# The Unlikelihood of Mike Fiers’ Second No-Hitter, Quantified

When baseball fans quibble with sabermetrics, one of the arguments I hear is, “If we can already predict everything that will happen, then why isn’t baseball just played on a computer?” It’s a funny stance to me for two reasons. First, statistics can’t predict everything; they can only tell you the odds of an event occurring. And, second, the randomness of baseball — and, really, sports in general — is something that even the most devout statisticians can marvel at.

Mike Fiers threw the second no-hitter of his career last week. Rachael McDaniel did a brilliant job of explaining how unlikely it was for Fiers, the individual, to have the fortunate of joining the group of 35 pitchers to throw two no-hitters in the big leagues. I just want to borrow a few lines from McDaniel’s prose, but you should really read the whole thing. It’s great:

That’s the wonderful thing about pitching achievements, the no-hitter and the perfect game. With their length and intensity, with the level of collaboration and the sprinkling of luck that is necessary to sustain that nine-inning walk along the knife’s edge, there is so much room for serendipity. In the annals of the no-hitter, you can just as easily find the greatest of all time proving why they’re the greatest as you can a roster of unlikely heroes — rookies, journeymen, washed-up veterans — who, for those few hours, reach out and find perfection.

I want to take a second crack of explaining how unlikely Fiers’ second no-hitter was, but with a different angle: math.

To figure out just how unlikely Fiers’ second no-hitter was, we first need to determine the odds that he’d throw a no-hitter in the first place. Luckily for us, Bill James developed a formula to determine expected no-hitters for a single pitcher over the course of a career. His formula uses innings pitched, how effective a pitcher is at getting outs, and career starts to arrive at an expected no-hitter number. Here are the current active leaders:

Name IP Hits Starts Projected No Hitters Actual No Hitters
Clayton Kershaw 2,126 1594 321 0.972 1
Justin Verlander 2,816.1 2431 428 0.597 2
Max Scherzer 2,151 1781 337 0.596 2
Cole Hamels 2,592.2 2309 401 0.465 1
CC Sabathia 3,495.1 3312 543 0.432 0
Chris Sale 1,431 1159 215 0.430 0
Felix Hernandez 2,688.2 2441 410 0.424 1
Zack Greinke 2,660.2 2481 423 0.372 0
Stephen Strasburg 1,280.2 1064 214 0.372 0
Jake Arrieta 1,370.1 1156 230 0.366 2
Stats through games played on May 10.

(With apologies to Hamels, for the purposes of this study, combined no-hitters have been omitted.)

First, all four of the pitchers who have the greatest number of expected no-hitters have thrown at least one, with two of them (Verlander, Scherzer) having thrown two. This makes CC Sabathia the active pitcher with the most expected no-hitters who hasn’t thrown one. I understand why Sabathia is on this list — he’s been good, and he’s been good for a long time. His 543 career starts is a whopping 115 greater than the next closest pitcher on this list, Verlander. Also interesting to see on this list are Chris Sale and Stephen Strasburg. Even though they both have fewer than half of the starts Sabathia has, they have been very successful at limiting hits when they pitch.

It is worth pointing out that even among the leaders, no one was expected to even throw one no-hitter. How can this formula be right, then? Well, the formula’s accuracy significantly increases with larger samples. In fact, among all active starters, there are a total of 19.808 expected no-hitters and 21 actual no-hitters. Among this group of 10, there are a total of 5.026 expected no-hitters and nine actual no-hitters. The odds of throwing a no-hitter may exponentially increase the more dominant a pitcher is, but, still, you can see the balance between dominance and longevity I described above among these leaders.

Let’s get back to Fiers. He ranks 58th among active pitchers in expected no-hitters, and third-to-last among pitchers who have thrown at least one. And, yet, he’s thrown two of them! That got me to thinking: does this make Mike Fiers the unlikeliest pitcher in baseball history to ever throw two?

Expected No-Hitters For Pitchers With 2+
Name IP Hits Starts Projected No Hitters Actual No Hitters
Nolan Ryan 5386.0 3923 773 2.715 7
Randy Johnson 4135.1 3346 603 1.213 2
Sandy Koufax 2324.1 1754 314 0.919 4
Bob Feller 3827.0 3271 484 0.715 3
Christy Mathewson 4780.2 4218 551 0.676 2
Warren Spahn 5243.2 4830 665 0.630 2
Max Scherzer 2177.0 1797 338 0.609 2
Justin Verlander 2816.1 2431 428 0.597 2
Cy Young 7354.2 7092 815 0.581 3
Jim Bunning 3760.1 3433 519 0.519 2
Addie Joss 2327.0 1888 260 0.515 2
Jim Maloney 1849.0 1518 262 0.486 2
Johnny Vander Meer 2104.2 1799 285 0.421 2
Allie Reynolds 2492.1 2193 309 0.385 2
Don Wilson 1748.1 1479 245 0.384 2
Jake Arrieta 1383.2 1166 230 0.368 2
Hideo Nomo 1976.1 1768 318 0.359 2
Virgil Trucks 2682.1 2416 328 0.356 2
Frank Smith 2273.0 1975 255 0.342 2
Tim Lincecum 1682.0 1506 270 0.304 2
Larry Corcoran 2392.1 2147 268 0.297 3
Roy Halladay 2749.1 2646 390 0.281 2
Ken Holtzman 2867.1 2787 410 0.278 2
Dutch Leonard 2192.0 2022 272 0.255 2
Pud Galvin 6003.1 6405 689 0.253 2
Bob Forsch 2794.2 2777 422 0.248 2
Adonis Terry 3514.1 3525 406 0.225 2
Mark Buehrle 3283.1 3472 493 0.192 2
Carl Erskine 1718.2 1637 216 0.166 2
Ted Breitenstein 2964.1 3091 341 0.146 2
Bill Stoneman 1236.1 1182 170 0.128 2
Steve Busby 1060.2 1003 150 0.121 2
Mike Fiers 944.0 917 162 0.110 2
Homer Bailey 1271.1 1325 220 0.095 2
Al Atkinson 915.0 943 106 0.049 2
Stats through games played on May 11.

Based on James’ formula, Fiers is actually not the unlikeliest pitcher in baseball history to throw multiple no-hitters. That title belongs to Al Atkinson, a pitcher who played only three seasons in the American Association, in 1884 and from 1886 to 1887. On May 24, 1884, Atkinson pitched the first no-hitter of his career against the Pittsburgh Alleghenys; he notably allowed a hit-by-pitch to the first hitter before retiring the next 27 in a row.

Even if we only focus on baseball’s modern era (1900-present), Fiers is still not the unlikeliest pitcher to throw multiple no-hitters. Homer Bailey, who has been expected to throw just 0.095 no-hitters over the course of his career, “bests” Fiers by a difference of just 0.015. To me, this makes sense, as outside of a couple decent years with the Reds in 2012 and 2013, he’s been a generally underwhelming pitcher on the whole. Though Bailey has 58 more starts than Fiers, his numbers have been significantly worse.

So there you have it. Mike Fiers is certainly an unlikely pitcher to have thrown two or more no-hitters, but, at least by this one metric, he’s not the unlikeliest in baseball history. No computer or formula could have predicted what happened last week, and that’s just what makes baseball great.

Devan Fink is a Contributor at FanGraphs. You can follow him on Twitter @DevanFink.