of them are commonly used.


Opponents may be allocated randomly (such as in the FA Cup); however, since the "luck of the draw" may result in the highest-rated competitors being scheduled to face each other early in the competition, seeding is often used to prevent this. Brackets are set up so that the top two seeds could not possibly meet until the final round (should both advance that far), none of the top four can meet prior to the semifinals, and so on. If no seeding is used, the tournament is called a random knockout tournament.

One version of seeding is where brackets are set up so that the quarterfinal pairings (barring any upsets) would be the 1 seed vs. the 8 seed, 2 vs. 7, 3 vs. 6 and 4 vs. 5; however, this is not the procedure that is followed in most tennis tournaments, where the 1 and 2 seeds are placed in separate brackets, but then the 3 and 4 seeds are assigned to their brackets randomly, and so too are seeds 5 through 8, and so on. This may result in some brackets consisting of stronger players than other brackets, and since only the top 32 players are seeded at all in Tennis Grand Slam tournaments, it is conceivable that the 33rd-best player in a 128-player field could end up playing the top seed in the first round. A good example of this occurring was when World No. 33 Florian Mayer was drawn against (and eventually defeated by) then-World No. 1 Novak Djokovic in the first round of the 2013 Wimbledon Championships, [8] in what was also a rematch of a quarterfinal from the previous year. [9] While this may seem unfair to a casual observer, it should be pointed out that rankings of tennis players are generated by computers, and players tend to change ranking positions very gradually, so that a more equitable method of determining the pairings might result in many of the same head-to-head matchups being repeated over and over again in successive tournaments.

Sometimes the remaining competitors in a single-elimination tournament will be "re-seeded" so that the highest surviving seed is made to play the lowest surviving seed in the next round, the second-highest plays the second-lowest, etc. This may be done after each round, or only at selected intervals. In American team sports, for example, the NFL and WNBA employ this tactic, but MLS and the NBA do not (and neither does the NCAA college basketball tournament). MLB does not have enough teams (10) in its playoff tournament where re-seeding would make a large difference in the matchups; only the NFL's at the minimum, which is six from each conference [or league in MLB] for a total of 12). The NBA's format calls for the winner of the first-round series between the first and eighth seeds (within each of the two conferences the league has) to face the winner of the first-round series between the fourth and fifth seeds in the next round, even if one or more of the top three seeds had been upset in their first-round series; critics have claimed that this gives a team fighting for the fifth and sixth seeding positions near the end of the regular season an incentive to tank (deliberately lose) games, so as to finish sixth and thus avoid a possible matchup with the top seed until one round later. MLS's format is identical, except that the top-seed gets a conference-quarterfinal bye to play 4th-5th seed winner.

In some situations, a seeding restriction may be implemented; from 1975 until 1989 in the NFL, and from 1994 until 2011 in MLB there was a rule where at the conference or league semifinal, should the top seed and last seed (wild card) be from the same division, they could not play each other; in that case, the top seed plays the worst division champion; the second-best division champion plays the wild card team. This is due to the scheduling employed for the regular season, in which a team faces any given divisional opponent more often than any given non-divisional opponent – the tournament favors matchups that took place fewer times in the regular season (or did not take place, in some cases). [ citation needed ]

In international fencing competitions, it is common to have a group stage. Participants are divided in groups of 6–7 fencers who play a round-robin tournament, and a ranking is calculated from the consolidated group results. Single elimination is seeded from this ranking.


The single-elimination format enables a relatively large number of competitors to participate. There are no "dead" matches (perhaps excluding "classification" matches), and no matches where one competitor has more to play for than the other.

The format is less suited to games where draws are frequent. In chess, each fixture in a single-elimination tournament must be played over multiple matches, because draws are common, and because white has an advantage over black. In association football, games ending in a draw may be settled in extra time and eventually by a penalty shootout or by replaying the fixture.

Another perceived disadvantage is that most competitors are eliminated after relatively few games. Variations such as the double-elimination tournament allow competitors a single loss while remaining eligible for overall victory. However, losing one game requires the competitor to win more games in order to win the tournament.

In a random knockout tournament (single-elimination without any seeding), awarding the second place to the loser of the final is unjustified: any of the competitors knocked out by the tournament winner might have been the second strongest one, but they never got the chance to play against the losing finalist. In general, it is only fair to use a single-elimination tournament to determine first place. To fairly determine lower places requires some form of round-robin in which each player/team gets the opportunity to face every other player/team.

Also, if the competitors' performance is variable, that is, it depends on a small, varying factor in addition to the actual strength of the competitors, then not only will it become less likely that the strongest competitor actually wins the tournament, in addition the seeding done by the tournament organizers will play a major part in deciding the winner. [10] [11] As a random factor is always present in a real-world competition, this might easily cause accusations of unfairness.

