Circle Method - Part 7

Alternative layout methods

For the last (at least for now) entry about the circle method, we abandon the circle method. Particularly for team counts that are power of 2 (like 8 and 16), there are more symmetric things that can be done.

I think the pattern of the pairs of rows below the first row in this 8-team layout is pretty obvious, at least after it is laid out.

1 v 2   3 v 4   5 v 6   7 v 8
1 v 3   2 v 4   5 v 7   6 v 8
1 v 4   2 v 3   5 v 8   6 v 7
1 v 5   2 v 6   3 v 7   4 v 8
1 v 6   2 v 5   3 v 8   4 v 7
1 v 7   2 v 8   3 v 5   3 v 6
1 v 8   2 v 7   3 v 6   4 v 5

Every team is paired up, and the pairs are aligned against each other. The top row has each pair's team playing its pair partner, then subsequent rows are the pairs playing other pairs. If you consider pair 1 & 2 to be "A", 3 & 4 to be "B", 5 & 6 to be "C", and 7 & 8 to be "D" you have essentially the simple 4-team layout making the rows below the first.

A v B   C v D
A v C   B v D
A v D   B v C

Each of those matchups represent 4 actual matchups. E.g., "A v B" covers 1 v 3, 2 v 4, 1 v 4, and 2 v 3. Clustering the teams together like this into "pods" can make it easier to build the matchups modularly. We are not building 24 matchups individually, we are making 6 "super" matchups (I again push the term "pods") that each get 4 actual matchups we readily know.

That may be less aesthetically appealing. If 1 is playing 5 or 6, then 2 is playing the other - that is very... I might say mechanical or mathematically, which is not my preference. But beauty is in the eye of the beholder - maybe something more clearly patterned like that is just what you want. As mentioned in an earlier part, having a pod of teams always together allows for mixing up the matchups among that pod at different times if that would be useful.

And it is not as though I can say I am doing things with variety instead of methodically in patterns. In most of what I do the same teams will be matched up against the same opponents at the same times because that is just easier to layout. Anyway, such a layout can offer more flexibility for making adjustments down the line in the build process, especially with multiple divisions all built from the same sort of template.

Regarding interdivision and interleague matchups, the most obvious alternative is to simply rotate through them in a consistent order. E.g., if you had 4-team divisions, you may have teams 1 through 4 in one division and 13 through 16 in another. You start out by aligning them against their corresponding opponents then move the teams from one division one slot at a time, like:

1 v13   2 v14   3 v15   4 v16
1 v14   2 v15   3 v16   4 v13
1 v15   2 v16   3 v13   4 v14
1 v16   2 v13   3 v14   4 v15

When there is assymmetry between the divisions (e.g., 8 teams in one division and 6 teams in another), this can be the easiest way to lay out the matchups. But with not all of the teams able to match up against, other effort is required to deal with the left out team(s), just as in the case of using the circle method for an odd number of teams in one division. Having to deal with such assymetries is typically the hardest the thing to have to do because of the lack of an easy systematic way to handle.