Perfect Game Percentage

By: Steven Silverman

After having the good fortune to attend Josh Beckett’s no-hitter against the Phillies on May 25, 2014, I started doing some reading about no-hitters out of curiosity. Eventually, I came across this article by Bill James on the likelihood of pitchers throwing a no-hitter. The natural extension was to update the standings for perfect games.

I utilized a similar method to James’s, except I calculated the “out percentage” as

(3*IP) / ((3*IP)+H+BB+HBP))

factoring in other outcomes that the pitcher is responsible for. Since I don’t include errors, defensive interference, or reaching on a dropped third strike, the end probability will be a small percentage higher than the actual probability. Think of it instead as how “deserving” the pitcher was of a perfect game. Taking the out percentage and raising it to the 27th gives us the chance of a perfect game in any particular start, and then multiply by career starts to get a final expectation.

Without further ado, here are the top 32 pitchers, sorted by expected perfect games thrown:

Pitcher Starts Expectation Actual
Walter Johnson 666 0.1492 0
Christy Mathewson 551 0.1449 0
Cy Young 815 0.1261 1
Ed Walsh 315 0.1183 0
Addie Joss 260 0.1150 1
Don Sutton 756 0.1124 0
Tom Seaver 647 0.1105 0
Pete Alexander 599 0.1037 0
Greg Maddux 740 0.1015 0
Tim Keefe 594 0.0992 0
Tommy Bond 408 0.0927 0
Juan Marichal 457 0.0915 0
Ferguson Jenkins 594 0.0869 0
Pedro Martinez 409 0.0865 0
Jim McCormick 485 0.0838 0
Monte Ward 261 0.0822 1
Mordecai Brown 332 0.0793 0
Robin Roberts 609 0.0780 0
Pud Galvin 689 0.0779 0
Gaylord Perry 690 0.0778 0
Roger Clemens 707 0.0777 0
Eddie Plank 529 0.0764 0
Catfish Hunter 476 0.0754 1
Warren Spahn 665 0.0742 0
Old Hoss Radbourn 503 0.0735 0
Babe Adams 355 0.0733 0
Will White 401 0.0715 0
Curt Schilling 436 0.0668 0
Bert Blyleven 685 0.0644 0
Jim Palmer 521 0.0630 0
Sandy Koufax 314 0.0623 1
Randy Johnson 603 0.0613 1

Note that of the top 32, only 6 actually did throw perfect games, with several others coming very close (most notably Pedro Martinez, who threw 9 perfect innings in a 0-0 game before giving up a hit in the 10th). The total expected perfect games is just under 3, with the discrepancy mostly arising from the tiny sample size: a perfect game is such a “lightning-in-the-bottle” incident that it’s challenging to get an accurate prediction. Overall, though, the rankings work pretty well- the bias toward 19th-century pitchers notwithstanding.

Below are the expectations for the 23 pitchers that have thrown perfect games, with the more shocking ones like Charlie Robertson and Philip Humber low on the list:

Pitcher Starts Expectation Expectation/100
Cy Young 815 0.1261 0.0155
Addie Joss 260 0.1150 0.0442
Monte Ward 261 0.0822 0.0315
Catfish Hunter 476 0.0754 0.0158
Sandy Koufax 314 0.0623 0.0198
Randy Johnson 603 0.0613 0.0102
Jim Bunning 519 0.0513 0.0099
Roy Halladay 390 0.0422 0.0108
Dennis Martinez 562 0.0346 0.0062
David Wells 489 0.0312 0.0064
Matt Cain 265 0.0302 0.0114
David Cone 419 0.0264 0.0063
Mark Buehrle 429 0.0255 0.0059
Félix Hernández 269 0.0245 0.0091
Tom Browning 300 0.0194 0.0065
Mike Witt 299 0.0136 0.0046
Kenny Rogers 474 0.0119 0.0025
Lee Richmond 179 0.0118 0.0066
Len Barker 194 0.0072 0.0037
Don Larsen 171 0.0050 0.0029
Dallas Braden 79 0.0035 0.0045
Charlie Robertson 142 0.0020 0.0014
Philip Humber 51 0.0012 0.0023

I created the “Expectation/100” column to show how likely a pitcher was to pitch a perfect game over 100 starts. This serves as a normalization of sorts, and it’s clear that Joss and Ward had by far the best per-game chance of a “perfecto.” In fact, Joss comes out on top of all pitchers with at least 50 starts. Joss’s abbreviated career (nine years, cut tragically short by tubercular meningitis in 1911) knocked him down the unadjusted list.

There’s nothing else to this analysis, really—it’s just a nice stat to think about.

Here’s to hoping you see a perfect game your next time at the ballpark.

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