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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 multiple 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.

These two senses are distinct. All golf tournaments meet the first definition, but while match play tournaments meet the second, stroke play tournaments do not, since there are no distinct matches within the tournament. In contrast, football (soccer) leagues like the Premier League are tournaments in the second sense, but not the first, having matches spread across many stadia over a period of up to a year. Many tournaments meet both definitions; for example, the Wimbledon tennis championship.

A tournament-match (or tie or fixture or heat) may involve multiple game-matches (or rubbers or legs) between the competitors. For example, in the Davis Cup tennis tournament, a tie between two nations involves five rubbers between the nations' players. The team that wins the most rubbers wins the tie. In the later rounds of UEFA Champions League of football (soccer), each fixture is played over two legs. The scores of each leg are added, and the team with the higher aggregate score wins the fixture, with away goals used as a tiebreaker and a penalty shootout if away goals cannot determine a winner.

Contents 1 History 2 Knockout tournaments 3 Group tournaments 4 Multi-stage tournaments 5 Promotion and relegation 6 Bridge tournaments 7 Poker tournaments 8 Rummy tournaments 9 Alternatives to tournament systems 10 See also

[edit] History

The word and general meaning derive from the mediaeval tournament or tourney. The word is still occasionally used for a military event such as the Royal Tournament.

[edit] Knockout tournaments

A knockout tournament is divided into successive rounds; each competitor plays in at most one fixture per round. The top-ranked competitors in each fixture progress to the next round. As rounds progress, the number of competitors and fixtures decreases, and the final round consists of just one fixture, the winner of which is the overall champion.

In a single-elimination tournament, only the top-ranked competitors in a fixture progress; in 2-competitor games, only the winner progresses. All other competitors are eliminated. This ensures a winner is decided with the minimum number of fixtures. However, most competitors will be eliminated after relatively few matches; a single bad or unlucky performance can nullify many preceding excellent ones. Some single-elimination tournaments such as NBA use a multiple-game format, in which teams would play each other more than one game (e.g. best-of-seven series in NBA) in order to determine who is the winner of this round. Other knockout formats provide a "second chance" for some or all losers.

A double-elimination tournament may be used in 2-competitor games to allow each competitor a single loss without being eliminated from the tournament. All losers from the main bracket enter a losers' bracket, the winner of which plays off against the main bracket's winner.

Some formats allow losers to play extra rounds before re-entering the main competition in a later round. Rowing regattas often have repechage rounds for the "fastest losers" from the heats. The winners of these progress, but are at a disadvantage in later rounds owing to the extra effort expended during the repechage.

In the playoffs of the Australian Football League, the teams with the best record before the playoffs are allowed to lose a game without being eliminated, whereas the lesser qualifiers are not. In athletics meetings, fastest losers may progress in a running event held over several rounds; e.g. the qualifiers for a later round might be the first 4 from each of 6 heats, plus the 8 fastest losers from among the remaining runners.

An extreme form of the knockout tournament is the stepladder format where the strongest team (or individual, depending on the sport) is assured of a berth at the final round while the next strongest teams are given byes according to their strength/seeds; for example, in a four team tournament, the fourth and third seed figure in the first round, then the winner goes to the semifinals against the second seed, while the survivor faces the first seed at the final. Three American sports organizations either currently use this format or have in the past:

• For over 30 years (generally from the mid-1960s to 1997), most events on the PBA Tour of ten-pin bowling used a stepladder final, usually involving five bowlers.
• Both brackets in the men's and women's postseason basketball tournaments in the West Coast Conference are organized as stepladder tournaments. The bottom four teams play in the first round; the survivors will face the #3 and #4 seeds, and the winners of those matches take on the top two seeds in the semifinals.
• Women's Professional Soccer used this format in its inaugural 2009 season.

[edit] Group tournaments

A group tournament, league, division or conference involves all competitors playing a number of fixtures. Points are awarded for each fixture, with competitors ranked based either on total number of points or average points per fixture. Usually each competitor plays an equal number of fixtures, in which case rankings by total points and by average points are equivalent.

In a round-robin tournament, each competitor plays all the others an equal number of times, once in a single round-robin tournament and twice in a double round-robin tournament. This is often seen as producing the most reliable rankings. However, for large numbers of competitors it may require an unfeasibly large number of rounds. A Swiss system tournament attempts to determine a winner reliably, based on a smaller number of fixtures. Fixtures are scheduled one round at a time; a competitor will play another who has a similar record in previous rounds of the tournament. This allows the top (and bottom) competitors to be determined with fewer rounds than a round-robin, though the middle rankings are unreliable.

There may be other considerations besides reliability of rankings. In some professional team sports, weaker teams are given an easier slate of fixtures as a form of handicapping. This occurs in the National Football League in the USA. Sometimes schedules are weighted in favour of local derbies or other traditional rivalries. For example, NFL teams play two games against each of the other three teams in their division, one game against half of the other twelve teams in their conference, and one game against a quarter of the sixteen teams in the other conference.

American sports are also unusual in providing fixtures between competitors who are, for ranking purposes, in different groups. Another, systematic, example of this was the 2006 Women's Rugby World Cup: each of the teams in Group A played each of the teams in Group B, with the groups ranked separately based on the results. (Groups C and D intertwined similarly.) An elaboration of this system is the Mitchell movement in duplicate bridge, discussed below, where North-South pairs play East-West pairs.

In 2-competitor games where ties are rare or impossible, competitors are typically ranked by number of wins, with ties counting half; each competitors' listings are usually ordered Wins-Losses(-Ties). Where draws are more common, this may be 2 points for a win and 1 for a draw, which is mathematically equivalent but avoids having too many half-points in the listings. These are usually ordered Wins-Draws-Losses. If there are more than 2 competitors per fixture, points may be ordinal (for example, 3 for first, 2 for second, 1 for third).

[edit] Multi-stage tournaments

Many tournaments are held in multiple stages, with the top teams in one stage progressing to the next. American professional team sports have a "regular season" (group tournament) acting as qualification for the "post season" or "playoffs" (single-elimination tournament). In the FIFA World Cup, each continent has one or more qualifying tournaments, some of which are themselves multi-stage. The top teams in each qualify for the finals tournament. There, the 32 teams are divided into eight round-robin groups of four, with the top two in each progressing to the knockout phase, which involves four single-elimination rounds including the final.

Sometimes, results from an earlier phase are carried over into a later phase. In the Cricket World Cup, the second stage, known as the Super Eight since 2007 and before that the Super Six, features two teams from each of four preliminary groups (previously three teams from two preliminary groups), who do not replay the teams they have already played, but instead reuse the original results in the new league table. Formerly in the Swiss Football League, teams played a double round-robin, at which point they were split into a top "championship" group and a bottom "relegation" group; each played a separate double round-robin, with results of all 32 matches counting for ranking each group. A similar system is also used in the Scottish Premier League since 2000. After 33 games, when every club has played every other club three times, the division is split into two halves. Clubs play a further 5 matches, against the teams in their half of the division. This can (and often does) result in the team placed 7th having a higher points total than the team placed 6th, because their final 5 games are considerably easier.

The top Slovenian basketball league has a unique system. In its first phase, 12 of the league's 13 clubs compete in a full home-and-away season, with the country's representative in the Euroleague (an elite pan-European club competition) exempt. The league then splits. The top seven teams are joined by the Euroleague representative for a second home-and-away season, with no results carrying over from the first phase. These eight teams compete for four spots in a final playoff. The bottom five teams play their own home-and-away league, but their previous results do carry over. These teams are competing to avoid relegation, with the bottom team automatically relegated and the second-from-bottom team forced to play a mini-league with the second- and third-place teams from the second level for a place in the top league.

