## Filling out the seating chart

That pretty grid from the previous part has all of the series nicely laid out in half-weeks. We just need to reorder those half-weeks into something that fits with design preferences. What should those be?### Choices

No consecutive series against the same opponent. You know, spread things around.Distribute the matchup somewhat evently - i.e., do not have like both 1 v 5 matchups in the first handful of series sets. You know, spread things around even more.

About 70% of the series are against division opponents, but the end of the schedule even more weighted toward division games like having only division series the last few weeks.

There are some other things I typically do that I will point out later.

### Organization

We have 26 half weeks to slot in the series sets. To put those together into a coherent whole, layout a simple grid for those half-weeks. On the left is the early-week series, and on the right is the weekend series.```
1 2
3 4
5 6
7 8
9 10
11 12
13 14
15 16
17 18
19 20
21 22
23 24
25 26
```

#### Set out the design preferences

Make the last 3 weeks be 6 intradivision series ("D"), which means 2 against each team. Otherwise spread out the interdivision series ("L"), but keep them in pairs - just another choice. In the original layout it is either all intradivision games or all interdivision, so we know what is what for all teams.```
1 2 D D
3 4 D D
5 6 L L
7 8 D D
9 10 D L
11 12 L D
13 14 D L
15 16 L D
17 18 D D
19 20 L L
21 22 D D
23 24 D D
25 26 D D
```

Next start deciding which rows go into which slots. I use team 1 as the identifier. So I use the opponent for team 1 from a row to identify the row. Right now, exactly which row does not matter. We just want to order the opponents for team 1 in a reasonable way.

With so few teams, the same opponent can crop up very quickly, but make sure to not slot in the same opponent consecutively. Also try to make sure the same pattern is not continuously used (i.e., do not have team 1 play 2 then 3 then 4 in that order every time). Again with so few teams combinations are limited and there will be some repeating, but try to have variety.

```
1 2 D D 4 3
3 4 D D 2 4
5 6 L L 7 8
7 8 D D 3 4
9 10 D L 2 6
11 12 L D 5 3
13 14 D L 2 8
15 16 L D 7 2
17 18 D D 4 3
19 20 L L 5 6
21 22 D D 4 2
23 24 D D 3 4
25 26 D D 3 2
```

#### Things to note...

Each division opponent appears 3 times early in a week and 3 times on the weekend. The division opponents are decently spread out to avoid cases like constantly playing a certain team after playing some other team, at least as well as can be done with only 3 division opponents.The interdivision pairings are familiar from the layout. 5 and 6 are paired together twice, and same for 7 and 8. The order of playing them is reversed though (i.e., first time plays 6 then 5 and second time plays 5 then 6). Unlike the division matchups against each opponent being spread between early-week and weekend, both matchups against each interdivision opponent are either early-week or weekend. The reason for that is so that if the pair of interdivision matchups against an opponent are swapped, it does not change the number of weekend series home vs away.

Looking backward, intending for these things went into putting the division slots in the places they went - one pair early-week then weekend, two pairs weekend then early-week, and the last pair early-week then weekend.

### Homestands and roadtrips, at least for team # 1

To further narrow down to which rows go exactly where, again through the eyes of team 1, decide on making each matchup either home or away. A lot to aim to do in that...- We want to target 2- and 3-series homestands and roadtrips.
- We want to to try to avoid play the same opponent either home or away in extremely short order. Again this is touch with so few teams. But a prime example is the pair of matchups against team 3 the last two weeks - make one of those home and the other away.
- Try to balance out the weekends home/away. There are 13 weekends, so the goal is half (either 6 or 7) of those being at home.

One possible distribution...

```
1 2 D D 4 3 H H
3 4 D D 2 4 A A
5 6 L L 7 8 H H
7 8 D D 3 4 A A
9 10 D L 2 6 H A
11 12 L D 5 3 H H
13 14 D L 2 8 A A
15 16 L D 7 2 A H
17 18 D D 4 3 H A
19 20 L L 5 6 A H
21 22 D D 4 2 H A
23 24 D D 3 4 A A
25 26 D D 3 2 H H
```

Pretty good... Split of 6 weekends home and 7 away. All 2- and 3-series homestands and roadtrips except for that 5th week (halfweeks 9 and 10) having a 1-series homestand and 1-series roadtrip.

Remember though that this is still just for team 1 (and team 5 in reverse since the second division was made a mirror of the first). The result may not be so pretty for other teams. And in shuffling things around to try to make them ideal, this layout for team 1 will surely be tweaked as part of the changes to address isues with other teams. But we are not quite ready to worry about that.

The last step for the ordering is deciding where to slot in the 4-game series against the division opponents, one home and one away for each. We can only put in one in a week so that there are no more than 7 games in a week. And we do not want to pile the weeks with them all together because that would lead to too many days in a row without an offday.

Sprinkling those 4 game series around...

```
1 2 D D 4 3 H H
3 4 D D 2 4 A4 A
5 6 L L 7 8 H H
7 8 D D 3 4 A A4
9 10 D L 2 6 H A
11 12 L D 5 3 H H4
13 14 D L 2 8 A A
15 16 L D 7 2 A H
17 18 D D 4 3 H A4
19 20 L L 5 6 A H
21 22 D D 4 2 H4 A
23 24 D D 3 4 A A
25 26 D D 3 2 H H4
```

Now we can put the order defined by this scheme on the matchups layout. Set each halfweek number (1-26) on the row that matches what was defined for the team 1.

