No-Hitter Probabilities: What Are the Odds?
This article was written by Bob Kapla
This article was published in 2004 Baseball Research Journal
A no-hitter turns a pitcher into an instant celebrity in the baseball world. Regardless of what he did before or what he does after, he’ll always be a member of an elite group, a fraternal brotherhood that links Cy Young and Nolan Ryan with the likes of Jose Jimenez, Mike Warren, and Bobo Holloman.
What are the odds of a pitcher throwing a no-hitter? How can we measure a pitcher’s potential for making the leap to celebrity? Who are the top pitchers who have never thrown a no-hitter? Of the pitchers who have thrown no-hitters, who was the least likely? These questions can be answered with some basic probability calculations along with the help of a desktop computer and a thorough statistics database.
When considering the probability of a pitcher throwing a no-hitter we are, in mathematical terms, trying to calculate the probability of a pitcher achieving 27 consecutive outs before allowing a hit. Walks, errors, hit batsmen, and other intervening events don’t concern us as long as there are 27 outs recorded before a single hit is allowed.
Accordingly, there are only two statistics that we need for each pitcher we wish to analyze: outs achieved (innings pitched multiplied by three) and hits allowed. The ratio of outs achieved (OA) to the sum of outs achieved and hits allowed (H) yields the probability of a pitcher getting an out instead of giving up a hit for all the batters he faced that did one or the other, or P(O). Mathematically, we would say: P(O) = OA/(OA+H).
Statistically speaking, the probability of a sequence of independent events is equal to the product of their individual probabilities. So, the probability of achieving 27 outs without a hit is P(O) x P(O) x P(O) . . . x P(O) (27 times). Mathematically, P(NH) = P(O) ^ 27.
I applied this formula to the career statistics for every pitcher in major league history with at least one career start through the 2004 season to ﬁnd the most likely pitcher to throw a no- hitter. I expected to see a lot of familiar names at the top of the list, but instead I found some statistical anomalies. There are 11 pitchers with at least one major league start who either never allowed a single hit, never got anyone out, or both. If a pitcher never allowed a hit, then the formula above predicts that they have a 100% chance of throwing a no-hitter every time they start a game. If they never achieved an out, then the formula will predict that they have 0% chance of ever throwing one. If, as three of them did, they didn’t give up any hits or achieved any outs, then the formula fails when you try to divide by zero. Fortunately, the pitching careers of these eleven players are not statistically signiﬁcant—they each had exactly one career start—and we can discount them while we examine the rest of the pitchers. The 11 pitchers are:
Table 1. One start and 0 innings pitched and/or 0 hits allowed
Name |
IP |
H |
Dave Pierson (1876 Reds) |
0 |
2 |
Jay Parker (1899 Pirates) |
0 |
0 |
Frank DuPee (Chicago WS – 1901) |
0 |
0 |
Charlie Fritz (1907 A’s) |
2q |
0 |
Pat McGehee (1912 Tigers) |
0 |
1 |
Jim Scoggins (Chicago WS – 1913) |
0 |
0 |
Dan “Babe” Sherman (1914 Whales) |
3 |
0 |
Clay Roe (Washington – 1923) |
1q |
0 |
Joe Brown (Chicago WS – 1927) |
0 |
2 |
Marty Walker (1928 Phillies) |
0 |
2 |
Cesar Tovar (1968 Twins) |
1 |
0 |
After discounting the 11 pitchers above, the one that moves to the top of the list is Randy Hennis of the 1990 Houston Astros. In three career games (one start) he allowed one hit in 9q innings. With 29 outs achieved and only one hit allowed his P(O)=0.9667 and his P(NH)=0.4004, or about 1 in 2.50. Since Hennis’s career of 9q IP is not a good statistical sample, I changed the criteria to only consider pitchers with at least 100 career starts. Table 2 details the 25 pitchers most likely (among the 1,202 pitchers through 2004) with at least 100 career starts.