Here are some examples of multi-stage and other tournament structures:

Method A:

At first each team is allocated a round-robin group in a drawing. The top 12 teams in the seeding rankings (which consists of points gained from the most recent 4 previous World Cups 40% 25% 20% & 15%) are in one bowl, and these 12 ultimately form 3 groups of 4 teams in each group (Group C, D & E). The other 8 teams to have qualified go in the other bowl/drawing, and these a drawn to form two groups of 4 (Group A & B). So mismatches are reduced right from the outset, and all teams are given a good chance of making the quarter-finals.

The Seeding rankings are to be arrived at by giving teams that performed best in previous World Cups points (20 for best; 19, 18,17,16,15,....2,1 with the number of games won given priority over points difference) times a weighting of 40%, 25%, 20% 15% for the 4 most recent World Cups. (The outcome of this could optionally be enhanced by giving the top 3 in the most recent 6-Nations competition a bonus & a subtraction for the worst 2.) The group names A B C D & E are chosen to maximise viewer interest in all five groups, rather than encouraging it to focus on just the 'top' one or two groups, and to prevent teams seeded 13-20 from feeling like they are in a lesser competition.

After three rounds of play, the round-robin groups are ended. The winner of each group + the three best runners-up from (the more difficult) groups C-E advance into the Quarter-Finals.

Round 4: Three of the Quarter-Finals are to consist of the three best group winners (in terms of the number of games won in their group > Points for minus points allowed among the five group winners) playing against the three best runners-up (also in terms of wins > points difference = Points for minus points allowed) among all non-group-winners in Groups C-E). Care is taken in the drawing to ensure that no two teams from the same group go into the same half of the draw. The 4th Quarter-Final is to consist of the two remaining group winners.

Also in round 4: match 5 = for a chance at 5th place = 7th from Groups C-E versus C-E.8 match 6 = for a chance at 7th : C-E.9 versus A-B.3 match 7 = for a chance at 9th : C-E.10 versus A-B.4 match 8 = for a chance at 10th : C-E.11 versus A-B.5 (the loser is declared 17th) match 9 = for a chance at 12th : C-E.12 versus A-B.6 (the loser is declared 19th) match 10 = for 18th (the loser is 20th): A-B.7 versus A-B.8

Then in round 5: The winners of the Quarter-Finals now play in the Semi-Finals (=matches 1 & 2). match 3 = for 5th place: the winner of round 4’s match 5 versus QFL1 The 4 Quarter-Finals losers are ranked according to their point difference (Points for minus points allowed) from the tournament so far, with only the Quarter-Final outcome and their worst other result in the tournament so far counting fully toward this + 0.5 times their second-best points difference score in the group stages + 10% of (=0.1 times) their best group stage outcome. This weighting system is used to ensure that no team can be QFL1 (the highest ranked Quarter-Finals loser) just through having had the easiest/most-out-of-form-or-depleted opponent in their group.

match 4 = for 7th place: QFL2 versus the winner of match 6 in round 4 (the loser is declared 8th) match 5 = for 9th place: QFL3 versus the winner of match 7 (the loser is declared 11th) match 6 = for 10th place: QFL4 versus the winner of match 8 (the loser is declared 13th) match 7 = for 12th place: the loser of match 5 versus the winner of match 9 (the loser is declared 14th) match 8 = for 15th place: the loser of match 6 versus the loser of match 7 (the loser is declared 16th)

Then in round 6: for 1st: the winners of the 2 semi-finals (the loser is declared 2nd); for 3rd: the losers of the 2 semi-finals (the loser is declared 4th); for best improver: Apart from the above 4 teams, the top 2 in terms of their world ranking minus their end ranking position at the end of round 5; for the giant’s trophy: Apart from the above 6 teams, the top two in end-of-round-5 standings of the three biggest in terms of national population play in this game; and for the little giants’ trophy: Apart from the 8 teams above, the top two in terms of ‘20 minus their end ranking position at the end of round 5, plus their ranking (of the 20 who entered) in terms of national population’.

To recap, teams not contesting the top 3 places are eligible for other trophies based on a combination of their results in this tournament so far and one other factor, to play a game for the (for example) sapphire, emerald, and ruby medals, or for the Little Giants’ Trophy, the Upandcomers’ Trophy, the Platinum Bowl, …, one being for the Best Improved teams (this time as compared to the previous 4 times in 40% 25% 20% 15% shares); a 2nd is for the best-performing small population countries (subtracting their rank in this tournament to their population rank, the smallest two differences are chosen); and a Giants’ trophy (for the two better-performing of the three highest population remaining countries to not be in any of the other four medal matches – this one is added to give the large viewership markets more of a final round interest).

Method B:

Round 1 is only for teams not ranked/seeded in the top 12. Teams seeded 13-16 play against teams seeded 17-20. The winners advance into the main competition; the losers advance into the consolation competition. In the main competition (which starts with its first two matches 3 days later and gives the teams who played in round one a further 3 days to recover until their first group matches), there are 4 round-robin groups of 4. Each group contains 4 of the 16 teams who were either seeded 1-12 or who won in round 1. Care is taken to ensure that no group contains two more teams from the same continent than any other.

Then in rounds 5-7 the 4 group winners move into the round-robin Group Winners Group, while the eight 2nds & 3rds go into the single-loss-elimination Sudden Death Bracket (SDB) with QF … SF .. F.

Then in round 8 the winner of the SDB plays the group winner’s group’s 2nd placed team (GWG2) for a chance at gold, while GWG3 plays SDB2 for a chance at bronze. A round 7 game between the best SF-loser and the best QF loser, both determined in terms of points difference (points for minus points allowed) when adding up all the results the teams have had in the tournament so far, with each team’s best performance weighted times 0.5 and all others times 1 so it doesn’t become a case of who had the easiest opponent.

Then in round 9, the games for 1st (which is held last of all, so that the winner of GWG2 vs SDB1 has time to be at their best in playing against the rested GWG1) & for 3rd (= the winner of GWG3 vs SDB2 against the loser of GWG2 vs SDB1) are played. The other three final round games from Method A are also included in Method B’s Round 9.

Method C:

The tournament consists of six rounds of play. The first three rounds are played within groups of 4 teams per group. This is Phase 1. And then who plays who in each round thereafter is decided by the outcomes in the round before.

The number of host venues is open, though it is worth considering the possibility that each phase one group could be held in a different host venue, with one of the countries in each group possibly hosting its group and that phase 2 be held such that each game is allocated to the venue it is likely to draw the maximum attendance at.

Phase One (= Rounds 1-3): Teams ranked 1-4 in the seedings/world rankings play World Cup rounds 1-3 in round-robin Group E; teams ranked 5-8 play in Group D; countries ranked 9-12 play in Group C; 13-16 in Group B and the 4 qualifiers (17-20) in Group A. The group names A B C D & E are again chosen to maximise viewer interest in all five groups, not just in the 'top' one or two groups, and to keep teams seeded 13-20 from feeling like they are in a lesser competition. These rankings/seedings are otherwise arrived at as in Method A, but with the most recently completed 6-nations event determining which (2 each) of its 6 member countries start in groups E, D & C..

So no group has a clear favourite, a massive underdog or a likelihood of a mismatch at all, just good old suspense, action, close lively games and excitement. Also, all teams enter the competition with a chance of winning it, and a good opportunity of finishing in the top 10.