`13 `__3__ 1 2 __3__ 3 4 __3__ 6 5 __3__ 8 7
22 __3__ 1 2 __3__ 3 4 __3__ 6 5 __3__ 8 7
3 __4__ 1 2 __4__ 3 4 __4__ 6 5 __4__ 8 7
9 __3__ 2 1 __3__ 4 3 __3__ 5 6 __3__ 7 8
16 __3__ 2 1 __3__ 4 3 __3__ 5 6 __3__ 7 8
26 __4__ 2 1 __4__ 4 3 __4__ 5 6 __4__ 7 8
7 __3__ 1 3 __3__ 4 2 __3__ 7 5 __3__ 6 8
23 __3__ 1 3 __3__ 4 2 __3__ 7 5 __3__ 6 8
18 __4__ 1 3 __4__ 4 2 __4__ 7 5 __4__ 6 8
2 __3__ 3 1 __3__ 2 4 __3__ 5 7 __3__ 8 6
25 __3__ 3 1 __3__ 2 4 __3__ 5 7 __3__ 8 6
12 __4__ 3 1 __4__ 2 4 __4__ 5 7 __4__ 8 6
4 __3__ 1 4 __3__ 2 3 __3__ 8 5 __3__ 7 6
24 __3__ 1 4 __3__ 2 3 __3__ 8 5 __3__ 7 6
8 __4__ 1 4 __4__ 2 3 __4__ 8 5 __4__ 7 6
1 __3__ 4 1 __3__ 3 2 __3__ 5 8 __3__ 6 7
17 __3__ 4 1 __3__ 3 2 __3__ 5 8 __3__ 6 7
21 __4__ 4 1 __4__ 3 2 __4__ 5 8 __4__ 6 7
19 __3__ 1 5 __3__ 2 6 __3__ 3 7 __3__ 4 8
11 __3__ 5 1 __3__ 6 2 __3__ 7 3 __3__ 8 4
10 __3__ 1 6 __3__ 2 5 __3__ 3 8 __3__ 4 7
20 __3__ 6 1 __3__ 5 2 __3__ 8 3 __3__ 7 4
15 __3__ 1 7 __3__ 2 8 __3__ 3 5 __3__ 4 6
5 __3__ 7 1 __3__ 8 2 __3__ 5 3 __3__ 6 4
14 __3__ 1 8 __3__ 2 7 __3__ 3 6 __3__ 4 5
6 __3__ 8 1 __3__ 7 2 __3__ 6 3 __3__ 5 4

Order the rows based on halfweek...

` 1 `__3__ 4 1 __3__ 3 2 __3__ 5 8 __3__ 6 7
2 __3__ 3 1 __3__ 2 4 __3__ 5 7 __3__ 8 6
3 __4__ 1 2 __4__ 3 4 __4__ 6 5 __4__ 8 7
4 __3__ 1 4 __3__ 2 3 __3__ 8 5 __3__ 7 6
5 __3__ 7 1 __3__ 8 2 __3__ 5 3 __3__ 6 4
6 __3__ 8 1 __3__ 7 2 __3__ 6 3 __3__ 5 4
7 __3__ 1 3 __3__ 4 2 __3__ 7 5 __3__ 6 8
8 __4__ 1 4 __4__ 2 3 __4__ 8 5 __4__ 7 6
9 __3__ 2 1 __3__ 4 3 __3__ 5 6 __3__ 7 8
10 __3__ 1 6 __3__ 2 5 __3__ 3 8 __3__ 4 7
11 __3__ 5 1 __3__ 6 2 __3__ 7 3 __3__ 8 4
12 __4__ 3 1 __4__ 2 4 __4__ 5 7 __4__ 8 6
13 __3__ 1 2 __3__ 3 4 __3__ 6 5 __3__ 8 7
14 __3__ 1 8 __3__ 2 7 __3__ 3 6 __3__ 4 5
15 __3__ 1 7 __3__ 2 8 __3__ 3 5 __3__ 4 6
16 __3__ 2 1 __3__ 4 3 __3__ 5 6 __3__ 7 8
17 __3__ 4 1 __3__ 3 2 __3__ 5 8 __3__ 6 7
18 __4__ 1 3 __4__ 4 2 __4__ 7 5 __4__ 6 8
19 __3__ 1 5 __3__ 2 6 __3__ 3 7 __3__ 4 8
20 __3__ 6 1 __3__ 5 2 __3__ 8 3 __3__ 7 4
21 __4__ 4 1 __4__ 3 2 __4__ 5 8 __4__ 6 7
22 __3__ 1 2 __3__ 3 4 __3__ 6 5 __3__ 8 7
23 __3__ 1 3 __3__ 4 2 __3__ 7 5 __3__ 6 8
24 __3__ 1 4 __3__ 2 3 __3__ 8 5 __3__ 7 6
25 __3__ 3 1 __3__ 2 4 __3__ 5 7 __3__ 8 6
26 __4__ 2 1 __4__ 4 3 __4__ 5 6 __4__ 7 8

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