You may be puzzled by the asterisk by Pedro Martinez’s name. For determining whether or not a pitcher has thrown a major league no-hitter I slightly altered the criteria from those recognized by Major League Baseball. I considered any pitcher who completed nine innings without allowing a hit including those that went on to give up hits in extra innings, such as Harvey Haddix, or were relieved sometime after nine innings.
Pedro Martinez threw nine perfect innings against San Diego on June 3, 1995, while pitching for the Montreal Expos, but gave up a leadoff double to Bip Roberts in the 10th inning. I also included Ernie Shore, who achieved 27 outs (though the first one was already on base) without allowing a hit in relief of Babe Ruth on June 23, 1917.
Table 2. 25 pitchers most likely w/at least 100 starts (through 2004 season)
(* has thrown a no-hitter)
Name |
IP |
G |
GS |
CG |
H |
O+H |
P(O) |
P(NH) |
“1 in” |
Herb Score |
858.1 |
150 |
127 |
47 |
609 |
3184 |
0.808731 |
0.003241 |
309 |
Nolan Ryan* |
5386.0 |
807 |
773 |
222 |
3923 |
20081 |
0.804641 |
0.002827 |
354 |
Sandy Koufax* |
2324.1 |
397 |
314 |
137 |
1754 |
8727 |
0.799015 |
0.002339 |
428 |
Pedro Martinez* |
2296.0 |
388 |
321 |
42 |
1746 |
8634 |
0.797776 |
0.002243 |
446 |
Sid Fernandez |
1866.2 |
307 |
300 |
25 |
1421 |
7021 |
0.797607 |
0.002230 |
448 |
J.R. Richard |
1606.0 |
238 |
221 |
76 |
1227 |
6045 |
0.797022 |
0.002186 |
457 |
Andy Messersmith |
2230.1 |
344 |
295 |
98 |
1719 |
8410 |
0.795600 |
0.002083 |
480 |
Kerry Wood |
1043.0 |
164 |
164 |
11 |
804 |
3933 |
0.795576 |
0.002082 |
480 |
Randy Johnson* |
3368.0 |
489 |
479 |
92 |
2612 |
12716 |
0.794589 |
0.002013 |
497 |
Sam McDowell |
2492.1 |
425 |
346 |
103 |
1948 |
9425 |
0.793316 |
0.001928 |
519 |
Ed Walsh* |
2964.1 |
430 |
315 |
250 |
2346 |
11239 |
0.791263 |
0.001797 |
556 |
Joe Wood* |
1436.1 |
225 |
158 |
121 |
1138 |
5447 |
0.791078 |
0.001786 |
560 |
Babe Ruth |
1221.1 |
163 |
148 |
107 |
974 |
4638 |
0.789996 |
0.001721 |
581 |
Bob Turley |
1712.2 |
310 |
237 |
78 |
1366 |
6504 |
0.789975 |
0.001720 |
581 |
Orval Overall |
1535.1 |
218 |
182 |
133 |
1232 |
5838 |
0.788969 |
0.001662 |
602 |
Jeff Tesreau* |
1679.0 |
247 |
206 |
123 |
1350 |
6387 |
0.788633 |
0.001643 |
609 |
Ed Reulbach |
2632.1 |
399 |
300 |
201 |
2117 |
10014 |
0.788596 |
0.001641 |
609 |
Dave Boswell |
1065.1 |
205 |
151 |
37 |
858 |
4054 |
0.788357 |
0.001628 |
614 |
Mario Soto |
1730.1 |
297 |
224 |
72 |
1395 |
6586 |
0.788187 |
0.001618 |
618 |
Jimmy Dygert |
986.0 |
175 |
104 |
62 |
798 |
3756 |
0.787540 |
0.001583 |
632 |
Addie Joss* |
2327.0 |
286 |
260 |
234 |
1888 |
8869 |
0.787124 |
0.001560 |
641 |
Jack Pfiester |
1067.1 |
149 |
128 |
75 |
869 |
4071 |
0.786539 |
0.001529 |
