What elimination method is being practice when a player or team get eliminated after losing twice?

Tai Tzu Ying Clinched Her Third Indonesia Open Title with Consecutive Comeback Victories

Tai Tzu Ying Clinched Her Third Indonesia Open Title with Consecutive Comeback Victories

2022-06-20 |

Scheduling games is a little more challenging than one might desire.

There are 2 well-known types of tournament formats that sport schedulers use.

• Single Elimination Tournaments.
• Round Robin Tournaments.

Single Elimination Tournaments.

In this format, one defeat is enough to eliminate a team from the tournament.

Scheduling a single elimination tournament is relatively easy. The first step is to get the number of teams to a power of two: 2, 4, 8, 16, 32...

The schedule for 8 teams is shown below.

With 20 teams, you might select eight of those teams to have a preliminary round. The four winners would then join the other twelve to fill out the sixteen-team field.

If you have 24 teams, you could have everyone compete in a preliminary round; this would leave 12 teams. Then, 4 of those teams (randomly selected) could get a bye and the other 8 teams would play to find the other 4 contestants for the next round.

Round Robin Tournaments.

In a Round Robin tournament every team plays every other team .

There is a systematic approach to scheduling a Round Robin tournament. This method assumes that there are enough fields / pitches / courts so that all the games in a round can be played simultaneously. The technique is called the polygon method .

Round Robin scheduling: Even number of teams.

Let N = number of teams in the tournament. There will be N -1 rounds (each team will play N-1 games). Since each team will play every other team once, no team will be idle during any of the rounds.

Let us schedule a round-robin tournament for 8 teams numbered from 1 to 8.

Draw a regular (N -1) sided polygon (i.e., a heptagon for 8 teams). Each vertex and the centre point represents one team.

Draw horizontal stripes as shown below. Then, join the vertex that has been left out to the centre. Each segment represents teams playing each other in the first round.

So (7, 6), (1, 5), (2, 4) and (3, 8) play in the first round.

Rotate the polygon 1/(N-1)th of a circle (i.e. one vertex point). The new segments represent the pairings for round two.

So (6, 5), (7, 4), (1, 3) and (2, 8) play the second round.

Continue rotating the polygon until it returns to its original position.

One more rotation will bring the polygon back to its original position.

If A, B, C and D are the fields / pitches / courts, the schedule could look like this:

We can also rotate the teams around so that each team plays in every field / pitch / court at least once (at present team 8 always plays in D).

Round Robin scheduling: Odd number of teams.

Let N = number of teams in the tournament. There will be N rounds (since each team will play every other team once, and will be idle for exactly one round ).

Let us work out the schedule for 7 teams, numbering the teams from 1 to 7. Draw a regular N-gon (heptagon for 7 teams). Each vertex represents one team.

Draw horizontal stripes as shown below. The vertex that has been left out gives the idle team. Each segment represents teams playing each other in the first round.

So (7, 6), (1, 5) and (2, 4) play in the first round.

Rotate the polygon 1/Nth of a circle (i.e. one vertex point.) The new segments represent the pairings for round two.

Continue rotating the polygon until it returns to its original position.

One more rotation will bring the polygon back to its original position. Therefore, the schedule could look like this:

Why does this work?

The restriction that no vertex has more than one segment drawn to/from it ensures that no team is scheduled for more than one game in each round.

Restricting ourselves to horizontal stripes ensures that no segment is a rotation or reflection of another segment. This means that no pairing will be repeated in a future round.

Notice that in the case where N (no. of teams) was odd, by having only one idle team in each round, the tournament can be completed in the minimum number of rounds.

Arunachalam Y. is a member of the HeyMath! team

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

A double-elimination tournament is one of the more complicated to understand tournament styles, but it's a great format for sports that often consist of series games. Unlike the college basketball tournament, which is single-elimination, a double-elimination tournament allows a team to lose and still have a chance to win the tournament as a whole.

A double-elimination tournament is broken into two sets of brackets, generally called the winner’s bracket and the loser’s bracket. Each team begins in the winner’s bracket, but once they lose, they move to the loser’s bracket, where they still have an opportunity to make it to the championship.

In a four-team bracket, which is what Division I college baseball uses in regional tournaments, the first round consists of two games.

In the second round, the two teams that lost in the first round play in an elimination game. The loser of that game is eliminated from the tournament. In addition, the two teams that won in the first round play each other.

The third round is a single game featuring the team that lost the game between the first-round winning teams and the team that won the game between the first-round losing teams. The loser is eliminated from the tournament, while the winner goes on to the championship.

The fourth round could be one or two games. If the team with one loss wins, both teams will each have one loss, and another game will be played to determine the winner. If the team with no losses wins, it is the champion. 

For example, in the 2016 Division I college baseball tournament, Dallas Baptist lost in the first round, but then won its next two games and played undefeated Texas Tech in the championship. Dallas Baptist won the first game, giving Texas Tech its first loss of the tournament and forcing a second game. Texas Tech won the second game and the championship.