I live in the San Francisco Bay Area, earthquake country. Earthquakes are literally unpredictable. You have no way of knowing in advance when or where they will happen. I have the feeling baseball no-hitters are the same way, so I thought I would investigate the games that pitchers threw before their no-hitter, to see if there is anything that can be teased out that might be of some predictive value. While I was at it, I decided to look at games pitched after a no-hitter as well, to see if pitching a no-no has any implications for the next start.
The tool I’ll use in my analysis is “game score,” a measure developed by Bill James that I’ve written about earlier. Here’s Bill’s definition:
Start with 50 points. Add 1 point for each out recorded, (or 3 points per inning). Add 2 points for each inning completed after the 4th. Add 1 point for each strikeout. Subtract 2 points for each hit allowed. Subtract 4 points for each earned run allowed. Subtract 2 points for each unearned run allowed. Subtract 1 point for each walk.
Bill’s thought when he came up with this was that the average game score would be about 50, but of course there’s no inherent reason that should be the case.
Only it turns out that’s more or less true. In June 2014 Ben Lindbergh of Baseball Prospectus calculated the average game score for each season from 1950 through 2014. And the average of the season averages (as opposed to the average of all the starts in that time frame, which he didn’t calculate) was 50.8. (One note: Lindbergh limited his analysis to starts of nine innings or shorter, since the game score formula is generous to longer outings. I believe he did this to be more fair to the contemporary pitcher, who rarely goes nine innings anyway and essentially never works longer. In the 16-year period from 1950 through 1965, at the early end of Lindbergh’s analysis, there were 1,015 pitcher starts that went more than nine innings, an average of more than 60 a year. In the 16-year period from 2000 through 2015 there have been exactly six…and only one of those has come in the last eight seasons.)
There is some notable variance in average game score from year to year. Lindbergh found that the average game score in 1968, when the average runs scored per game was the second lowest in history, was 56.2…whereas in 1999 and 2000, when teams averaged more than five runs a game, among the highest since 1900, the average game score was 47.4.
I used Baseball-Reference.com’s Play Index to calculate the average game score for all games (including starts of longer than nine innings) since 1914 through September 5, 2015…nearly 350,000 pitcher starts. (This process wasn’t nearly as tedious or time consuming as I feared.) And the average is 50.6, almost exactly what Lindbergh came up with, with a median of 51. (But I was surprised to find the mode — or the game score that has most frequently been recorded — is 55, followed by 52 and 54. The values from 50 to 59 are all pretty close in frequency. I’ll have a little more analysis at the end of this post.)
I’m giving you this context because I’m going to look at the game scores of pitchers in games before and after throwing their no-hitter, going back to 1914, the period for which Baseball-Reference.com has game scores in its database. I’m using the definition of “no-hitter” for this purpose as a complete game of nine innings or more, and I’m excluding the five no-hitters in the Federal League of 1914 and 1915, so American and National League games only. Jake Arrieta’s no-hitter on August 30, 2015 was the 206th such no-hitter during this time period, thrown by 176 different pitchers (here’s the complete list). Not all of them have “before” and “after” game scores, as 12 came in the pitcher’s first start of the season and nine came in his last start of the year.
Game scores of no-hitters range from 83 (Cliff Chambers in 1951 and Francisco Liriano in 2011) to 102 (Clayton Kershaw in 2014, the second-highest game score since 1914 for a nine-inning game; the highest was 105, Kerry Wood’s 1998 one-hitter in which he struck out 20 and walked no one). [ADDED 4/27/16: After this post was written, Max Scherzer had a 17-strikeout, no-walk no-hitter with a score of 104 on the next-to-last day of the 2015 season.] The average no-hitter game score is 91.5 and the median is 91. But what about the games before and after?
Let’s start by looking at the distribution of game scores. The chart below includes all games through September 5, 2015 (when Arrieta made the start following his no-hitter) along with the starts made immediately before a pitcher’s no-hitter and the starts immediately after. Note some of these are 10-point ranges and others near the median are 5-point ranges.