654 |
Cy Morgan |
1445.1 |
210 |
172 |
107 |
1180 |
5516 |
0.786077 |
0.001505 |
664 |
Jose DeLeon |
1897.1 |
415 |
264 |
21 |
1556 |
7248 |
0.785320 |
0.001466 |
682 |
Jim Maloney* |
1849.0 |
302 |
262 |
74 |
1518 |
7065 |
0.785138 |
0.001457 |
686 |
Table 3. 25 pitchers most likely w/at least 100 starts who have never thrown a no-hitter
Name |
IP |
G |
GS |
CG |
H |
O+H |
P(O) |
P(NH) |
“1 in” |
Herb Score |
858.1 |
150 |
127 |
47 |
609 |
3184 |
0.808731 |
0.003241 |
309 |
Sid Fernandez |
1866.2 |
307 |
300 |
25 |
1421 |
7021 |
0.797607 |
0.002230 |
448 |
J.R. Richard |
1606.0 |
238 |
221 |
76 |
1227 |
6045 |
0.797022 |
0.002186 |
457 |
Andy Messersmith |
2230.1 |
344 |
295 |
98 |
1719 |
8410 |
0.795600 |
0.002083 |
480 |
Kerry Wood |
1043.0 |
164 |
164 |
11 |
804 |
3933 |
0.795576 |
0.002082 |
480 |
Sam McDowell |
2492.1 |
425 |
346 |
103 |
1948 |
9425 |
0.793316 |
0.001928 |
519 |
Babe Ruth |
1221.1 |
163 |
148 |
107 |
974 |
4638 |
0.789996 |
0.001721 |
581 |
Bob Turley |
1712.2 |
310 |
237 |
78 |
1366 |
6504 |
0.789975 |
0.001720 |
581 |
Orval Overall |
1535.1 |
218 |
182 |
133 |
1232 |
5838 |
0.788969 |
0.001662 |
602 |
Ed Reulbach |
2632.1 |
399 |
300 |
201 |
2117 |
10014 |
0.788596 |
0.001641 |
609 |
Dave Boswell |
1065.1 |
205 |
151 |
37 |
858 |
4054 |
0.788357 |
0.001628 |
614 |
Mario Soto |
1730.1 |
297 |
224 |
72 |
1395 |
6586 |
0.788187 |
0.001618 |
618 |
Jimmy Dygert |
986.0 |
175 |
104 |
62 |
798 |
3756 |
0.787540 |
0.001583 |
632 |
Jack Pfiester |
1067.1 |
149 |
128 |
75 |
869 |
4071 |
0.786539 |
0.001529 |
654 |
Cy Morgan |
1445.1 |
210 |
172 |
107 |
1180 |
5516 |
0.786077 |
0.001505 |
664 |
Jose DeLeon |
1897.1 |
415 |
264 |
21 |
1556 |
7248 |
0.785320 |
0.001466 |
682 |
Pete Richert |
1165.2 |
429 |
122 |
22 |
959 |
4456 |
0.784785 |
0.001440 |
695 |
Rube Waddell |
2961.1 |
407 |
340 |
261 |
2460 |
11344 |
0.783145 |
0.001361 |
735 |
Jake Weimer |
1472.2 |
191 |
180 |
143 |
1227 |
5645 |
0.782640 |
0.001337 |
748 |
Tommy Byrne |
1362.0 |
281 |
170 |
65 |
1138 |
5224 |
0.782159 |
0.001315 |
760 |
Fred Beebe |
1294.1 |
202 |
153 |
93 |
1090 |
4973 |
0.780816 |
0.001256 |
796 |
Doc Scanlan |
1252.0 |
181 |
149 |
102 |
1061 |
4817 |
0.779738 |
0.001210 |
827 |
Barry Zito |
981.0 |
153 |
153 |
9 |
832 |
3775 |
0.779603 |
0.001204 |
831 |
Gary Gentry |
902.2 |
157 |
138 |
25 |
770 |
3478 |
0.778608 |
0.001163 |
860 |
Chuck Estrada |
764.1 |
146 |
105 |
24 |
652 |
2945 |
0.778608 |
0.001163 |
860 |
Herb Score’s impressive career statistics put him at the top of the list ahead of such notable no-hit artists as Nolan Ryan and Sandy Koufax, though he never actually threw a no-hitter. Table 3 details the 25 most likely pitchers with at least 100 career starts who have never thrown a no-hitter.
