Zermelo Swiss Tournaments

To run a large tournament like a 10-round Swiss teams using the Zermelo rating method a suitable startup method is needed. The proviso of the validity of the Zermelo rating system is that there is a path from each team to each other team. This is easily secured by the structure below.

Round 1

In round one you can decide pairings randomly. Better results will be obtained, however, if the field is seeded such that strong teams do not face eachother in this round.

Round 2

At the start of round 2 we have a ranking list where the leading team has played the last team, the second team has played the penultimate team, etc. Let's assume a team number is equal to its ranking and assume we have 2N teams in total. We then make the pairings similar to tieing shoelaces:

1 vs 2N-1
2N vs 3
2 vs 2N-3
2N-2 vs 5
...
N-1 vs N+1 (n odd)
N vs N+2 (n even)

Now we have created the chain that satisfies the Zermelo proviso and other pairings are now set according to a Swiss scheme:

Round 3 - end

Create the ranking according to the Zermelo strength of the teams and then pair each unpaired team with the highest ranking team that does not have an opponent yet (Swiss).