Other tournament systems

Variations of the single-elimination tournament include:

Other common tournament types include:

Related Research Articles

The playoffs, play-offs, postseason and/or finals of a sports league are a competition played after the regular season by the top competitors to determine the league champion or a similar accolade. Depending on the league, the playoffs may be either a single game, a series of games, or a tournament, and may use a single-elimination system or one of several other different playoff formats. Playoff, in regard to international fixtures, is to qualify or progress to the next round of a competition or tournament.

A tournament is a competition involving a relatively large number of competitors, all participating in a sport or game. More specifically, the term may be used in either of two overlapping senses:

  1. One or more competitions held at a single venue and concentrated into a relatively short time interval.
  2. A competition involving a number of matches, each involving a subset of the competitors, with the overall tournament winner determined based on the combined results of these individual matches. These are common in those sports and games where each match must involve a small number of competitors: often precisely two, as in most team sports, racket sports and combat sports, many card games and board games, and many forms of competitive debating. Such tournaments allow large numbers to compete against each other in spite of the restriction on numbers in a single match.
Bracket (tournament) diagram of a tournament

A bracket or tournament bracket is a tree diagram that represents the series of games played during a knockout tournament. Different knockout tournament formats have different brackets; the simplest and most common is that of the single-elimination tournament. The name "bracket" is American English, derived from the resemblance of the links in the tree diagram to the bracket punctuation symbol ] or [. The closest British term is draw, although this implies an element of chance, whereas some brackets are determined entirely by seeding.

Archery at the Summer Olympics

Archery had its debut at the 1900 Summer Olympics and has been contested in 16 Olympiads. Eighty-four nations have competed in the Olympic archery events, with France appearing the most often at 31 times. The most noticeable trend has been the excellence of South Korean archers, who have won 23 out of 34 gold medals in events since 1984. It is governed by the World Archery Federation. Recurve archery is the only discipline of archery featured at the Olympic Games. Archery is also an event at the Summer Paralympics.

Double-elimination tournament

A double-elimination tournament is a type of elimination tournament competition in which a participant ceases to be eligible to win the tournament's championship upon having lost two games or matches. It stands in contrast to a single-elimination tournament, in which only one defeat results in elimination.

Repechage practice amongst ladder competitions

Repechage is a practice in series competitions that allows participants who failed to meet qualifying standards by a small margin to continue to the next round. A well known example is the wild card system.

A Swiss-system tournament is a non-eliminating tournament format that features a set number of rounds of competition, but considerably fewer than that of a round-robin tournament. In a Swiss tournament, each competitor does not necessarily play all other entrants. Competitors meet one-on-one in each round and are paired using a set of rules designed to ensure that each competitor plays opponents with a similar running score, but not the same opponent more than once. The winner is the competitor with the highest aggregate points earned in all rounds. All competitors play in each round unless there is an odd number of players.

There are a number of formats used in various levels of competition in sports and games to determine an overall champion. Some of the most common are the single elimination, the best-of- series, the total points series more commonly known as on aggregate, and the round-robin tournament.

A wild card is a tournament or playoff berth awarded to an individual or team that fails to qualify in the normal way, for example by having a high ranking or winning a qualifying stage. In some events, wild cards are chosen freely by the organizers. Other events have fixed rules. Some North American professional sports leagues compare the records of teams which did not qualify directly by winning a division or conference.

A bye in sports refers to organizers scheduling a competitor to not participate in a given round of competition, due to one of several circumstances.

Atlantic Coast Conference Baseball Tournament

The Atlantic Coast Conference Baseball Tournament, sometimes referred to simply as the ACC Tournament, is the conference championship tournament in baseball for the Atlantic Coast Conference (ACC). In 2014, the event adopted a modified ten-team pool play format. The winner receives the conference's automatic bid to the NCAA Division I Baseball Tournament.

The 1988 NCAA Division I Men's Ice Hockey Tournament was the culmination of the 1987–88 NCAA Division I men's ice hockey season, the 41st such tournament in NCAA history. It was held between March 18 and April 2, 1988, and concluded with Lake Superior State defeating St. Lawrence 4-3 in overtime. All First Round and Quarterfinals matchups were held at home team venues with the 'Frozen Four' games being played at the Olympic Center in Lake Placid, New York.

The 1989 NCAA Division I Men's Ice Hockey Tournament was the culmination of the 1988–89 NCAA Division I men's ice hockey season, the 42nd such tournament in NCAA history. It was held between March 17 and April 1, 1989, and concluded with Harvard defeating Minnesota 4-3 in overtime. All First Round and Quarterfinals matchups were held at home team venues with the 'Frozen Four' games being played at the St. Paul Civic Center in St. Paul, Minnesota.