The P(NH) in the above tables is the calculated probability that a pitcher would throw a no-hitter in any single start based on his career stats. There is another way to analyze the data using each pitcher’s P(NH) and his number of career starts. With these two numbers it is possible to calculate the probability that a pitcher would throw at least one no-hitter in his career number of starts.
The math is similar to that we used to find P(NH). The prob- ability of a pitcher throwing at least one no-hitter in “x” starts is equal to 1 minus the probability that he would go “x” starts without any no-hitters at all. The probability of a pitcher not throwing a no-hitter in a single start is: 1 – P(NH), or P’(NH). So, the probability of a pitcher not throwing any no-hitters in “x” consecutive games is P’(NH) x P’(NH) x . . . x P’(NH) (“x” times). If we use a pitcher’s number of career starts for “x” we get a product equal to the probability that the pitcher would throw exactly zero no-hitters in his career. Subtracting that probability from 1 yields the probability that the pitcher would throw at least one no-hitter in his career. In math terms, if GS is a pitcher’s number of career starts and P’(NH) = 1-P(NH) is the calculated probability that he would not throw a no-hitter in a start, then the probability that he would throw at least one no- hitter is his career is: P(at least one career NH) = 1 – (P’(NH) ^ GS).
Table 4. Pitchers most likely to have at least one no-hitter
(* has thrown a no-hitter)
Name |
GS |
P(NH) |
Probability |
Nolan Ryan* |
773 |
0.002827 |
88.79% |
Randy Johnson* |
479 |
0.002013 |
61.91% |
Walter Johnson* |
666 |
0.001361 |
59.63% |
Tom Seaver* |
647 |
0.001365 |
58.67% |
Sandy Koufax* |
314 |
0.002339 |
52.06% |
Roger Clemens |
639 |
0.001139 |
51.73% |
Pedro Martinez* |
321 |
0.002243 |
51.36% |
Don Sutton |
756 |
0.000910 |
49.75% |
Sid Fernandez |
300 |
0.002230 |
48.82% |
Sam McDowell |
346 |
0.001928 |
48.71% |
Jim Palmer* |
521 |
0.001202 |
46.57% |
Andy Messersmith |
295 |
0.002083 |
45.95% |
Steve Carlton |
709 |
0.000865 |
45.87% |
Bob Gibson* |
482 |
0.001238 |
44.95% |
Tim Keefe |
594 |
0.000967 |
43.72% |
Ed Walsh* |
315 |
0.001797 |
43.26% |
Bob Feller* |
484 |
0.001149 |
42.69% |
Catfish Hunter* |
476 |
0.001127 |
41.53% |
Christy Mathewson* |
551 |
0.000948 |
40.71% |
Eddie Plank |
529 |
0.000961 |
39.86% |
Gaylord Perry* |
690 |
0.000716 |
38.99% |
Ed Reulbach |
300 |
0.001641 |
38.90% |
J.R. Richard |
221 |
0.002186 |
38.35% |
Warren Spahn* |
665 |
0.000725 |
38.26% |
Phil Niekro* |
716 |
0.000666 |
37.96% |
Not surprisingly, Nolan Ryan is at the top of this list because of his relatively high probability of throwing a no-hitter in a single start and a large number of starts. Based on this analysis it would have been incredibly unlikely that he could go through his career without throwing a no-hitter at all.