Phase Two / Round Four: We now move on to the Quarter Final stage of the competition. The Quarter Finals matches are as follows: QF1: D2 vs C1; QF2: D1 vs A1 QF3: B1 vs E2 QF4: E1 vs C2 (= matches 1 – 4) Notice that all teams are given a chance to win the World Cup, regardless of which group they started in.

All other teams are still fighting for a chance at a good finish: Match 5: E3 vs D3 (the winner can still finish in the top 3) Match 6: E4 vs B2 (the winner still has a chance to finish in the top 5) Match 7: D4 vs C3 (the winner can still finish 7th) Match 8: A2 vs B3 (the winner can still finish 8th) Match 9: C4 vs A3 (the winner can still finish 10th) A4 & B4 rest and recover this round so they are stronger (and have more of a chance) in round five.

A point to note here is that the above allocation is anything but random. A geometric provisional ranking order is used: E1 comes before D1 comes before E2 comes before C1 comes before D2 comes before E3 B1 C2 D3 E4 A1 B2 C3 D4

  > A2 B3 C4  >      A3 B4               A4           We use the reasoning that you have to balance doing well in your group with having had harder opponents to arrive at a measure of who has the most potential, and that this geometric pattern will gain acceptance more easily than anything more complex or random looking. 

Round 5: Semi-Final 1: Winner of QF2 versus Winner of QF3 Semi-Final 2: Winner of QF1 vs Winner of QF4

Match A: QFL1 vs Winner of Match 5 (the winner gets a chance at 3rd place and a guaranteed top 4 finish)

Match B: QFL2 vs Winner of Match 6 (the winner gets a chance at 5th place and a guaranteed top 6 finish)

Match C: QFL3 vs Winner of Match 7 (the winner gets a chance at 7th place and a guaranteed top 9 finish)

[The ranking order of the 4 QF losers QFL1-QFL4 is arrived at as follows: The teams are provisionally ranked within the sequence E1 > E2 > D1 > D2 > C1 > C2 > B1 > A1 (= prioritising who beat the more highly ranked opponents in the run-up to the Quarter Finals over who won their group). This first ranking order arrangement is then altered as follows: first the team or teams that lost their QF match by the smallest margin overtakes the team one above it and then the team that lost their QF by the biggest margin goes down one, again swapping places with the team one below them.]

Match D: Loser of Match 5 vs Winner of Match 8 (the winner gets a chance at 8th place and a guaranteed top 11 finish)

Match E: QFL4 vs Winner of Match 9 (the winner gets a chance at 10th place and a guaranteed top 13 finish)

Match F: Loser of Match 6 vs Loser of Match 7 (the winner gets a chance at 12th place and a guaranteed top 15 finish)

Match G: Loser of Match 8 vs B4 (the winner makes the top 16 finishers)

Match H: Loser of Match 9 vs A4 (only the winner is among the top 18 finishers) [Loser G = 19th, Loser H = 20th]

Round Six : for 1st place: the SF winners for 3rd: Winner of Match A vs the better of the two SF losers (according to only their points difference against opponents they have both played in the 5 rounds so far + against each other if they are from the same group) [ > if this does not bring about a winner, then the team that is higher up according to E1 > D1 > C1 > B1 > A1 > E2 > D2 goes into the 3rd-place match] for 5th: Winner of Match B vs the other SF loser [the loser of this game finishes 6th] for 7th place: Winner of Match C vs Loser of Match A [loser= declared 9th] for 8th Winner of Match D vs Loser of Match B [loser=11th] for 10th place: Winner of Match E vs Loser of Match C [loser=13th] for 12th place: Winner of Match F vs Loser of Match D [loser=15th] for 14th: Loser of Match E vs Loser of Match F [loser = 17th] = End of Tournament

Method D:

The top 5 in the seeding rankings all play in round-robin Group D; seeds 6-10 play in Group C; seeds 11-15 play in Group B, and Group A is for all the qualifiers who are not in the top 15 in the rankings of recent World Cups (40% 25% 20% & 15%). Phase One is round-robin play within each of these 4 groups.

Phase 2 is a single-loss elimination knockout tournament with 3 + 2 + 1 + 0 top placed teams automatically advancing from Pools D C B & A into the Quarter-Finals (the harder the group, the more berths to the QF it gets). Phase Two’s Round One is the qualifying play-off round for the teams who narrowly missed the above allocation of the first 6 QF places: Match 1 = A1 versus C3 and match 2 = B2 vs D4. The winners of these games advance to play each other in the 4th Quarter-Finals game.

Match 3 (= A2 vs D5) and match 4 (= B3 vs C4) are for a chance of a top-10 finish.

In Phase 2 Round 2: the QF pairings are as follows: QF1=D1 vs C2 ; QF2 = D2 vs B1; QF3 = D3 vs C1; QF4 = the winner of Match 1 vs Winner of Match 2. The battle for top 10 finishes sees the winners of matches 3 & 4 play against the losers of matches 1 & 2.

Phase 3 Round 3 = the 2 Semi-Finals (winner of QF1 vs winner of QF4 and winner of QF2 vs winner of QF3). It also features either three other trophy games (Best Improver, the Giant’s Trophy & Little Giant – see Method A), or Semi-Finals for 5th and for 9th place .

Phase 3 Round 4 = only the games for 1st, 3rd & 5th (the game for 5th is, if the 5 trophies system is used, between the two teams who lost their QFs by the smallest margin, or if the “Semi-Finals for 5th” system is used, the winners of the two Semi-Finals for 5th meet).

Method E: Quarter-Folds

Round 1 of the World Cup = the teams seeded 8th vs 9th; 7th vs 10th; 6th vs 11th; 5th vs 12th; 1st vs 13th; 2ndvs 14th; 3rd vs15th; 4th vs 16th; Teams seeded 17th to 20th are allocated round 1 opponents among one-another in a 4 team drawing.

Round 2 = Whichever team won its top 16 game by the largest margin versus whichever team won its game by the smallest margin; the teams with the 2nd-largest and 2nd smallest winning margin meet in game 2; the teams with the 3rd-largest and 3rd smallest winning margin meet in game 3; the teams with the 4nd-largest and 5th largest winning margin meet in game 4; the teams who lost their round one game by the smallest and by the largest margin meet in game 5; the teams who lost their round one games by the 2nd-smallest and by the 2nd-largest margin meet in game 6; …. ; game 9 = the winners of the two 17th-20th games meet for a chance at a top 5 finish; match 10 = the losers of the 17th-20th games meet for a chance at a top 15 finish.