The Inline Hockey World Championships are an annual inline hockey tournament organized by the Comité International Roller In-Line Hockey (CIRILH), an organization and discipline of Fédération Internationale de Roller Sports (FIRS). First held in 1995, it is the sport's highest profile annual international tournament. The first World Championship that was held was in 1995 in which twelve nations participated in pool play followed by single elimination games to determine the champion. This basic format would be used until 2006.

The 1996 ECAC Hockey Men's Ice Hockey Tournament was the 35th tournament in league history. It was played between March 5 and March 16, 1996. Preliminary and quarterfinal games were played at home team campus sites, while the 'final four' games were played at the Olympic Arena in Lake Placid, New York. By winning the tournament, Cornell received the ECAC's automatic bid to the 1996 NCAA Division I Men's Ice Hockey Tournament.

The 1994 ECAC Hockey Men's Ice Hockey Tournament was the 33rd tournament in league history. It was played between March 8 and March 19, 1994. Preliminary and quarterfinal games were played at home team campus sites, while the 'final four' games were played at the Olympic Arena in Lake Placid, New York. By winning the tournament, Harvard received the ECAC's automatic bid to the 1994 NCAA Division I Men's Ice Hockey Tournament.

The 1993 ECAC Hockey Men's Ice Hockey Tournament was the 32nd tournament in league history. It was played between March 9 and March 20, 1993. Preliminary and quarterfinal games were played at home team campus sites, while the 'final four' games were, for the first time, played at the Olympic Arena in Lake Placid, New York.The third place game was brought back after a three year hiatus. By winning the tournament, Clarkson received the ECAC's automatic bid to the 1993 NCAA Division I Men's Ice Hockey Tournament.

Classic Tetris World Championship

The Classic Tetris World Championship (CTWC) is a video game competition series, hosted by the Portland Retro Gaming Expo. The competition launched in 2010, during the filming of Ecstasy of Order: The Tetris Masters to determine the world's greatest Tetris player. The first two years the competition was held in Los Angeles, California, but has since moved to Portland, Oregon, and has been held there annually since 2012.

The 2013 NCAA Division I Women's Soccer Tournament was the 32nd annual single-elimination tournament to determine the national champion of NCAA Division I women's collegiate soccer. The semifinals and championship game were played at WakeMed Soccer Park in Cary, North Carolina from December 6–8, 2013 while the preceding rounds were played at various sites across the country from November 15–30.

ESL One Cologne 2014

Electronic Sports League One Cologne 2014, known as ESL One Cologne 2014 for short, was the third Counter-Strike: Global Offensive Major Championship that was held during Gamescom 2014 from August 14–17, 2014 at the Cologne Exhibition Centre in Cologne, North Rhine-Westphalia, Germany. It was the second CS:GO Major of 2014. It was organized by Electronic Sports League with sponsorship from Valve Corporation. The tournament had a total prize pool of US$250,000.


  1. In singles only (the other disciplines have fewer rounds)
  2. "Coupe de France : football, résultats, calendrier, reportage, photos" (in French). French Football Federation. Archived from the original on 19 July 2012. Retrieved 16 July 2012.
  3. "Premier League clubs want the FA Cup moved to midweek and replays scrapped". talkSPORT. 31 May 2018 [2017]. Retrieved 31 March 2019.; Emirates FA Cup (17 February 2017). "We do now! The sixth round has been renamed as the quarter-finals from this season". @EmiratesFACup. Twitter. Retrieved 31 March 2019.
  4. "Gentlemen's Singles – 2012 Official Site by IBM". Wimbledon Championships Website. Retrieved 16 July 2012.
  5. "2012 Tournament Schedule". US Open. Archived from the original on 17 July 2012. Retrieved 16 July 2012.
  6. Cary, Tim (21 November 2014). "What's in a Name? March Madness First Round Is the 'First Round' Again". The Cheat Sheet. Retrieved 6 June 2015.
  7. Maurer, Willi (1975), "On most effective tournament plans with fewer games than competitors", The Annals of Statistics, 3: 717–727, doi:10.1214/aos/1176343135, JSTOR   2958441, MR   0371712 .
  8. Wimbledon: Novak vs Mayer in R1; Andy, Roger, Rafa all in bottom half, Novak Djokovic official website, 21 June 2013
  9. Wimbledon 2013: Men's matches to watch out for, The Roar, 22 June 2013
  10. Ryvkin, Dmitry (March 2005). "The Predictive Power of Noisy Elimination Tournaments" (PDF). CERGE-EI. Retrieved 21 October 2010.
  11. Kim, Michael P.; Suksompong, Warut; Vassilevska Williams, Virginia (2017). "Who Can Win a Single-Elimination Tournament?". SIAM Journal on Discrete Mathematics. 31 (3): 1751–1764. arXiv: 1511.08416 . doi:10.1137/16M1061783.