In fact, Ryan and ﬁve of the other six pitchers with a greater than 50% expectation of a career no-hitter (Randy Johnson, Walter Johnson, Tom Seaver, Pedro Martinez, and Sandy Koufax) have all actually thrown no-hitters. Of the top 25 listed above, 15 (60%) have thrown major league no-hitters. Though he has the highest probability among pitchers with at least 100 career starts of throwing a no-hitter in an individual start, Herb Score doesn’t appear in the this top-25 list because of his comparatively low number of career starts (127).
Through the 2004 season, Roger Clemens tops the list of those with the greatest career probability of a no-hitter who have never done it:
Table 5. Pitchers most likely to throw at least one no-hitter
Name |
GS |
P(NH) |
Probability |
Roger Clemens |
639 |
0.001139 |
51.73% |
Don Sutton |
756 |
0.000910 |
49.75% |
Sid Fernandez |
300 |
0.002230 |
48.82% |
Sam McDowell |
346 |
0.001928 |
48.71% |
Andy Messersmith |
295 |
0.002083 |
45.95% |
Steve Carlton |
709 |
0.000865 |
45.87% |
Tim Keefe |
594 |
0.000967 |
43.72% |
Eddie Plank |
529 |
0.000961 |
39.86% |
Ed Reulbach |
300 |
0.001641 |
38.90% |
J.R. Richard |
221 |
0.002186 |
38.35% |
Charlie Hough |
440 |
0.001080 |
37.83% |
Rube Waddell |
340 |
0.001361 |
37.06% |
Luis Tiant |
484 |
0.000950 |
36.87% |
Whitey Ford |
438 |
0.001015 |
35.91% |
Greg Maddux |
604 |
0.000735 |
35.86% |
Fergie Jenkins |
594 |
0.000729 |
35.15% |
Herb Score |
127 |
0.003241 |
33.79% |
Bob Turley |
237 |
0.001720 |
33.50% |
John Smoltz |
361 |
0.001093 |
32.61% |
Don Drysdale |
465 |
0.000847 |
32.56% |
Early Wynn |
612 |
0.000636 |
32.24% |
Jose DeLeon |
264 |
0.001466 |
32.12% |
Pete Alexander |
599 |
0.000646 |
32.08% |
Mordecai Brown |
332 |
0.001158 |
31.94% |
Mario Soto |
224 |
0.001618 |
30.42% |
Of the pitchers on this list, only Roger Clemens, Greg Maddux, and John Smoltz are active and still have an opportunity to throw a major league no-hitter.
Among the pitchers who have thrown major league no-hitters, who overcame the greatest odds to do so? Table 6 lists the 25 most unlikely pitchers since 1900 to have thrown no- hitters based on the probability of throwing at least one no- hitter in their career number of starts:
Table 6. Pitchers to have thrown a no-hitter based on career probability of at least one
Name |
GS |
Prob. |
Year |
Team |
LG |
Bobo Holloman |
10 |
0.29% |
1953 |
STL |
AL |
Bud Smith |
24 |
0.52% |
2001 |
STL |
NL |
George Davis |
22 |
0.81% |
1914 |
BOS |
NL |
Jose Jimenez |
38 |
0.84% |
1999 |
STL |
NL |
Mike Warren |
27 |
1.05% |
1983 |
OAK |
– AL |
Bill McCahan |
40 |
1.45% |
1947 |
PHI |
AL |
Charlie Robertson |
142 |
2.30% |
1922 |
CHI |
AL |
George Culver |
57 |
2.31% |
1968 |
CIN |
NL |
Ed Lafitte |
75 |
2.51% |
1914 |
BKN |
FL |
Paul Dean |
87 |
2.64% |
1934 |
STL |
NL |
Ernie Koob |
55 |
2.70% |
1917 |
STL |
AL |
Juan Nieves |
81 |
2.70% |
1987 |
MIL |
AL |
Bob Keegan |
87 |
2.85% |
1957 |
CHI |
AL |
Mal Eason |
113 |
2.86% |
1906 |
BKN |
– NL |
Clyde Shoun |
85 |
2.91% |
1944 |
CIN |
NL |
Bobby Burke |
88 |
3.47% |
1931 |
WAS |
– AL |
Ed Head |
53 |
3.47% |
1946 |
BKN |
– NL |
Cliff Chambers |
113 |
3.84% |
1951 |
PIT |
NL |
Nixey Callahan |
177 |
4.01% |
1902 |
CHI |
AL |
Big Jeff Pfeffer |
69 |
4.05% |
1907 |
BOS |
NL |
Don Black |
113 |
4.45% |
1947 |
CLE |
AL |
Don Nottebart |
89 |
4.46% |
1963 |
HOU |
– NL |
Dick Fowler |
170 |
5.05% |
1945 |
PHI |
AL |
Derek Lowe |
120 |
5.17% |
2002 |
BOS |
AL |
Alex Main |
44 |
5.17% |
1915 |
KC |
FL |
Bobo Holloman overcame incredibly long odds to throw his no-hitter considering he started only 10 games in his one- year career with the St. Louis Browns. Derek Lowe and Jose Jimenez are still active and could increase their career odds by accumulating more career starts before they are done, though Jimenez is now a reliever and has started only seven of the 296 games he has pitched in since his no-hitter season of 1999.
