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LGO covered much of the ground, but I'll try to add a little bit.
Indeed the season-to-season juggling adds a nice bit of variety with the same base schedule. Unless it was something like Sox-Yanks or LA-SF with the division title on the line every time to end the season, it would get old playing the exact same teams at the exact same times every year. But in the game where you are playing divisional, interdivision, or interleague games you will always be playing those types of games, just likely against different teams.
I'm not sure what you are getting at about the variety in championship winners. I've been playing (mostly simming quickly) a 12-team league much of this year, and you are right that you will tend to have over a period of just a few years a limited number of teams regularly being the leading contenders. But if a league is brand-new off a fantasy draft the teams are usually very evenly matched for a couple years, and the more teams in a league the more possible winners. The schedule should not play a big role in that as within divisions the different teams will most likely play the same other teams at least almost the same number of times. Maybe you are thinking of something I am not grasping, but I never really think of the schedule (as long as it is decent) really affecting competitive balance.
16 teams (2 league, 2 divisions, 4 teams) playing 162 games is very straightforward if that is what you want. Unless something otherwise is requested, I try to follow current MLB standards in my schedule construction, at least the rules of no more than 20 days in a row with games for any team, no homestands or roadtrips over 14 games, and the All-Star Break 1-2 weeks after the mid-point of the season. If that is good, then what might you like in a schedule?
How about interleague play? If so, how much? There's lots of possibilities. Maybe have each team play one series home and one away against each team in the other league. That's maybe quite a bit, so perhaps less suchas one series against each of the 8 teams of the other league or the two series but against just one of the divisions of the other league. Or maybe make it very rare with only one series against the 4 teams of one division of the other league.
A balanced schedule playing each non-divisional opponent as many times as each divisional opponent or unbalanced playing the divisional opponents more? And if unbalanced, how unbalanced - a lot more games against the other teams in the division or just a little more?
Interleague or not and balanced or unbalanced can set the tone to your league if you have a preference. Personally, in leagues I track closely and control a team I like to have interleague where each team plays home and away at least a short series against everybody, if the league is small enough to make that reasonable. I also like what I consider moderately unbalanced with games per division opponent outnumbering games per non-divisional league opponent by a ratio of something like 2:1 or 3:2. On the other hand I think many other people prefer not having interleague, and I think LGO tends to prefer in general a little stronger unbalanced schedules.
Sometimes people make requests and already have the number of games against each opponent worked out, and sometimes they give at most rough guidelines and I find something usually along the lines of my own preferences where the numbers work out.
But besides just how many games, maybe you want them set out a certain way, like having the last few weeks mostly if not all division games so the races might be more exciting assuming you get some head-to-head matchups between contending teams. I think most everybody likes that, and I try to do it in general.
People usually do not get too exact in their requests and there are limits to how exact specifications can be with me still being able to meet them. Still, if you would like something it would not hurt to ask, especially with a 16-team setup where things are much easier to layout than when there are odd factors to the number of teams. Basically whatever you can think you might like as far as the schedule goes, feel free to make a request (as specific or vague as you want) and we'll see if we can't get you hooked up.
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