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Fun with probability

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I mentioned earlier today that no saves were recorded yesterday. It hasn't happened since 1978, which would suggest it's pretty rare. Mathematically speaking, just how rare is it?

In 2005, there were 1254 saves in 2431 MLB games, so there was not a save in 48.4% of games. The likelihood, then, that a random sample of 15 games (a full MLB schedule) would have no saves is .484 raised to the 15th power. That's 0.00001874, or 1 in 53,373. In other words, there should be a save-less day in Major League Baseball about every 50,000th time there's a full schedule.

If we assume that there are about 150 days per MLB season in which there is a full schedule of 15 games, that suggests a save-less day should only happen once every 355 years. Now that's rare!

Back in 1978, the last time there wasn't a save for an entire day, many things were different. A "full schedule" consisted of only 13 games, because there were still only 26 Major League teams. (However, the save-less 1978 day included a doubleheader, so there were 14 games.) Also, saves were considerably less common. Rather than occuring about once every two games, saves occurred in less than 40% of games, making it more likely that a day would go by without a single save.

These two factors--fewer games in a full schedule, and fewer saves--made such an event far more likely. The likelihood of having no saves in a day's worth of 1978 games was 0.001898, or 1 in 527, almost 100 times more likely than the same occurrence in 2006. Instead of once every 350 years, you could expect it to happen more than twice per decade.

Saves steadily increased throughout the 1980s, but the size of the Major Leagues didn't. It's a bit of a surprise that, for all that time MLB consisted of 26 teams, there wasn't another save-less day. But it's far more of a shocker that, given the state of the game today, it happened at all.

Want to be around for the next full day of baseball without a save? You might first want to look into cryogenic preservation, because you may well have to wait another few centuries.