Circle Method - Part 6

For interdivision and interleague matchups

So far we have been building only for a single division. But this matchup generating scheme can be used also to set up interdivision and interleague matchups where the opposing divisions/leagues have the same number of teams.

In this example we will work with two 10-team divisions. That makes it easy to recognize the corresponding teams in the two division - i.e., team 1 in the first division corresponds to team 11 in the other division, 2 corresponds to 12, 3 corresponds to 13, etc.

The first step is layout the intradivision matchups for one division, just like was done in previous parts. In fact, we can go ahead and show for both divisions. The second division will simply be the mirror of the first.

1 v10   2 v 9   3 v 8   4 v 7   5 v 6     20 v11  19 v12  18 v13  17 v14  16 v15
1 v 9  10 v 8   2 v 7   3 v 6   4 v 5     19 v11  18 v20  17 v12  16 v13  15 v14
1 v 8   9 v 7  10 v 6   2 v 5   3 v 4     18 v11  17 v19  16 v20  15 v12  14 v13
1 v 7   8 v 6   9 v 5  10 v 4   2 v 3     17 v11  16 v18  15 v19  14 v20  13 v12
1 v 6   7 v 5   8 v 4   9 v 3  10 v 2     16 v11  15 v17  14 v18  13 v19  12 v20
1 v 5   6 v 4   7 v 3   8 v 2   9 v10     15 v11  14 v16  13 v17  12 v18  20 v19
1 v 4   5 v 3   6 v 2   7 v10   8 v 9     14 v11  13 v15  12 v16  20 v17  19 v18
1 v 3   4 v 2   5 v10   6 v 9   7 v 8     13 v11  12 v14  20 v15  19 v16  18 v17
1 v 2   3 v10   4 v 9   5 v 8   6 v 7     12 v11  20 v13  19 v14  18 v15  17 v16

We probably already made those for the intradivision matchups if we were doing a schedule for this configuration. Here we will use them to illustrate from where the interdivision matchups. Also we will only do single matchups and not worry about evening out home/away.

The first interdivision matchups we make outside the circle method by simply pairing up the corresponding teams in the two divisions because those cases of playing against their mirror teams are not represented in the circle.

1 v11   2 v12   3 v13   4 v14   5 v15   6 v16   7 v17   8 v18   9 v19  10 v20

Now we begin adding matchups defined from the circle method. There are a couple different ways to view what we will do, but I think it is simpler to think from the perspective of using the first division's intradivision matchups. Basically you take each matchup there and create two matchups by making replacements using the corresponding teams from the other division. What does that mean?

We can start with the very upper left from the intradivision matchups above. That matchup is 1 v 10. We use that as a template to make two new versions, one each replacing one of the first division teams with the corresponding team from the other division. So for 1 v 10 we make 1 v 20 and 11 v 10. The next matchup is 2 v 9, which produces 2 v 19 and 12 v 9. Fast-forwarding through the rest of the generation we get...

1 v20  11 v10     2 v19  12 v 9     3 v18  13 v 8     4 v17  14 v 7     5 v16  15 v 6
1 v19  11 v 9    10 v18  20 v 8     2 v17  12 v 7     3 v16  13 v 6     4 v15  14 v 5
1 v18  11 v 8     9 v17  19 v 7    10 v16  20 v 6     2 v15  12 v 5     3 v14  13 v 4
1 v17  11 v 7     8 v16  18 v 6     9 v15  19 v 5    10 v14  20 v 4     2 v13  12 v 3
1 v16  11 v 6     7 v15  17 v 5     8 v14  18 v 4     9 v13  19 v 3    10 v12  20 v 2
1 v15  11 v 5     6 v14  16 v 4     7 v13  17 v 3     8 v12  18 v 2     9 v20  19 v10
1 v14  11 v 4     5 v13  15 v 3     6 v12  16 v 2     7 v20  17 v10     8 v19  18 v 9
1 v13  11 v 3     4 v12  14 v 2     5 v20  15 v10     6 v19  16 v 9     7 v18  17 v 8
1 v12  11 v 2     3 v20  13 v10     4 v19  14 v 9     5 v18  15 v 8     6 v17  16 v 7

Again, we have not considered home/away balance here. That must be handled if there are not an even number of matchups that allow for the same number of games home and away. In other words, it is easy in a case like two 3-game series (one home and one away) against each interdivision opponent, but odder cases take more work.

Conceptually this may not be the easiest way to set up intradivision matchups. A significant benefit of doing things this way though is that it allows for easy swapping of matchups if that becomes useful sometime down the line in the development. E.g., take the matchups in the 7 v 8 variety, which includes teams 7, 8, 17, and 18. When one pair of those teams is playing within that set, the other two are also playing each other. E.g., when you have 7 v 18, you also have 8 v 17, and when you have 7 v 8, you also have 17 v 18. So if for some reason you wanted to do so, you could switch a case of 7 v 18 & 8 v 17 with 7 v 8 & 17 v 18.

In the next part we will look at a couple alternatives to the circle method that work in at least certain situations.