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Expected No-Hitters

by Bill James

Rob, when we were at Fenway you posed the question, Who was the most likely pitcher to have thrown a no-hitter not to have thrown one. On the plane home I thought of what I assumed had to be the correct answer, which is Roger Clemens. Clemens has never thrown a no-hitter at any level: majors, minors, college, high school, amateur, little league.

But actually, Clemens is not the answer to the question, amazingly enough. I established a method to answer this question, which is this:

1. Figure the “out percentage” for each pitcher as

    (3 * IP) / ((3 * IP) + hits)

(Essentially, 1 minus the batting average allowed, although not quite.)

2. Raise that to the 26th power. (We’re assuming 26 outs for a no-hitter. I have used a similar method before, and knew that the 26th power works better than the 27th, since most no-hitters, somewhat surprisingly, do involve a caught stealing, a double play, or a runner running into an out on the bases.

The result is the probability of a pitcher throwing a no-hitter in any one start.

3. Multiply that by his career starts.

Not a perfect method, obviously, but I can demonstrate that this method is quite accurate in terms of predicting the number of no-hitters within a given number of starts. For example, all pitchers in major league history with 9.00 to 9.99 hits per nine innings made 136,388 starts before 2003, not counting those by pitchers with less than 10 career starts. There should be, by this math, 58 no-hitters in those 136,388 starts. There are actually 57.

Anyway, by this method, there are only four pitchers in major league history who SHOULD have pitched at least 1.000 (one full) no-hitters in their major league career, those being Nolan Ryan, Walter Johnson, Tom Seaver and Randy Johnson, all of whom actually did throw no-hitters. This is the list of actual and expected no-hitters, spots 1 through 40:

                                     No-Hitters
Pitcher          Hits/9  Starts   Expected  Actual
Nolan Ryan        6.56     773     2.715      7
Walter Johnson    7.47     666     1.166      1
Tom Seaver        7.47     647     1.127      1
Randy Johnson     7.02     444     1.092      2
Sandy Koufax      6.79     314      .920      4
Don Sutton        7.99     756      .891      0
Pedro Martinez    6.72     288      .889      0
Roger Clemens     7.73     606      .867      0
Sam McDowell      7.04     346      .840      0
Sid Fernandez     6.85     300      .839      0
Jim Palmer        7.83     521      .804      1
Steve Carlton     8.06     709      .797      0
Andy Messersmith  6.94     295      .771      0
Bob Gibson        7.60     482      .765      1
Tim Keefe         7.91     594      .743      0
Bob Feller        7.69     484      .716      3
Ed Walsh          7.12     315      .715      1    
Catfish Hunter    7.72     476      .689      1
Ch. Mathewson     7.94     551      .676      2
Eddie Plank       7.92     529      .657      0
Gaylord Perry     8.31     690      .646      1
Warren Spahn      8.29     665      .631      2
Phil Niekro       8.40     716      .626      1
Ed Reulbach       7.24     300      .625      0
Charlie Hough     7.77     440      .612      0
J.R. Richard      6.88     221      .606      0
Bert Blyleven     8.39     685      .604      1
Luis Tiant        7.94     484      .595      0
Vida Blue         7.91     473      .593      1
Rube Waddell      7.48     340      .591      0
David Cone        7.77     419      .582      1
Cy Young          8.68     815      .581      2
Whitey Ford       7.77     438      .575      0
Greg Maddux       8.22     571      .569      0
Ferguson Jenkins  8.28     594      .566      0
Jim Bunning       8.22     519      .518      2
Addie Joss        7.30     260      .516      2
John Smoltz       7.74     361      .514      0
Early Wynn        8.46     612      .512      0
Bob Turley        7.19     237      .512      0

Thirty expected no-hitters, 37 actual, with Nolan Ryan creating most of the discrepancy.

Anyway, the pitcher who most should have thrown a no-hitter, but didn’t, is not Clemens but Don Sutton. Sutton’s hits/innings ratio is only a little higher than Clemens (7.99 to 7.73), but he had 150 more starts than Clemens entering this season. Which is frigging amazing, since Clemens has been pitching since the Civil War. Clemens may have passed him on this list (expected no-hitters) this season . . . don’t know, but it would be close. (He did pass him. Clemens after 2004 is at 0.936).

The ten least likely pitchers who actually did throw a no-hitter:

                                     No-Hitters
Pitcher          Hits/9  Starts   Expected  Actual
Bumpus Jones      9.07      7       .0038     1
Bobo Holloman     9.55     10       .0039     1
Bud Smith         9.92     24       .007      1
Walter Thornton  10.51     48       .009      1
Iron Davis        9.19     22       .011      1
Bill Hawke       10.63     66       .012      1
Jose Jimenez      9.78     38       .012      1
Mike Warren       9.12      7       .014      1
Bill McCahan      9.19     40       .020      1
George Culver     9.05     57       .031      1

The most improbable pitcher to have thrown a no-hitter, given his hits allowed rate, was Bill Hawke, who allowed 10.63 hits per nine innings, which creates a 1-in-5,594 chance of throwing a no-hitter in any one start. Hawke’s hits/innings rate was actually very near the league average in his time, when batting averages were very high. He was a contemporary of the great Bumpus Jones.

The highest hits/innings ratio for a pitcher with two no-hitters is 9.62, by Pud Galvin; that translates to exactly one no-hitter expected for every 2,766 starts. The two pitchers who threw more than three no-hitters (Ryan and Koufax) are also, by a weird coincidence, the two pitchers in history who have the lowest ratios of hits per nine innings.

I wondered, “Wasn’t there somebody like Jim Colborn who threw two no-hitters?” to which you suggested Steve Busby. The guy I was thinking of was actually Bob Forsch, who threw two no-hitters, but actually Busby is the most improbable pitcher to have thrown two no-hitters, 2 against an expectation of .121. Forsch is actually sixth on that list, ahead of my cousin Jesse Barnes and your buddy Bill Stoneman:

                                   No-Hitters
Pitcher        Hits/9  Starts   Expected  Actual
Steve Busby     8.51    150       .121      2
Bill Stoneman   8.59    170       .129      2
Jesse Barnes    9.40    314       .133      2
Carl Erskine    8.57    216       .167      2
Pud Galvin      9.62    682       .247      2
Bob Forsch      8.94    422       .248      2

********************

Bill, thanks for sending this along (and letting me publish it). I should mention that Pedro Martinez really doesn’t deserve that 0 in his Actual No-Hitters column, because he did once throw nine no-hit (perfect, actually) innings, but officially it’s not a no-hitter because he gave up a hit in the 10th. For the purposes of this study, though, that was a no-hitter.