Who should you watch today if you want to see a no- hitter? Among the 182 pitchers active in 2004 with at least 50 career starts, the 25 listed below have the highest probability of throwing a no-hitter in an individual start. So, if you want to maximize your odds of seeing a no-hitter, buy a ticket to see Pedro Martinez pitch against Kerry Wood. Some of these pitchers have taken their skills from the rotation to the bullpen (Mike Remlinger, Arthur Rhodes, John Smoltz, and Tom Gordon), but still have the minimum 50 career starts to appear on the list. If they get pressed into starting duty it may be worth seeing—history could be made.
Table 7. 25 active pitchers most likely to throw a no-hitter in a single start (min. 50 career starts)
Name |
IP |
G |
GS |
CG |
H |
O+H |
P(O) |
P(NH) |
“1 in” |
Pedro Martinez |
2296.0 |
388 |
321 |
42 |
1746 |
8634 |
0.797776 |
0.002243 |
446 |
Kerry Wood |
1043.0 |
164 |
164 |
11 |
804 |
3933 |
0.795576 |
0.002082 |
480 |
Randy Johnson |
3368.0 |
489 |
479 |
92 |
2612 |
12716 |
0.794589 |
0.002013 |
497 |
A.J. Burnett |
644.2 |
102 |
99 |
10 |
535 |
2469 |
0.783313 |
0.001369 |
731 |
Johan Santana |
624.1 |
151 |
75 |
1 |
519 |
2392 |
0.783027 |
0.001355 |
738 |
Oliver Perez |
412.2 |
70 |
69 |
2 |
345 |
1583 |
0.782059 |
0.001311 |
763 |
Barry Zito |
981.0 |
153 |
153 |
9 |
832 |
3775 |
0.779603 |
0.001204 |
831 |
Roger Clemens |
4493.0 |
640 |
639 |
117 |
3846 |
17325 |
0.778009 |
0.001139 |
878 |
Brandon Webb |
388.2 |
64 |
63 |
2 |
334 |
1500 |
0.777333 |
0.001113 |
899 |
John Smoltz |
2699.2 |
602 |
361 |
47 |
2327 |
10426 |
0.776808 |
0.001093 |
915 |
Carlos Zambrano |
539.2 |
101 |
80 |
4 |
467 |
2086 |
0.776127 |
0.001067 |
937 |
Mike Remlinger |
817.0 |
560 |
59 |
4 |
711 |
3162 |
0.775142 |
0.001031 |
970 |
Hideo Nomo |
1871.1 |
301 |
299 |
16 |
1631 |
7245 |
0.774879 |
0.001022 |
979 |
Josh Beckett |
430.1 |
77 |
74 |
1 |
376 |
1667 |
0.774445 |
0.001006 |
994 |
Mark Prior |
446.2 |
70 |
70 |
4 |
393 |
1733 |
0.773226 |
0.000964 |
1037 |
Arthur Rhodes |
922.0 |
551 |
61 |
5 |
816 |
3582 |
0.772194 |
0.000930 |
1075 |
Curt Schilling |
2812.2 |
482 |
370 |
82 |
2492 |
10930 |
0.772004 |
0.000924 |
1082 |
Tony Armas Jr. |
565.0 |
102 |
102 |
0 |
502 |
2197 |
0.771507 |
0.000908 |
1101 |
Al Leiter |
2248.2 |
386 |
356 |
16 |
1998 |
8744 |
0.771500 |
0.000908 |
1101 |
Chan Ho Park |
1454.2 |
269 |
224 |
9 |
1294 |
5658 |
0.771297 |
0.000902 |
1109 |
Kazuhisa Ishii |
473.0 |
86 |
86 |
2 |
421 |
1840 |
0.771196 |
0.000898 |
1113 |
Orlando Hernandez |
876.1 |
139 |
136 |
8 |
780 |
3409 |
0.771194 |
0.000898 |
1113 |
Victor Zambrano |