Game Score | All | Before |
After | |||
Below 0 | 258 | 0.1% | 0 | 0.0% | 0 | 0.0% |
0 to 9 | 1760 | 0.5% | 1 | 0.5% | 1 | 0.5% |
10 to 19 | 10417 | 3.0% | 5 | 2.6% | 4 | 2.0% |
20 to 29 | 34186 | 9.8% | 12 | 6.2% | 13 | 6.6% |
30 to 39 | 53181 | 15.3% | 29 | 14.9% | 21 | 10.7% |
40 to 44 | 29971 | 8.6% | 10 | 5.2% | 17 | 8.6% |
45 to 49 | 32268 | 9.3% | 18 | 9.3% | 13 | 6.6% |
50 to 54 | 34909 | 10.0% | 14 | 7.2% | 17 | 8.6% |
55 to 59 | 35020 | 10.1% | 18 | 9.3% | 24 | 12.2% |
60 to 69 | 61580 | 17.7% | 46 | 23.7% | 40 | 20.3% |
70 to 79 | 39071 | 11.2% | 28 | 14.4% | 31 | 15.7% |
80 to 89 | 13677 | 3.9% | 10 | 5.2% | 13 | 6.6% |
90 to 99 | 1419 | 0.4% | 2 | 1.0% | 3 | 1.5% |
100 or higher | 115 | 0.03% | 1 | 0.5% | 0 | 0.0% |
(Note: 18 pitchers actually worked in relief in the appearance preceding their no-hitter, the last of whom was Jonathan Sanchez in 2009. And 11 pitchers followed their no-hitter by coming out of the bullpen, the latest being Clay Buchholz in 2007. But the chart above includes information about the most recent starts before and after.)
Pitchers are just as likely to toss a real stinker (game score less than 10) before or after a no-hitter as at any other time…it’s extremely unlikely in any event, but no less so adjacent to a no-hitter. But you’ll note pitchers are less likely to have what I’ll call a “poor” performance (game score less than 40) or a “below-average” performance (game score from 40 to 49) both before and after a no-hitter and are much more likely to have a “good” performance (game score 60 or higher).
Game Score | All | Before | After |
39 or lower | 28.7% | 24.2% | 19.8% |
40 to 49 | 17.9% | 14.4% | 15.2% |
50 to 59 | 20.1% | 16.5% | 20.8% |
60 or higher | 33.3% | 44.8% | 44.2% |
The average game score for a start before a no-hitter is 54.4 and the average for a start after is 55.5 — both above average. What kind of a game does that translate to? It so happens it almost exactly corresponds to what Tom Seaver did on either side of his 1978 no-hitter:
Nothing special, but nothing to be ashamed of either. Of course, just how relatively good such performances are depends on the season context. In 1968 they would be below average and perhaps result in two losses. In 2000 they would be above average and likely result in two wins. (Seaver won the first of these games and lost the second…in most seasons these lines would probably yield a win and a loss, these game scores are close to the definition of a .500 pitcher.) Perhaps a more mathematically sophisticated analysis that I am capable of would compare each score to the norm for that season in determining whether, as a group, pitchers who throw no-hitters are indeed above average in their starts immediately preceding and following.
And maybe the most useful analysis would compare the performances not only to what is normal for the season but what is normal for that particular pitcher in that season. Because it could be one reason the average before-and-after game scores are above average is because pitchers who throw no-hitters are, as a group, above average. Now that may sound like it makes perfect sense — if you go a whole game without giving up a hit, you must be pretty good, right? Yet you don’t have to have a good career or be having a good season to throw a no-hitter. The list of no-hit pitchers includes George “Iron” Davis, who had a career record of 7-10; Virgil Trucks, a fine pitcher in other seasons who went 5-19 the year he pitched two no-hitters; Mike Warren, who had a career mark of 9-13 with a 5.06 ERA; Jose Jimenez, whose no-no came during a season in which he went 5-14 with a 5.85 ERA; Bud Smith, who won seven games in the big leagues; Philip Humber, who pitched a perfect game and finished his career with a 5.31 ERA; and, most dramatic of all, Bobo Holloman, who won only two other games in a major league career that lasted three months.
All that list does is show that a no-hitter really is unpredictable and can happen to almost anyone. But don’t make the mistake of jumping to the conclusion that no-hitters are truly random events. Because, when you look at the list of pitchers who have done it, it turns out to be a list largely made up of pretty good pitchers.
