8 teams, 84 games - Part 5

We saw the grid and statistics for the initial layout in the previous part.  For a first step in making revisions it would be better to see exactly what we want to revise.  Parameters can be defined for each schedule that set the thresholds we want for the statistics, and the grid can show where something is outside the desired bounds.

8 teams, 84 games - Part 4

The Working Grid

Before I actually get into the working product described below I must mention the significant behind the scenes pieces that I am skipping over here.  Maybe someday I can make all this available, but so far my ambition has already far exceeded my followthrough.  So I know better than to say too much.  Perhaps this can provide momentum in that direction.

I use Perl scripts I have developed to turn the series layout as described in earlier parts into the HTML and Javascript that make up the tool with the data contained in it.  I may call it a webpage, which is true in the sense that I work with it in a web browser, but misleading in the sense that it is still just local and not out on the internet.  Again, I hope someday I can get beyond the current point.  The jump from doing a lot of the work in a spreadsheet to having this tool did happen, so maybe more can too.

8 teams, 84 games - Part 3

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

Next steps...

We have the structure all laid out, so we could turn it into the schedule that OOTP uses.  But first it can still gain refinement, character, and personalization.  That is just fancy talk for saying it can be further edited to make sure teams have reasonable homestands and roadtrips, spread around the offdays, and make sure other design parameters are met.  This layout may be great for team # 1 but others may be quirky like with lots of 1-series homestands and roadtrips (e.g., team # 2 goes H-A-H-A-H the first 5 half-weeks).  And I prefer not having everybody always playing on all the same days.  It would be nice to have a good tool for making edits to various details to try to make the schedule as good as possible collectively.

8 teams, 84 games - Part 2

Lay out the series

I use a spreadsheet for setting out the series.  It provides a nice structure for gridding things and simple math functions can be used to take care of some of the work like duplicating series and adding +1 to team numbers to create subsequent matchups.

I defined a series with a triplet of numbers.  From left to right the numbers in the triplet are:

1. number of games in series
2. away team
3. home team.

The number of games I underline to make it stand out visually when working in the spreadsheet.  Here I will show the info with a fixed-width font rather than copying spreadsheet views.

So this represents a 3-game series of team 1 playing at team 2:

 3 1 2

That is one series, and we need to do all the series.

8 teams, 84 games - Part 1

Define parameters

We are going to build a ILN_BGN_SL1_D1_T4_D2_T4_C_ schedule!  That is the OOTP formatting for defining league structure and means...

One subleague, with 2 divisions, each with 4 teams

Games

84 games
Play each of 3 other teams in division 20 times (10H/10A)
Play each of 4 teams in other division 6 times (3H/3A)

That seems a likely choice for distribution of games for such a league configuration, but mostly it turns out nicely for illustrative purposes.

Revisiting Square 1

This is a something of a reboot just to try to get back on the wagon here.  I want to avoid going so long without doing something here.  My plans can come to overwhelm my actions.  So this is another sort of background post to set the scene.

There are four broad types of work in building a schedule.

Circle Method - Part 8

For interdivision matchups with odd number of divisions each with same even number of teams

Consider a league (or subleague) setup of 18 teams in 3 divisions of 6 teams. For the 6-team divisions the circle method could be used to set up all the divisional matchups with all teams able to play divisional games at the same time. The next step would be to lay out the interdivision matchups. But an odd number of divisions means you could not have whole divisions matched up against each other - if every team in division 1 is playing against a division 2 opponent, those divisions are covered, but division 3 is left out.

A solution is to break up the divisions into pieces and do the initial layout steps on those pieces rather than either by whole division or by individual team.

Personal Preferences

How do I "want" to make a schedule?  Well, I do want to satisfy whatever requests/requirements are specified.  But I have more experience and comfort when that means something in a form like MLB has.  My tools have been developed to work more easily for such a form.  That is due in part to various factors that all can relate - I am familiar with and thus like the form, I believe other people tend the same way overall, and OOTP is probably geared toward that form.

What are the characteristics of that form to which I pay particular attention when building a schedule?

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.

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.

Circle Method - Part 5

Balancing home/away

So far there has been no consideration of the home/away nature of the matchups as the goal has been to simply get all the matchups defined. But you could consider each "A v B" as "A @ B", such that "A" is away and "B" is home. Where does that put us toward even home/away splits for teams?

Circle Method - Part 4

Odd number of teams

For an odd number of teams there are a couple possible approaches. One team must always be left out - perhaps it will be playing interdivision or interleague games when it is the one left out. Ignoring for now what we doing with that left-out team, we can build the matchups the same sort of way.

Circle Method - Part 3

Examples showing 8 teams and 10 teams

Not doing anything spectacular here, just using the circle method to make matchups for a couple more scenarios.

Circle Method - Part 2

Using the algorithm instead of the brain

The circle method is a systematic way to determine the matchups without having to think much. There are other things you can find online that can provide more info. The way I will show things is not the only way to employ the method. The goal is to find something that works and is easy for you.

Circle Method - Part 1

Building round robin matchups

For a balanced schedule you want to make sure every team plays every other team some number of times. For almost any schedule through there may be at least "local" balance - e.g., you may want a team to play all its divisional opponents an equal (or nearly so) number of times.

How do you determine the matchups? First, we will charge straight in without any real plan and see where that takes us as we try to build a round robin that gets every team playing every other team.

What do you mean, "blogs aren't really a thing anymore"?

So I was gone for a while. A long while. I am back at it again, at least for now.

I am trying to pick up where I left off, which is pretty much the beginning of the road here. I am trying to make my tools better to get results I like better and more quickly.

I still have a tendency toward trying to make schedules that have characteristics like MLB. Recently MLB has lengthened the season to add a few more offdays across the season. That means now instead of 51 there are 52 halfweeks for the 162 games. With an additional halfweek for the All-Star break, the schedule generally spans from end of March or beginning of April to end of September to beginning of October. E.g., ignoring the overseas games Sea/Oak games earlier in March, 2019 spans from Mar28 through Sep29.

MLB schedules are great at limiting very short and very long homestands and roadtrips. At the top of my list in getting back into this is to try to find ways to minimize the single-series and 4-series homestands and roadtrips and maximize the 2- and 3-series homestands and roadtrips (i.e., usually 6-10 games). I do not expect to ever be getting great results in that regard like MLB since I want to churn out schedules quickly, but I want to find ways to get better.