Round 3: In the ‘highest rung of the ladder’ match, the two teams who (of those who participated in round 2’s matches 1-4) won their matches with the biggest winning margins play for the overall lead + a guaranteed top 4 finish; In the 2nd rung match: the other two winners of round 2’s matches 1-4 meet (for a chance of winning the tournament overall + a guaranteed top 4 finish); in the 3rd rung match: the two teams with the best points difference (total points scored in matches so far minus total points allowed) after two rounds among the teams who won their top 16-seeds’ round one match meet (for a chance to win the tournament or finish in the top 3); in the 4th rung match: the team who has the next-best points difference after two rounds of play among those who won their round one match versus the team who has the best points difference among ALL the top 16 teams apart from the above (for a chance to finish in the top 3) in the 5th rung match: the team who won round 2’s match 9 (thus far undefeated and impressive, having started outside the top 16 seeds) versus the team who has the best points difference among all the top 16-seeded teams to have won one match so far apart from the above (for a chance to finish in the top 5) in the 6th rung match: the two teams who have the best points difference among all the top 16-seeded teams apart from the above and excluding teams who have yet to win a match meet (for a chance to finish in the top 7); 7th rung: the final remaining top-16-seeded team to have lost only one game versus the team who has the best points difference among all the top 16-seeded teams who have yet to win a match (for a chance to finish in the top 9); 8th rung: the 2nd-best of the top 16-seeded teams who have yet to win a match versus the winner of round 2’s match 10 (for 15th & 17th places); 9th rung: the 3rd-best of the top 16-seeded teams who have yet to win a match versus the loser of round 2’s match 9 (for 16th & 19th places) 10th rung: the worst of the top 16-seeded teams versus the loser of round 2’s match 10 (for 18th & 20th places)

Round 4: in class & match A and for a guaranteed top 2 finish: the winner of round 3’s rung 1 match vs the winner of the rung 2 match; in match B: winner of rung 3 vs loser of rung 1 (for a chance at 1st/2nd place); match C: winner of rung 4 vs loser of rung 2 (for a chance at 3rd/4th place); match D: winner of rung 5 vs loser of rung 3 (for a chance at 5th place); match E: winner of rung 6 vs loser of rung 4 (for a chance at 8th place); match F: winner of rung 7 vs loser of rung 5 (for a chance at a top-10 finish); match G: loser of rung 6 vs loser of rung 7 (for 12th & 14th places)

Round 5: top rung: winner of match B vs loser of match A (the winner goes into 1st/2nd place match, the loser goes into the 3rd/4th place match) 2nd rung: winner of match C vs loser of match B (the winner goes into 3rd/4th place match, the loser goes into the 5th/6th place match) 3rd rung: winner of match D vs loser of match C (the winner goes into the 5th/6th place match, the loser is 7th) 4th rung: winner of match E vs loser of match D for 8th place (the loser is 9th) 5th rung: winner of match F vs loser of match E for 10th place (the loser is 11th)

+ a special handicap match between the winner of match A and a combined forces all-stars team composed of players from all the bottom six teams. This team plays with an extra player on the field at all times and has double the allocation of substitutions, including the right to change players it has taken out back in again later on. As an incentive: if the winner of match A fails to win this handicap challenge match, it must accept a penalty of 3 points into the gold medal game (which would mean the game starts with the winner of round 5’s top rung match 3-0 ahead against the winner of round 4’s match A, but if it does win in spite of the handicap rules, it gets a cash bonus prize equivalent to 2% of the tournament’s overall prize money).

Round 6: Matches for 1st; 3rd (=loser of rung 1 vs winner of rung 2) & 5th (L2 vs W3) + optionally matches for the three other Method A trophies

Method F: Rolling Cut

Rolling Cut System: 20-22 teams play in rounds 1-2. All teams are in the same pool from the beginning. There is an all-in drawing held with no seedings at all. the outcome of the drawing determines who plays who in the first two rounds: 1 vs 2; 3 vs 4; 5 vs 6; 7 vs 8; ….; 21 vs 22; 2 vs 3; 4 vs 5; 6 vs 7;…..; 20 vs 21; 22 vs 1.

After every round, all teams are ranked according to the number of win-points so far in the tournament taking priority over ‘points difference’ as the 2nd instance and teams that are even in both methods are ranked according to who has had the harder opponents so far, which is measured as the combined points difference of all opponents they have played so far. As the tournament progresses, and more and more teams are cut, the third instance becomes ‘the combined points difference of all opponents they have played in the 3 most recent rounds’; the second instance (points difference): only the 2 most recent games + 10% of the game before that count towards each team’s points difference. And note that the win-points go up with every round. So in Round 1 of play a team gets 3 points for a win and 1 for a draw; in round 2 they get 4 points for a win, 2 for a draw; in round 3 they get 6 points for a win, 3 for a draw; in round 4 they get 8 points for a win, 3 for a draw; in round 5 they get 10 points for a win, 4 for a draw; and in round 6 they get 12 points for a win, 5 for a draw;

At the end of round 2, only the top 14 in the standings survive into the next 2 rounds. Then after round 4, only the top 10 survive the next cut and advance into round 5; then only the top 6 survive. These 6 play another round, then we go straight into the Gold & Bronze matches (+ optionally the three other trophies from Method A). It is suggested that all teams play one last ‘placings’ match after they are eliminated (one match is for 19th vs 20th; one for 17th vs 18th;…. one for 7th vs 8th).

From rounds three onwards, a ‘three stack shuffle’ system determines who plays who next, so the 14 who advance into round 3 are ‘three stack shuffled’ as follows: 2 3 1 5 6 4 8 9 7 11 12 10 14 13 So the round three fixtures will be: 2 vs 5; 8 vs 11; 14 vs 3; 6 vs 9; 12 vs 1; 4 vs 7; 10 vs 13 and round 4: 5 vs 8; 11 vs 14; 3 vs 6;…..; 13 vs 2, and after each new round of play, another ‘three stack shuffle’ is conducted to ensure that teams are not playing the same opponents a 2nd time.

Method G1: ‘2LE’

Two-Loss-Elimination tournament with the round one games, arrived at as in Method F above (final paragraph) in a drawing with no seedings at all.

The only separating action is that all the balls representing the teams from Europe are put in one bowl, all others in the other, and so each round one game consists of a European team playing against a non-European team (except the last game to be drawn if Europe has 9 teams participating). This way we can guarantee that no two teams from the same continent play each other (to make sure of this we could have a ‘switch the 9th and 10th to be drawn from the intercontinental bowl around if….’ clause).

We express the outcome of round 1 as “.. 10 & 10” meaning that 10 teams remain in the undefeated teams bracket and ten have fallen into the last-chance bracket. Similarly, we express the outcome of round 2 as 8 & 8. bye .. 8&8 .. 4&8 .. 4&4 .. 2&4 .. 2&2 SF & F & 3rd (& 5th & 7th & 9th) place match.

So every round after round one either consists of matches being held in the (upper=) undefeated teams bracket and matches in the (lower=) last-chance bracket, or as in the case of rounds 3, 5 & 7, it may only consist of =) last-chance bracket matches.

The round one games are doubly important, as not only do they determine which ten teams go into round 2 with both of their lives still intact, but its overall points difference rankings also determine who has to play in round 2 (=the winners of the 4 closest round 1 games and the 8 losers of the least-close games) and who gets to skip round 2 without losing a life (=the top 6 winners and the top 2 losers).

The outcome of round 1 is that 10 teams have fallen into the last-chance bracket. The outcome of round 2 is that 8 remain in the undefeated teams bracket and 8 others in the last-chance bracket. It is suggested that the 4 teams who have already been eliminated play one-another in a 17th/18th and a 19th/20th game in round 3, and that all other teams also be given a similar placings match when they are eliminated from the last-chance bracket.

The outcome of round 3 is that 4 remain in the undefeated teams bracket and 8 others in the last-chance bracket. The outcome of round 4 is that 4 remain in the undefeated teams bracket and 4 others in the last-chance bracket. The outcome of round 5 is that 2 remain in the undefeated teams bracket and 4 others in the last-chance bracket. The outcome of round 6 is that 2 remain in the undefeated teams bracket and 2 others in the last-chance bracket.

