Phil Birnbaum explains…I think.
Imagine a reasonably large number of baseball games—a team-season, or decade, or whatever. Pick 10 games at random, and then pick one of the teams randomly in each of those 10 games. Add 1 run to those ten teams’ score.
You’ve now added 10 runs. How does that change things?
Well, for many of those games, it won’t change things at all. If the game didn’t go into extra innings, and was won by 2 runs or more, than adding one extra run can’t change the outcome.
In the 1990s, 68.4 percent of games were decided by more than one run. That means that 6.84 of those extra 10 runs are “wasted”, and don’t do anything.
Now, consider the 9-inning games decided by exactly one run. That was 22.5 percent of all games. Half of the time, the extra run will go to the winning team—so that run doesn’t do anything.
That leaves 11.3 percent of games where the run goes to the team who lost by a run. That 11.3 percent of the time, the game will now go into extra innings. The team that gets the run will win half of those. That means that 5.6 percent of those extra 10 runs turn a loss into a win. That’s 0.56 wins.
That leaves only games that went into extra innings. In the 1990s, that was 9 percent of all games.
If we add a run to one of those teams, that team now wins the game outright. It would have won half of them anyway, so half those runs don’t do anything. But, the other half, the run turns a loss into a win. That’s 4.5 percent of all games, or 0.45 wins.
Add 0.56 wins to 0.45 wins, and you get ... 1.01 wins.
That’s how every 10 runs leads to one win.