This website visualizes several methods for constructing sports league schedules (containing n teams) with different properties.

Using the applets contains general information. A Glossary explains the used notions. Under Literature references for the construction methods can be found.

## Single round robin tournaments

In a single round robin tournament each team plays against each other team exactly once. If the number of teams n is even, the schedules contain n-1 rounds and each team plays exactly one match in each round. If n is odd, the schedules contain n rounds and in each round one team has a bye (i.e. it does not play).
The so-called canonical 1-factorization can be used for even and odd n. For even n also the so-called binary 1-factorization can be used where the teams are partitioned into 2 groups. Here it must be distinguished whether n is divisible by 4 or not.

## Single round robin tournaments with a minimum number of breaks

In these tournaments additionally for each match it has to be decided where it takes place (home or away). The objective is to minimize breaks (i.e. to avoid a large number of consecutive home or away matches for the teams). The minimum number of breaks is n-2 for even n and 0 for odd n.

## Double round robin tournaments with a minimum number of breaks

In a double round robin tournament each team plays against each other team exactly twice. The tournament is divided into two half series, where in each half series each team plays against each other team (once at home, once away). The objective is to minimize breaks (i.e. to avoid consecutive home or away matches for the teams). In so-called mirrored tournaments the rounds of the second half series are scheduled in the same order as in the first half series (then the minimum number of breaks is 3(n-2)). In the so-called English system the first round of the second half series is the same as the last round of the first half series, afterwards the rounds are scheduled in the same order as in the first half series. This system ensures that only 2(n-2) breaks are needed.

## Single round robin tournaments on a single court minimizing waiting times

In these tournaments for an odd number of teams every team plays exactly two matches in each round and all matches have to be scheduled consecutively on a single court. The objective is to minimize waiting times for the teams between their two matches. It is distinguished whether zero waiting times are allowed or not.

## Single round robin tournaments with group changes

In these tournaments the teams are additionally partitioned into groups (e.g. according to their strengths). The objective is to find so-called group-changing schedules in which no team plays two consecutive matches against teams of the same group.

## Single round robin tournaments balancing carry-over effects

In these tournaments carry-over effects should be balanced for the teams as much as possible. The best schedules known so far are based on the algebraic structure of a starter.

Last update: 27.02.08 (SK)