These final four then play in the tournament semi-finals in round 7. Round 7 also contains the 5th & 7th place matches. Round 8 consists of only the 1st-place and 3rd-place matches (+ optionally the three other trophies as outlines in Method A above)

Method G2: E10+2LE

This is a variation of the above Method. It gives each team a chance to test itself against two other teams from the same half of the seedings (the top 8 or 10 seeds, known as the Elite Pool, and the other 10-12, known as the General Pool). The better a team does in these first two rounds, the better its starting position in the two-loss-elimination tournament. This Method avoids the worst of the mismatches, while also ensuring that each team is given a reasonable opponent in its first two games.

The third round of play is the start of the 2LE-part of the tournament, with a similar shape as in Method G1: 8&8 .. 4&8.. 4&4.. 2&4.. 2&2 .. SFs

The top 5 from the Elite Pool and the top 3 from the General Pool (both ranked according to win-points > points scored minus points against > combined opponents’ ‘psmpa’) win the right to start in the two-lives-left bracket, while the 6th – 9th from the Elite Pool and the 4th – 7th from the General Pool start in the last-chance bracket.

Method H1: ‘E8+SLE’

The top 8 seeds begin in the Elite Pool; the 12 others in the General Pool. Rounds 1-2 are played within these pools with the exact fixtures determined in a drawing (rd 1: 1 vs 2; 3 vs 4; …… ; 11 vs 12; rd 2: 2 vs 3; 4 vs 5; …. 12 vs 1).

Then each pool breaks up into a top four and a rest halves (named Pools E1, E2, G1, G2 or you could name them Pools 3 - 6) for a two round phase two. In other words, only the top four from each phase one pool advance into the “1” pools. All others go into the “2” pools as the phase one pools are cut into two each. At this stage, all teams still have a chance of winning the tournament overall, but more teams from the “1” pools E1 and G1 qualify than from the “2” pools, and with easier QF opponents too.

Then in the phase three Quarter-Finals: the top half of the draw = E1.1vsG1.3 & E1.3vsG1.2; the other half of QFs being G1.1vE2.1 & E1.2vG2.1

If any lower placings (or three other trophies’-) games are to be included, they are best held in the Semi-Finals round, so that the overall final is the last game to be played.

Method H2: ‘E10+SLE’

The top 10 seeds begin in the Elite Pool; the 12 others in the General Pool. Rounds 1-2 are played within these pools with the exact fixtures determined in a drawing (rd 1: 1 vs 2; 3 vs 4; …… ; 11 vs 12; rd 2: 2 vs 3; 4 vs 5; …. 12 vs 1).

Round 3 is all about 6 teams having to defend/earn the privileged later entry status against other teams. Losing here means that more work will be required to reach the same round and the same end position. The round 3 fixtures are: E4vsE5, E2vE3, E8vE9, G5vG8, G6vG7, G2vG3; round 4 = G3vsE8, G4vs E7, G5vsE6, G6vsE5; round 5 = the winners of round 4 vs E3, E4, G1 & G2 (QFs). Also E1 vs E2 (super-semi-game 1);

round 6 = the winners of round 5 play each other (Semi-Finals, Part A)

In round 7, the winners from round 6 meet in one Super-Semi; E1vE2 in the other (game 2, all scores count double in this 2nd game, added onto those from their game in round 5); round 8 = gold & bronze games (+ optionally any other)

Method I: (E10+Ldr)

2 rounds as 2 uneven pools, the Elite 10 (probably the tri nations + five of the six nations + Americas1 & Oceania3) play each other & the General 10 play each other for two rounds in an unseeded drawing (like in the Methods G1 & H2 above).

The end raking positions after these two rounds determine the starting position in Phase Two, the 3 ½ ladder rounds, with the first ladder round starting as E1vE2 (in top rung match) > E3vE4 (in 2nd rung match) > E5vE6 (in 3rd rung match) > E7vG1 > E8vG2 > E9vG3 > E10vG4 > G5vG6,… So as not to be disadvantaged over E3, E5 & E7 for their superior points difference … E2, E4 & E6 are given a 15, 10 & 5 min window of opportunity right after the end of the last Round Three match to announce, unanimously by the team captain and the coach/manager, whether or not they wish to swap down to the next rung down (swapping E2/E3, or E4/E5, or E6/E7’s round 3 starting rung of the ladder) – if they say nothing, then they will not.

Then round 4’s top rungs are as follows: top rung A = Winner1 vs W2; 2nd rung (match B) = W3 vs L1; 3rd rung (match C) = W4 vs L2; match D: winner of rung 5 vs loser of rung 3 (for a chance at 5th place); match E: winner of rung 6 vs loser of rung 4 (for a chance at 8th place); match F: winner of rung 7 vs loser of rung 5 (for a chance at a top-10 finish); match G: winner of rung 8 vs loser of rung 6 (for a chance at 12th) match H: winner of rung 9 vs loser of rung 7 (for a chance at 14th place) match I: winner of rung 10 vs loser of rung 8 (for a chance at 16th place, the loser is 19th) match J: loser of rung 9 vs loser of rung 10 (for 18th & 20th places)

 (Same final 3 rounds as in Method E above). 

Round 5: top rung: winner of match B vs loser of match A (the winner goes into 1st/2nd place match, the loser goes into the 3rd/4th place match) 2nd rung: winner of match C vs loser of match B (the winner goes into 3rd/4th place match, the loser goes into the 5th/6th place match) 3rd rung: winner of match D vs loser of match C (the winner goes into the 5th/6th place match, the loser is 7th) 4th rung: winner of match E vs loser of match D for 8th place (the loser is 9th) 5th rung: winner of match F vs loser of match E for 10th place (the loser is 11th) 6th rung: winner of match G vs loser of match F for 12th place (the loser is 13th) 7th rung: winner of match H vs loser of match G for 14th place (the loser is 15th) 8th rung: winner of match I vs loser of match H for 16th place (the loser is 17th) + a special handicap match between the winner of round 4’s match A and a combined forces all-stars team composed of players from all the bottom 3 teams. This team plays with an extra player on the field at all times and has double the allocation of substitutions, including the right to change players it has taken out back in again later on. If the winner of match A fails to win this handicap challenge match, it must accept a penalty of 4 points into the gold medal game (which would mean the game starts with the winner of round 5’s top rung match 4-0 ahead against the winner of round 4’s match A).

Round 6: Matches for 1st; 3rd (=loser of rung 1 vs winner of rung 2) & 5th (L2 vs W3) + optionally matches for the three other Method A trophies

Method J: (Megapool then 3 Pools then Ldr)

The 20 or 22 teams who have qualified for the World Cup all go into one big pool. A big all-in-one-bowl unseeded drawing determines the round one and round two fixtures (Round 1: 1 vs 2; 3 vs 4; ….. 21 vs 22; Round 2: 2 vs 3; 4 vs 5; …. 22 vs 1)

The standings at the end of round 2 of play (in win points > points difference) determine which top 10 advance into Phase 2’s Pool A. The teams in 11th-16th places go into Pool B, and the rest go into Pool C. Rounds 3 & 4 are played within these new pools. A 3-stack-shuffle within each pool ensures that no 2 teams who have already met play each other a 2nd time within rounds 1-4.