495.2 |
138 |
64 |
1 |
442 |
1929 |
0.770866 |
0.000888 |
1126 |
Tom Gordon |
1896.2 |
671 |
203 |
18 |
1703 |
7393 |
0.769647 |
0.000851 |
1175 |
Wade Miller |
768.0 |
127 |
123 |
5 |
699 |
3003 |
0.767233 |
0.000782 |
1279 |
Who is at the other end of the spectrum among pitchers active in 2004? These are the pitchers to watch if you’re an offensive-minded fan and really want to see some hits instead of a pitching duel.
Table 8. 25 active pitchers most unlikely to throw a no-hitter in a single start (min. 50 career starts)
Name |
IP |
G |
GS |
CG |
H |
O+H |
P(O) |
P(NH) |
“1 in” |
Nate Cornejo |
313.0 |
56 |
56 |
3 |
404 |
1343 |
0.699181 |
0.000064 |
15707 |
Josh Towers |
348.1 |
64 |
52 |
2 |
422 |
1467 |
0.712338 |
0.000105 |
9495 |
Chad Durbin |
331.1 |
75 |
56 |
3 |
396 |
1390 |
0.715108 |
0.000117 |
8550 |
Kevin Jarvis |
749.1 |
174 |
114 |
4 |
894 |
3142 |
0.715468 |
0.000119 |
8435 |
Brian Meadows |
816.1 |
218 |
122 |
3 |
972 |
3421 |
0.715873 |
0.000120 |
8307 |
Ryan Drese |
427.2 |
80 |
71 |
3 |
502 |
1785 |
0.718768 |
0.000134 |
7449 |
Mark Hendrickson |
378.1 |
78 |
64 |
3 |
443 |
1578 |
0.719265 |
0.000137 |
7311 |
Jimmy Anderson |
574.2 |
122 |
96 |
3 |
672 |
2396 |
0.719533 |
0.000138 |
7238 |
Glendon Rusch |
1163.1 |
225 |
183 |
10 |
1342 |
4832 |
0.722268 |
0.000153 |
6533 |
Jason Jennings |
607.0 |
104 |
104 |
2 |
696 |
2517 |
0.723480 |
0.000160 |
6244 |
La Troy Hawkins |
901.0 |
443 |
98 |
2 |
1028 |
3731 |
0.724471 |
0.000166 |
6018 |
John Halama |
816.2 |
205 |
114 |
2 |
931 |
3381 |
0.724638 |
0.000167 |
5980 |
Paul Quantrill |
1186.2 |
791 |
64 |
1 |
1349 |
4909 |
0.725199 |
0.000171 |
5857 |
Mike Maroth |
539.0 |
87 |
87 |
3 |
611 |
2228 |
0.725763 |
0.000174 |
5735 |
Esteban Loaiza |
1663.0 |
300 |
263 |
12 |
1883 |
6872 |
0.725990 |
0.000176 |
5687 |
Jimmy Haynes |
1200.2 |
227 |
203 |
2 |
1358 |
4960 |
0.726210 |
0.000177 |
5641 |
Darren Oliver |
1407.0 |
306 |
228 |
11 |
1591 |
5812 |
0.726256 |
0.000178 |
5631 |
Elmer Dessens |
914.0 |
249 |
128 |
2 |
1031 |
3773 |
0.726743 |
0.000181 |
5530 |
Tomokazu Ohka |
665.2 |
124 |
115 |
4 |
750 |
2747 |
0.726975 |
0.000182 |
5482 |
Brian Anderson |
1516.1 |
285 |
239 |
12 |
1704 |
6253 |
0.727491 |
0.000186 |
5378 |
Matt Kinney |
377.2 |
98 |
57 |
1 |
424 |
1557 |
0.727681 |
0.000187 |
5341 |
Tanyon Sturtze |
706.0 |
187 |
83 |
4 |
792 |
2910 |
0.727835 |
0.000188 |
5310 |
Ramiro Mendoza |
796.0 |
341 |
62 |
2 |
889 |
3277 |
0.728715 |
0.000195 |
5140 |
Jose Lima |
1381.2 |
312 |
199 |
8 |
1539 |
5684 |
0.729240 |
0.000198 |
5041 |
Todd Ritchie |
835.2 |
184 |
120 |
7 |
929 |
3436 |