For instance, 35 of the 206 no-hitters were thrown by pitchers who are in the Hall of Fame. That’s 17%, whereas Hall of Fame pitchers have only 6.6% of the starts since 1914. Granted that 35 is boosted by the seven no-hitters for Nolan Ryan, the four for Sandy Koufax and the three for Bob Feller…but hey, they’re Hall of Famers for a reason.
Or how about pitchers who were on the roster for the All-Star Game in the season in which they pitched a no-hitter? That accounts for 59 of the 179 no-hitters pitched since the year of the first All-Star Game in 1933, or 33%. I haven’t calculated the exact figure for how many of the total pitcher starts have been by All-Stars, but I’ll guarantee you it isn’t one out of three or anything close to it. (By the way, I determined what pitchers were on All-Star rosters by using this list.)
Why don’t we combine the two: no-hitters thrown by Hall of Famers in a season in which they made the All-Star Game? That accounts for 18 no-hitters, or 10% of the post-1933 total (and it includes only four of Ryan’s and two of Feller’s).
So it would appear excellent pitchers are disproportionately likely to pitch a no-hitter.
Then there’s the other category, what I’ll call “regular guys,” who neither made the Hall of Fame nor were All-Stars in the year in question. That’s not to disparage their skills; some of them might have been All-Stars had there been an All-Star Game before 1933, others wound up having fine seasons even though they weren’t selected as All-Stars (for instance, Jake Arrieta didn’t make the All-Star Game in 2015 but is looking like he’ll finish in the top three in the Cy Young Award voting) [ADDED 4/27/16: actually, he won the award]. Maybe some of the active pitchers on the list will wind up in the Hall of Fame. And some of these “regular guys” wound up being Bobo Holloman.
Let’s look at the average game scores for each of these categories:
Before | After | |
Hall of Famer | 57.7 | 60.0 |
All-Star | 58.4 | 61.6 |
HoF + All-Star | 58.1 | 65.9 |
Regular guy | 52.0 | 53.1 |
Note that Hall of Famers and All-Stars typically have an above-average start both before and after their no-hitters, whereas “regular guys” are darn close to average both before and after their moment of fame. But maybe these numbers reflect what are typically average starts for pitchers in these categories. I suspect the “regular guy” numbers are a little bit higher than what the average game score for a non-Hall of Famer not having an All-Star season would be, and I suspect that’s because this group of “regular guys” is still a little bit better than the overall pool of “regular guys.” But I can’t prove that hypothesis.
I find it interesting that all these breakouts show the average start after a no-hitter being just a little bit better than the average start before. Does the no-hitter instill a smidgen of extra confidence in the pitcher going forward? Create trepidation for the next opponent? Or is it just Small Sample Size Theater?
Three pitchers actually had a higher game score in the start after their no-hitter than they did in the no-hitter itself!
- Hod Eller followed up his 1919 no-hitter with a 13-inning five-hit shutout, his game score going from 92 to 99. That gives him the best-ever game score in the start following a no-hitter and is an example of the impact on game scores of extra inning performances. By the way, the game after the no-hitter was an odd one, a scoreless tie through 12 innings before the visiting Reds score 10 runs (!) in the 13th.
- Howard Ehmke had a no-hitter in 1923 followed by a one-hit shutout, his game score going from 87 to 89. Oddly enough, in the start prior to his no-hitter, Ehmke gave up six runs in five innings and had a game score of 24, the eighth-worst game score in a start just before a no-hitter.
- Ken Holtzman, like Eller, followed up his no-hitter with an extra-inning performance in 1971, a 12-inning shutout in which he struck out 12. His game score improved from 89 to 96. In between those games, Cubs manager Leo Durocher used Holtzman in relief; two days after the no-hitter Leo brought Holtzman in to face two lefthanded batters with the winning run on base in the bottom of the 11th in Atlanta, but after Holtzman retired Ralph Garr for the second out of the inning, Mike Lum launched a game-ending three-run homer. And yet another oddity: four days before his no-hitter Holtzman was racked for eight runs in 3-2/3 innings and had a game score of 12, tied for the second-worst game score immediately before a no-hitter.
