The outcome of a one run game is mostly random.
Uh.... not really.
Teams which have bad bullpens have trouble holding onto saves when they are on the road and will lose games by one run when the run scores without anyone out, or only one out or even with two outs, or they will come back in the top of the 9th, but still fall one run short of tying it.
In other words, they will score fewer runs, on fewer outs. The better team, the winning team, would often end up scoring more than the one run needed to win it if they played out all 27 of their outs.
In other words, the game is set up so bad teams lose by "just one run" far more often than they would if games were played out fully.
If games were in fact played out fully (and with the winning team continuing to try to score more runs until the last out), bad teams (like the Cubs) would lose no more games, but they would lose fewer of them by just one run. If every out available in a game were played out, THEN there might be some randomness to one-run losses.
But that is not the case.