Football fixture generator: the round robin schedule
Your data
With an odd number of teams there is no way around a rest: one team sits out each round, and over the whole table each of them rests exactly once.
Results
Rounds the table takes
—
| Matches in the whole table | — |
| Home matches, from the team with fewest to the team with most | — |
| Longest run any team spends on the same side | — |
The pairings come from the circle method: line the teams up in two rows, play column against column, then hold the first team still and rotate all the others. That alone guarantees every pair meets and nobody plays twice in the same round.
What it does not guarantee is the home and away balance, and this is where most hand made tables fall apart. Straight out of the rotation, in a twenty team table, one club ends up playing all nineteen matches away from home and another plays nineteen in a row at home. Here the sides are handed out afterwards, to whoever has been home less often, which brings the longest run on the same side down from nineteen to five.
Playing home and away is the one arrangement that settles the matter completely: the second half repeats the first with the sides swapped, so every team ends with exactly as many home matches as away ones.
How is a round robin table actually built?
By the circle method. Line the teams up in two rows, play the first column against the last, the second against the second to last, and so on, then hold one team still and rotate all the others by one place.
That guarantees two things at once: every pair meets, and nobody is scheduled twice in the same round. With an odd number of teams a phantom is added, and whoever draws the phantom rests that round.
How many rounds and matches does it take?
With an even number of teams it is one less than the number of teams, and with an odd number it is the number of teams, because everyone has to rest once. The matches are the number of pairs, which is teams times teams minus one, divided by two.
Six teams give five rounds and fifteen matches. Twenty teams give nineteen rounds and one hundred and ninety. Playing home and away doubles both.
Why does the page report the longest run on the same side?
Because that is the number that exposes a badly built table, and the rotation on its own produces terrible ones. Taken straight from the circle method, a twenty team table has one club playing all nineteen matches away and another playing nineteen straight at home.
Here the sides are handed out after the pairings, always to whoever has been at home less often. Measured on the same twenty team table, the longest run drops from nineteen to five and the home count goes from a range of nine to nineteen down to eight to eleven.
Does playing home and away fix the balance?
Completely, and that is the reason most leagues do it. The second half repeats the first with the sides swapped, so every team finishes with exactly as many home matches as away ones.
In a single round table there is no arrangement that gives everyone the same number, because the matches each team plays is odd whenever the number of teams is even. Something has to give, and the page shows you how much.
Reactions
0
0 Comments
Be the first to comment