Phase 3’s tier 1 match = Pool A’s top two teams at the end of round 4. Phase 3’s 2nd rung match = Pool A’s 3rd vs 4th placed teams (the winner is either 1st or 2nd, the loser is either 5th or 6th place) 3rd rung match = Pool A’s 5th vs 6th placed teams (the winner is either 3rd or 4th; the loser is either 7th or 8th place) 4th rung match = Pool A’s 7th vs 8th placed teams (the winner is either 5th or 6th; the loser is either 9th or 10th place) 5th rung match = Pool A’s 9th vs Pool B’s 1st placed teams (the winner is either 7th or 8th place, the loser is 11th or 12th) 6th rung match = A10 vs B2 7th rung match = B3 vs B4 8th rung match = B5 vs C1 9th rung match = C2 vs B6 10th rung match = C3 vs C4 bottom rung match = C5 vs C6

Final round of play (=round 6): For 1st place: the winners of the tier 1 & 2 matches For 3rd: Winner of 3rd rung vs loser of top rung For 5th: W4 vs L2 For 7th: W5 vs L3 For 9th: W6 vs L4 (….the organisers are to decide how many round six matches to have / how many final placings matches to have, 5, 6, 7, 8, 9, 10 or 11)

Method 11A) Two rounds as one big megapool (as in Method J above), then the top two get byes into the QFs, where they will meet twice, and the other 12 top 14 in the standings after two rounds teams (3rd-14th) play in the round three single-loss-elimination knockout matches for places in the QFs, where the winners play for the three places in the SFs where they will be joined by the W of the 1v2 QF (a QF so big it consists of 2 matches and counts as 2 rounds of play – all points from the first game are carried forward into the 2nd game between these 2 titans, where all tries count double).

Method 11B) Rounds 1-3 are played in two uneven pools, an elite 10 & a general 12, and the top 7 from each qualify into the above 14 team showdown (in which E1vE2 in the super QF, leaving G1-7and E3-7 to play the round four matches) and the rest either go into consolation/placing games or are out.

Method 12A) Double Champion vs Challenger system (This option with matches to decide who earns a title shot and each team’s second chance has to be against a team it has not played already) then SLE SFs for 1st, 5th, 9th & (“12th”) places.

Three title 18 team example: Round one (Sat/Sun) = Seeds 7-18 all go into a wide-open all-in drawing, whoever comes out first & 2nd play in round one. Whoever is drawn 3rd vs 4th; 5th vs 6th; 7th team drawn vs 8th; 9th vs 10th; 11th vs 12th.

In round two (Tue/Wed) the 6 winners all play against each other for the three titles. Also in Round two, the remaining six teams (These are seeded 1st, 2nd, 3rd, 4th,5th & 6th based on previous World Cups) play three games for the right to challenge the three newly crowned title holders according to a drawing.

Then in round three: the winners of round two meet in the title defences, while the losers of ALL Round one matches play matches (Fri) for title chances in round four. Unlike the other rounds (where there is a rest day in between), round four (Sunday) is played the day after round three (Saturday). This is because it features the supposedly weakest challengers, and we would hate to see any dull games.

Then in round four: the losers of all round two matches play for the right to challenge the champions in round five, while the round three winners meet in champion versus challenger title matches.

Then in round five, the winners from round four meet in the title matches. Also, 6 teams have only had one life so far because they were involved in round three title matches. Those who now need their 2nd life (because they do not enter round 5 as title holders) play against the top (however many it takes to have 3 non title matches again) teams so far based on number of matches won > points difference > opponents’ p.d. for the right to have the round six (final) title shot.

Once all the teams have had their two chances at titles, the final standings before the final two rounds (round seven & eight) are the three round six match winners (must be the top 3) > total number of matches won > points difference > cumulative opponents’ p.d (shows who had the harder opponents). The teams placed 1-4, 5-8 and 9-12 and 13-16 all go into separate Semi-Finals & Finals.

Method 12B) Champion versus Challenger matches with 20 teams involved and 2 titles being defended every day (with no rest days in between). In round 1- 9, all teams are given a title defence (in an order determined ‘the luck of the draw’ in an almost unseeded drawing from two bowls). Round 1 = entry positions 1-4 in two title matches; round 2 = the two winners of round 1 defend against entry positions 5-6. Round 3 = the two winners of round 2 defend against entry positions 7-8; …... ….

The top 8 seeds are drawn entry positions 7-14; the other 12 teams (seeded/ranked 9-20 from previous World Cups) are drawn entry positions 1-6 & 15-20. This way, the ‘other 12’ are guaranteed either a good chance of being an early champion or to be entering near the end and this way not to require too many wins to become the winner of the final round. All 20 have a fair chance of making the top 3 overall, and of successfully defending the title.

To earn a 2nd title shot, all teams have to win a (right-to-challenge-the-champion) match, similar to Method 11. This way, none of the under-performing teams go into title mismatches, and all teams have a chance to improve their situation so far. A similar system applies to the 3rd-life Upper, Middle and Lower titles (see below).

In round 8, the 4 losers of rounds 1 & 2 play for a title shot. + the titles are defended against entry positions 17 & 18.

In round 9, the 4 losers of the 4 round 3 & 4 matches play for a title shot + the titles are defended against entry positions 19 & 20.

In round 10, the two winners of the round 9 title matches defend their titles against the two teams who won a title shot in the round 8 non-title matches. + the losers of the round 5 & 6 matches play for a title shot.

In round 11, the two winners of the round 10 title matches defend their titles against the two teams who won a title shot in the round 9 non-title matches. + the losers of the round 7 & 8 matches play for a title shot.

In round 12, the two winners of the round 11 title matches defend their titles against the two teams who won a title shot in the round 10 non-title matches. + the losers and winners of the round 9 matches play (avoiding repeat fixtures) for a title shot.

Also, the third life tournament gets underway, as the first 12 teams to have been eliminated with two losses go into three new title tournaments: the top 4 of these 12 (as ranked in terms of number matches won > points difference > opponents’ combined p.d.) go into the Upper Title tournament draw; the 5th-8th ranked teams go into the Middle Title draw (the ultimate winner of which is to be declared 5th place overall and Middle Champion), and the 9th-12th ranked teams go into the Lower Title draw (the ultimate winner of which is to be declared 10th place overall and Lower Champion). These round 12 matches determine who qualifies for- and hence earns a right to be in the Upper, Middle and Lower title matches, and who goes home.

In round 13, the two winners of the round 12 title matches defend their titles against the two teams who won a title shot in the round 11 non-title matches.

In round 14, the two winners of the round 13 title matches defend their titles against the two teams who won a title shot in the round 12 non-title matches involving the teams who played in round 9. This is the final match for these titles and the winners of these games get to keep the titles forever. Also, the winners of the round 12 Upper, Middle and Lower matches meet in the first Upper, Middle and Lower title matches And in the Upper, Middle and Lower title-shot earning qualification matches, the 13th-18th teams to have lost a 2nd game now play for a title shot at these three titles (having been ranked according to their number of wins > pd>… and based on this the top two of these 6 go into the Upper, the middle two into the Middle and the bottom two into the Lower title series).

In round 15, the winners of the Upper, Middle and Lower matches meet and play for the Upper, Middle and Lower titles. The winners of the Middle and Lower matches are crowned Middle and Lower Champions and thereby ranked 5th & 10th overall (thereby overtaking some of the teams who played in the series one above them in the official overall end-placings). Also in round 15, the two winners of the two round 1-14 titles (which should either be named after sponsors, cities, vips, legends or host countries).

Final round: the winner of the Upper Title match versus the winner of the Round 1-14 titles match and for 3rd place: the losers of those two round 15 champions/title matches meet .

Method 13) The seven-stadium circle system (with the bottom six seeded teams, 15-20, starting round one in qualification games, the winners of which replace the worst two teams in the circle on goal difference in round two). The 8 stadiums are diagrammatically shown in a circle. In round one, every second stadium hosts two teams seeded 5-12 (a, c, e, g), every 4th stadium (b, f) hosts teams seeded 1-4 and every other 4th one hosts (d) 13-14.

