Rigging weekend home/away splits

I have come to make it a high priority to balance the number of home and away weekend series for all the teams.  There is an attendance boost in the game for weekend games, so it is not optimal to have some teams with several more home weekends than away and others with several more away than home.

The current MLB pattern has 52 half-weeks.  With the season starting on a weekend plus the weekend after the All-Star Break, that makes the 52 split to 25 early week series and 27 weekend series.  To balance as best as possible, that 27 weekend series per team splits to half the teams being 14 home & 13 away and the other half being 13 home & 14 away.

How to get the numbers to work out that way?  Slightly randomly distributing the series then manually swapping matchups to balance out the home/away for the weekends can be tedious and not even work out correctly in the end if the starting point is happens to be bad.

So rather than doing a highly random layout of games, what I have taken to doing where possible is forcing that balance by laying out the series in a way that locks in that balance.

Consider a scenario of 2 subleagues, each with 2 divisions of 8 teams.  Every team plays each division opponent in 4 series (28 total), each other league opponent in 2 series (16 total), and all the teams in one interleague division in 1 series (8 total).  Each subset of 28 division, 16 league, and 8 interleague has an even split of home and away series.  This allows for what I show here because all teams can be playing the same type of game (division, league, or interleague) at the same time.

What can be done is make all the weekend series be division series.  That uses up 27 of the 28 division series, so the other one must fall in some early week.  A good candidate for that is the very last week of the season so the last three series of the season are division.  If a team has that one early week division series home, that means they got 13 home weekend series and 14 away.  If it was away the weekend split is 14 home and 13 away.  Another benefit to this is that within a division there is balance between the teams with extra home and away weekends, so different division teams all do not have the benefit or detriment of the extra home or away.

Here is how that looks as I would prep the layout.  The pair of columns on the left are the numbers for the halfweeks of the season with the left column being early week and the right column being the weekend.  The middle pair of columns show a layout of the series by type - green/D for division, yellow/L for league, red/X for interleague.  The right pair of columns are a possible layout of the opponents for team 1 fitting with the game type layout.

Layout of series with all weekend series being in division

With this, when trying to get to more reasonable homestands/roadtrips, any swaps of matchups between a pair teams (this series home and that series away switched to this series away and that series home) will be either both weekend or both not weekend.  So any teams number of weekend home/away series will not change.  The one exeception is that early week division matchup, in this case 1v7 - if that is swapped with another instance, then those teams will flip between which has 14 home weekend series and which has 13.

Conceptually that method is not my favorite.  No interleague weekend series?  Not even weekend league series?  That feels... wrong.  But it assures getting the end result with the weekend balance.

For layout in general I prefer the idea of chunks - e.g., maybe two straight league series, then three division, then 2 interleague.  And perhaps things work out that way even more sensibly - like team X plays those two interleague series in a row at that point in the schedule both on the road.  That feels better as a more realistic layout.  But just putting matchups wherever, then flipping home/away for team combinations to improve homestand/roadtrip lengths, and you can be heading toward some teams with 17 home weekend series, and some with 10.

There can be middle ground.  An option is to put all the series for 4 of the division opponents on weekends and all the series for 4 league opponents on weekends.  That is (4*4)+(4*2)=24 of the weekend series.  Fill that out by either 1 home & 2 away interleague series and 2 home & 1 away interleague series.

Here is an example like that.  To make the team matchups easier to notice, I made all the matchups with even-number teams for division and league games those on the weekends.  That is a better feeling mix, but there is still the sense of too much separation.

Layout of series with mix of game types on weekends

Much prettier if at least those 7 division opponents involve 2 series (1 home & 1 away) early week and 2 series (1 home & 1 away) on weekend.  In that case the series swapping for homestand/roadtrip adjustments must be limited to the pair on one side of the week.  Or, you could allow to flip individual opponents across the week (e.g., go to 3 home & 1 away) if balanced out (another going to 1 home & 3 away).  With that though we are quickly getting toward the more random initial layout, just working to hew toward having to maintain balance as opposed to working to get to balance.

Ultimately it is sort of solving a sort of math problem, or perhaps better described as an optimization problem.  I put more emphasis on certain collective statistics, like not having too-long homestands and roadtrips and balancing home/away weekends.  So I will be inclined toward ugly shortcuts like making all weekend series be division series.  That seems like something relatively noticeable, and the benefit of even home/away weekends seems like it would be harder to recognize.