IStock Photo 641314 © Rob Friedman

Bobo Holloman was not much of a major league pitcher. He pitched for only one season, going 3-7 with a 5.23 ERA for the 1953 St. Louis Browns. That Holloman received even that much playing time was a fluke; already 30 at that point, he had been purchased by the Browns for $10,000, promptly going 0-1 with a 9.00 ERA as a reliever.

Still, due to the insistence of owner Bill Veeck, Holloman eventually got a chance to start May 6 on a rainy night in St. Louis. Facing the Philadelphia Athletics, Holloman gave up line drive after line drive, but the balls kept miraculously going at fielders.

With a number of rain delays providing some much-needed rest, Holloman managed to survive all 9 innings without giving up a hit, and become just the third pitcher to throw a no-hitter in his first major league start. Veeck knew it should have been his last, but kept him in the rotation: “I don’t think it’s really wise to send a man back to the minor leagues right after he’s become immortal,” he said.

Holloman eventually pitched himself off the roster, and he never got a call back. His no-hitter would go down as the least likely ever pitched of the 253 that were thrown from 1876 to 2008 (Counting only those no-hitters where one pitcher recorded all the outs). On the flip side of Holloman is Hall of Famer Nolan Ryan, who threw 7 no-hitters in his career. Ryan was known for striking a ton of hitters out (and walking quite a few as well), making him a prime candidate for throwing multiple no-hitters.

Still, much like Holloman, Ryan managed to outperform all expectations. The number of no-hitters a pitcher is expected to throw in a season or a career can be predicted very easily. All we have to do is find the approximate probability that he will not allow a hit in a given at-bat, which can be estimated as 1 – Hits/(Hits + Innings x 3). Raise that to the 27th power, because that’s the number of outs it takes to get through a 9-inning game, and multiply that by his games started (Note that this is based on a formula originally posited by Bill James).

So Ryan, for example, allowed 3,923 hits in 5,386 career innings. That means that in any given at-bat, Ryan had something like a 19.5 percent (3,923/(3,923 + 5,386 x 3) probability of allowing a hit (that’s equivalent to a .195 batting average against —pretty freaking good). Ryan’s probability of going 27 consecutive at-bats without allowing a hit (and therefore, presumably, getting a no-hitter) was then (1 – .195)^27 = .003 percent, which, multiplied by his 773 career games started, equals roughly 2.2 expected no-hitters.

If we do that calculation for every one of Ryan’s seasons instead of his career so as to better capture his peak, we find a slightly higher number of expected no-hitters: 2.6. That’s still nowhere near his actual 7. Ryan is not the only famous over-performer: Sandy Koufax had 4 no-hitters versus an expectation of 0.8, and Cy Young had 3 versus an expectation of 0.6.

On the other hand, we would have expected Roger Clemens to pitch one no-hitter where he has none, and the same goes for his replacement in Boston, Pedro Martinez, though it should be noted that Pedro once had a no-hitter through nine innings before losing it in the tenth.

Holloman, of course, had one no-hitter despite an expected .003. His odds of pitching a no-hitter were still better than the odds you’ll see one if you attend just one major league game a year; only 1 in 775—or about three games per year—end with a 0 in the “H” column on the scoreboard.