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I'm referring to the checkbox in the first screenshot, which says something very similar to "Automatically adjust league totals for accuracy".
I'm no expert in this stuff, and I hope someone will correct me if I'm mistaken, but when it says "adjust for accuracy", my understanding is that it means "adjust for historical accuracy". You can either set up your league in 1930 and have it remain constant forever, or you can set up your league in 1930 and have it evolve the same way real baseball did. But once you get past 2015, the game has no statistical totals it can use to be "accurate". So the setting makes no difference once you pass 2015.
The game doesn't produce random fluctuations in the league totals, no matter what you do with that checkbox. You will of course see some changes in your league stats output based on the balance of talent in your league (a few strong drafts for pitching will make your overall pitching stats better). Then there's league evolution, and I've never understood properly how that works (I actually suspect it doesn't work, at least in OOTP16). That might work, if it's enabled, by changing league totals, not sure.
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