 The losers of round one circle games move one position in a clockwise direction (and again, two teams are replaced in round three on the basis of cumulative G.D. by the winners of the two qualification games among teams currently out of the circle) and the losers of round two circle games move three positions clockwise. Round four onwards is ladder games, with the starting point in the ladder being on the basis of round 3 wins > rd1+rd2 wins > rd1+2+3 points dif.. In the event of a draw, the challenger (or in the 1st round, lower seeded team) wins the right to stay in its stadium. 

Method 14) one round as mega-pool (as in Method J above), then round 2 = the first two teams to win round 1 games meet; the next 2 teams to clinch a top-14 place at the end of round 1 meet in match 2; the next 2 teams to definitely clinch a top-14 place at the end of round 1 meet in match 3; …. ….., then four ladder rounds (as in Method E above). For variation 14B, see

 http://sports.groups.yahoo.com/group/TournamentStructures/message/27  

Method 15) Round one as Elite 12 & General 8or10, then round two of play sees the bottom four on goal difference drop from E to G and from G to ‘G2’, leaving 8 in E & 8or10 in G, then round three onwards is part-pre-seeded, part mega-pool start to ladder play: Every second place in the ladder (A2,B2,C2,…) is awarded on the basis of the standings after round 2 (with wins>GD and all E teams>G>G2), and every second team planted into the start of the ladder (A1, B1, C1…) is on the basis of 45% the standings after round two and 55% the pre-tournament rankings/seedings from the overall sum of recent years.

Method 16 A+B+C: 3 phases times 2-3 rounds each: 2 uneven pools (e.g. 8 team elite & 14 team gnrl level), then 5 from elite level + 3 from gnrl level form phase two’ highest pool/level; 3from E + 5 from G form the 2nd level > rest in 3rd level, then SLE or ladders ending.

Method 30A: 2 uneven pools of elite 8 & gnrl 12 play rounds 1-3, then 5 (E) + 3 (G) qualify for Phase 2’s Pool A, and E5-8 and G4-8 for pool B, then ladder ending (final 4 rounds = as in Method E above)

If using SLE (=Method 30B), then suggest the winner of A7+B1+B2+B3 SF & F then joins A4-A6 in SF & F, then the winner of that joins A1-A3 in SF & F; Or Method 30C: SF=A1-A3+B1orA4.

Method 17) Uneven groups (five levels of four round-robin groups each), then ladder with the following start: 1.1v1.2 > 1.3v2.1 > 1.4v2.2,> 3.1v2.3,> 3.2v2.4,> 3.3v4.1 …

Method 18) Round one & two = three mini-tournaments of SFs of 4th-7th seed; 8th-11th & 12th to 15th, then Round three to five (the final part) are round robin groups, each containing one newly promoted winner: Group A: seeds 1 to 3 plus the winner of the 4th-7th seed mini-tournament; group B = the other three from 4th-7th plus the winner of 8th to 11th, group C ….

Method 19 A+B+C) 20 team tournament with Quarter folds system for round one & 2: If 16 teams, round one is 1st seed v 5, 2v6, 3v7, 4v8, 9v13, 10v14,… 12v16; round two is the 4 upper half losers vs the 4 lower half winners, while the other 8 teams do one of three possibilities (1-4 vs 13-16 (all with an extra man on & extra substitutions) handicap matches, or 1-4 vs 13-16 (not handicap matches) Points Difference decides which 2 stay in the top 4 or 1v3, 2v4, 13v15 & 14v16), then in round three to five is ladder matches, with one of a variety of possible starts. Round 3’s rungs if the ladder are as follows: the 4 Unbeaten winners on top > WL1vWL2 > WL3 v 17-20W > WL4 v LW1 > LW2vLW3 > L4v 13-16.1 > 13-16.2v13-16.3 > 13-16.4v17-20.2 > 17-20.3v.4 Then the final round is the five/six medal matches (see end of tournament part in Method A above).

Method 20) 2 rounds as two uneven pools of 10&10, then two rounds as three pools/levels (7from Elite+1General pool > 3 from each or (3E + 5G) > rest), then 3 ½ round ladder

Method 21 A-D: Even groups (4x5 or 5x4), then four-round ladder or 2LE with a 8 & 8 start (and 3rd, 5th, …. place matches)

Method 22: 22 teams playing rounds 1 to 3 as Pool A (seeds 1-8), Pool B (seeds 9-14), & Pool C (seeds 15-22), then SLE KO tournament ending with A1-3 & B1 getting a bye into the QFs, and 3 from each pool (minus one) playing in the Eighth-finals (or, 9b) two from each pool waiting in the eight-finals where they are joined by two round four winners).

Method 23: 5 even groups of 4, then the top 12 go into 2 even pools of 6, while 13-16 & 17-20 go into two lower groups (or SF & F) “playing for 12th & 16th place“ (as the winners of these groups each overtake one other team), then upper pool 2ndsv 3rds, then SF, Gold & Bronze matches.

Method 24: Pure 2LE, with 4 1st-round matches & 12 1st-round byes (20..16&4) .. 8&12 .. 8 &6 .. 4&7 (1 bye is awarded on the basis of G.D. from the two most recent matches each only) .. 4&4 .. 2&4 .. SF, F & 3rd & 5th placed matches

Method 25A: 5 even groups of 4, followed by 3 uneven pools of 10 > 6 > 4 teams, followed by a ladder phase Method 25 B: 5 even groups of 4, then 2 groups of 4 teams, then (plus/minus inserting a 2nds V3rds round and 1stv1st as one semi-final and hence one half of the draw) .. SF & F conclusion.

Method 26 (only ranked so low because of its similarity with Method C) 5 uneven groups of 4 each (rounds 1-3), then SLE, starting at the bottom and moving up, round 4: (and 1.2v2.1 in the separate wildcard game A) 4.4v5.3 & 4.3v5.2; round 5: the 2 winners (+1) join 2.4, 3.3, 3.4, 4.2 & 5.1 (in 4 matches), plus 1.1 defends his super-finals against the winner of 1.2v2.1 in wild card game B; round 6: the 4 winners join 1.4, 2.2, 2.3, 3.1, 3.2 & 4.1 (in 5 matches); round 7: the 5 winners are joined by 1.2, 1.3, 2.1 in the silver QFs, the winners play in the silver SFs, the winners of that in the silver finals (while the top two QF losers play for a chance at bronze), then the winner of wildcard game B plays the winner of the silver finals for the trophy/gold, and the loser of the silver finals plays the winner of the top QF losers’ game for 3rd place/bronze – all drawings ensure they avoid rematches where possible.

Method 27: 2 rounds as two uneven pools of 10elite&10general (like A, B & F), then SLE: E1-E4 get a bye to the QFs, G1 & E5-7 get a bye to the round before QFs (round four) and E8-10 and G2-6 play in round three

Method 28: Is JUST 4-round ladder system (see Method E above) – no need to restrict it to one host country – could do it as all the top 24 in the world all host at least one of their 4 games each

Method 29: Just Swiss/Dutch (forgot which is the official name) system: the one where the overall standings after each round (number of wins>points difference) determine the fixtures for the next round 1st v 2nd; 3rs v 4th; 5th v 6th; …. ….. 4-5 rounds of play.

