For much of the past century, since the deadball era, the magic number in MLB is 5. Score exactly 5 runs/game, you'll win more than lose. Score 4, you'll lose more than you win.
There's been a couple short exceptions. The late 90's, early 2000s saw that number reach 6 in several seasons.
Occasionally, particularly through the 60s and 70s, the number was 4.
I know this doesn't address the issue at hand--variability--but I've always found it interesting.
If you could somehow put up 810 runs, exactly 5 per game, you likely have one of the best regular season teams in baseball.