In thinking more about the runner-on-second rule for extra innings, it's worth looking at how many games exactly that would impact. There were 208 extra-innings games last year, which represents 4.3% of all games played, or roughly one out of every 22. https://twitter.com/craigcalcaterra/status/1275498184119328769
Over the course of a season, that's an extra-innings game every other day or so. And most of those games didn't go that long: About half ended in the 10th inning. Only 113 went past the 10th; that's just 2.3% of the season, or one out of every 43.
And of those games that went past the 10th, only 16 reached the 15th inning or beyond—0.3% of the season, or once every 325 or so games, which is about twice a month. Ultra marathons are rare in baseball; most extra-innings games don't last long or take long to complete.
The great majority of extra-innings games also end pretty quickly in terms of time. The games that went 10 innings in 2019 lasted an average of 214 minutes, or 3:36—or a half hour longer than the nine-inning league average. That's not nothing, but it's not a huge gap.
The extra-innings runner won't materially affect most games and is unlikely to result in much of a time or innings savings. It makes sense to deploy in a short season, but it's the kind of tinkering that disrupts the feel and legitimacy of the game to accomplish relatively little
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