Method 30 A+B: 5 even groups of 4, then Super 8 play either 2 groups of 4 or 3 rounds as one mega-pool, then SF (+ matches for 5th, 7th,…) & F & 3rd place match

Method 31A: Round one is seeds 13v15 & 14v16 (or by a drawing), round two: the winners meet; round three: the winner plays seeds 10-12 in a new (2nd) SF, round 4: the winners meet (F), the losers meet. rd. 5: the Winner v seeds 7-9 in a 3rd SF & F, AND the bottom four (= the three who lost in rounds one & two plus the team who lost in rounds 3 AND 4) start off the 2nd-life bracket (SFs); rd 6: the winners meet (F) rd 7: W v seeds 4-6 (in SFs) and 2nd life winners versus the next three up, …

Method 31B: A Phase-1 of 3 rounds of play for the top 10 seeds (Pool A) and 2 rounds of play for Pool B, leading into the above as the conclusion to the tournament

Method 31C (the best of all non-top 30 options): Instead of making each winning team then have the added disadvantage of then facing a well-rested team: Round 1-2 = seeds 1-4, 5-8, 9-12, …. in separate SF & F groups, then all the double-winners go up one level and all the losers down one level for round robin group play in rounds 3-5.

Method 32: Two even pools, then 1 from each is through to SFs & one to QFs, while the A3vB4 & A4vB3 for the remaining QF places (H.2 alternative, A5vB5 for a QF against their choice of the Pools.1s)

Method 33 A-H: 4 or 5 even groups, then the top two from each group play in Pool A (2 rounds), all others in B (1 round), then either ladder or SLE conclusion (or Dutch or 2LE).

Method 34: 4 even groups of 5, then the group 1sts V 2nds; 3rds V 4ths; then (1/2)Ls V (3/4)Ws, then QF, SF, …

Method 35: Round 1 = seeds 11-22 only. The winners then join seeds 1-10 in 4 even groups of 4, the rest play 2 ladder rounds in Pool E. Then in round 5, the 2ndsV3rds for a place in the Single Loss Elimination QFs.

[edit] Promotion and relegation

Where the number of competitors is larger than a tournament format permits, there may be multiple tournaments held in parallel, with competitors assigned to a particular tournament based on their ranking. In chess, Scrabble, and many other individual games, many tournaments over one or more years contribute to a player's ranking. However, many team sports involve teams in only one major tournament per year. In European sport, including football, this constitutes the sole ranking for the following season; the top teams from each division of the league are promoted to a higher division, while the bottom teams from a higher division are relegated to a lower one.

This promotion and relegation occurs mainly in league tournaments, but also features in Davis Cup and Fed Cup tennis:

• In the Davis Cup:
  • The first-round losers in the top-level World Group compete in playoff ties against the winners of the second-round ties in Group I of the competition's three regional zones, with the winners of each playoff tie remaining in or promoted to the World Group.
  • In the three regional zones, Group II is conducted in a knockout format. The winner of the knockout tournament is promoted to Group I of its zone. The first-round losers then play relegation ties, with the losers relegated to Group III.
  • Groups III and IV in each zone are contested in a round-robin format. The top two teams in each group are promoted, while the bottom two teams are relegated (assuming there is a lower group in their zone).
• In the Fed Cup:
  • The four first-round losers in World Group I compete in playoff ties against the four winners in World Group II, with the winners remaining in or promoted to World Group I.
  • The losers in World Group II play ties against the four zonal Group I winners (two from Europe/Africa and one each from Asia/Oceania and Americas), with the winners playing in World Group II the following season.
  • Groups I and II in all zones, plus Group III in the Europe/Africa Zone only, are conducted in a round-robin format. The bottom two teams in each group are relegated to the next group down, assuming one exists, while the top two teams in Groups II and III are promoted to the next-higher group.

The hierarchy of divisions may be linear, or tree-like, as with the English football league pyramid.

[edit] Bridge tournaments

In contract bridge a "tournament" is a tournament in the first sense above, composed of multiple "events", which are tournaments in the second sense. Some events may be single-elimination, double-elimination, or Swiss style. However, "Pair events" are the most widespread. In these events, an identical deal (or board) is played in multiple rubbers. The North-South (NS) pair in one such rubber is measured not against the East-West (EW) pair in that same rubber, but rather against all the other NS pairs playing the same board in other rubbers. Thus pairs are rewarded for playing the same cards better than others have played them. Several systems provide a predetermined schedule of fixtures based on the number of pairs and boards to be played, to ensure a good mix of opponents, and that no pair plays the same board twice (see duplicate bridge movements).

[edit] Poker tournaments

In poker tournaments, as players are eliminated, the number of tables is gradually reduced, with the remaining players redistributed among the remaining tables. Play continues until one player has won all of the chips in play. Finishing order is determined by the order in which players are eliminated: last player remaining gets 1st place, last player eliminated gets 2nd, previous player eliminated gets 3rd, etc.

In a "shootout" tournament, players do not change tables until every table has been reduced to one player.

[edit] Rummy tournaments

In rummy tournaments, multiple players join a single tournament. There can be tournaments between multiple players in multiples of 2. Eg: 4, 16, 32, 64, 128 players so on and so forth. As part of overall tournament, all players join one-on-one individual matches. Winners in each match move to the next round. Tournament continues until one player has won the final match. Finishing order of winners is determined by the order in which players are eliminated: last player remaining gets 1st place, last player eliminated gets 2nd, previous player eliminated gets 3rd, etc.

[edit] Alternatives to tournament systems

While tournament structures attempt to provide an objective format for determining the best competitor in a game or sport, other methods exist.

Challenge

In this format, champions retain their title until they are defeated by an opponent, known as the challenger. This system is used in professional boxing (see lineal championship). Prior to 1993, it was also used in the World Chess Championship. The right to become a contender may be awarded through a tournament, as in chess, or through a ranking system: the ranking systems used by boxing's governing bodies are controversial and opaque. If the champion retires or dies, then the current top challenger may be declared champion or the title may be vacant until a match between two challengers is held. Prior to 1920, the reigning Wimbledon champion received a bye to the final; the official name of the FA Challenge Cup reflects a similar arrangement which applied only in that tournament's very early years. The America's Cup is decided between the winners of separate champion and challenger tournaments, respectively for yachts from the country of the reigning champion, and of all other countries. The Ranfurly Shield in New Zealand rugby union is a challenge trophy between provincial teams, in which the holders of the Shield retain it until they are beaten by a challenging province.

Ladder

An extension of the challenge system. All competitors are ranked on a "ladder". New contestants join the bottom of the ladder. Any contestant can challenge a competitor ranked slightly higher; if the challenger wins the match (or the challenge is refused) they swap places on the ladder. Ladders are common in internal club competitions in individual sports, like squash and pool. Another ladder system is to give competitors a certain number of ranking points at the start. If two competitors play each other, then the winner will gain a percentage of the loser's ranking points. In this way competitors that join later will generally start in the middle, since top competitors already have won ranking points and bottom competitors have lost them.

Selection

A champion may be selected by an authorised or self-appointed group, often after a vote. While common in non-competitive activities, ranging from science fairs to cinema's Oscars, this is rarely significant in sports and games. Though unofficial, the polls run by the Associated Press and others were prestigious titles in American college football prior to the creation in 1998 of the Bowl Championship Series, a quasi-official national championship (to this day, the NCAA does not officially award a championship in the top division of college football). As of the 2005 season, the AP Poll operates independently of the BCS and can crown a different national champion, while two other polls are part of the BCS formula.

[edit] See also

• Playoff format
• Qualifying stages
• Apertura and Clausura