0.729627 |
0.000201 |
4969 |
None of the pitchers on the list above have thrown a major league no-hitter. The most unlikely among pitchers active in 2004 to have actually accomplished the no-hit feat are Terry Mullholland (1 in 4,061) and Scott Erickson (1 in 4,440).
An extra look at Nolan Ryan: Whenever the topic is no-hitters, Nolan Ryan warrants special attention. Since it’s clear he should have thrown at least one no-hitter—nearly an 89% probability—I was wondering how unlikely it was that even Nolan Ryan would do it seven times. Calculating the probability that a pitcher would throw a speciﬁc number of no-hitters is only slightly more complex than the math we’ve already done.
Given the probability of throwing a no-hitter – P(NH) – and the probability of not throwing a no-hitter – P’(NH) – and the number of starts to be considered we can use what’s known as binomial probability to calculate the probability of throwing “n” no-hitters in “x” starts.
According to binomial probability, the probability of “n” successes (no-hitters) in “x” trials (starts) is equal to: [P(success)n * P(failure)(x-n) * C(x,n)], where C(x,n) is the number of combinations of “x” items taken “n” at a time. The C(x,n) factor is included to account for the number of different ways to arrange the “n” no-hitters among the “x” starts and is calculated as: (x!)/[(n!)(x-n!)], where x! = 1*2*3* . . . x. When all the pieces are put together it looks far more daunting than it actually is:
P(“n” no-hitters in “x” starts) = [P(NH)n * P’(NH)(x-n) * (x!)/[(n!)(x-n!)]
In Nolan Ryan’s case, P(NH) = 0.0028266, P’(NH) = 0.9971734, and x=773 career starts. The table below shows the probabilities of Ryan throwing 0-7 no-hitters in his career.
Table 9: Probability of Nolan Ryan throwing seven no-hitters
No-Hitters | Probability in 773 starts |
0 | 11.213% |
1 | 24.570% |
2 | 26.884% |
3 | 19.585% |
4 | 10.687% |
5 | 4.659% |
6 | 1.690% |
7 | 0.525% |
You can see that Ryan was far more likely to throw one or two no-hitters in his career than to not throw any at all. In fact, he was almost as likely to throw four (10.687%) as he was to throw none (11.213%)! But even for him, seven no-hitters was quite a feat.
As long as the odds are against them, no-hitters will continue to fascinate fans and immortalize the pitchers that throw them.
Acknowledgments
Special thanks to SABR member Pete Hepopski for helping refine my original formulas into the simpler, more complete versions used above following a regional meeting in Minneapolis. Sean Lahman’s database (available at www.baseball1.com) provided all the statistical data.