Two other pitchers had a game score in their next start that was the same as the one in their no-hitter: Ewell Blackwell in 1947 (both were 86) and Tommy Greene in 1991 (both were 90). In each case the follow-up game was a shutout.
Two pitchers actually had a better game score in the start before their no-hitter. Of course, in the case of Johnny Vander Meer, the start before his no-hitter on June 15, 1938 was also a no-hitter, on June 11. The game score of the first was 88 and the second 86. These games came during a remarkable six-start streak for Vander Meer in which he had an 0.65 ERA and gave up just 17 hits in 55 innings. He gave up only one run in each of the other four starts, and his game scores were all 70 or higher. (The record for the longest streak of 70+ game scores is nine.)
The other pitcher whose no-hitter was a “letdown” was Max Scherzer. On June 14, 2015, Scherzer pitched a one-hit shutout in which he walked one and struck out 16 for a game score of 100, the best ever in the start preceding a no-hitter. (The only baserunner came on a hit batsman with two out in the ninth inning.) Six days later he threw a no-hitter in which he walked no one and struck out 10 for a score of 97. I can’t verify if that’s the highest ever combined game scores for two consecutive starts, but I can say there are only 233 starts with a game score of 97 or better in the entire post-1914 database through September 5, 2015 (0.07% of the total), and Scherzer has two of them. Walter Johnson had nine such games just in the period of his career from 1914 forward, with three of them in 1918, and Nolan Ryan had seven such games (all 99 or higher), three in 1990, but neither they nor anyone else has had game scores of 97 or higher in consecutive starts.
Aside from Scherzer and Vander Meer, what other pitchers had outstanding outings before a no-hitter?
Dennis Eckersley, who earned his spot in the Hall of Fame as a relief ace, was an excellent starting pitcher early in his career. His 1977 no-hitter came five days after he pitched a 12-inning complete game in a 2-1 win (game score 92)…Hall of Famer Dazzy Vance pitched a one-hit shutout (game score 91) five days before his 1925 no-hitter (he got rocked for nine runs in his next start, game score 24)…Before pitching his famous no-hitter in 1934 (brother Dizzy had pitched a three-hit shutout in the opening game of the doubleheader), Paul Dean had given up one run in 11 innings five days earlier (game score 87). And three days before that, he had pitched a 12-inning shutout (game score 94). In those three games he allowed one run and gave up 12 hits in 32 innings. Dean was a “regular guy” by my earlier definition who had an excellent season. His streaks of three straight game scores of 87+ and four straight of 84+ are both tied for the longest ever, at least since 1914….Hall of Famer Ted Lyons pitched his 1926 no-hitter five days after pitching a 10-inning three-hit shutout (game score 86)…Dave Righetti, who like Eckerlsey gained greater fame as a relief pitcher, tossed his 1983 Independence Day no-hitter on the heels of a five-hit shutout (game score 86)…And while the wheels came off for Johan Santana soon after pitching the first (and at this writing only) no-hitter in Mets history, six days before that he had pitched a four-hit shutout (game score 86).
One other pitcher worth mentioning here: Lew Burdette is the only man to pitch a shutout in the starts both before and after his no-hitter (in 1960), but because he didn’t strike out many, his game scores weren’t super high (78 before, 77 after).
Now for the worst games preceding a no-hitter…and the worst of all was one that prompted me to write this post in the first place. In researching pitchers who had the biggest difference in game scores in consecutive starts, I came across Bill Dietrich, who had an ugly start just three days before his 1937 no-hitter. In the earlier game he was blasted for 10 runs in just 3-1/3 innings for a game score of 0 (yes, zero). In my earlier post I asked, “was that the worst performance ever in the start before a no-hitter?” Now I can answer definitively, yes, at least since 1914.
Here are some of the others who threw duds before their glory: tying Ken Holtzman for the second-worst pre-no-hitter score was Jim Abbott, whose 1993 no-hitter came six days after he gave up seven runs and 10 hits in 3-2/3 innings (game score 12)…Fernando Valenzuela gave up eight runs in 5-1/3 innings (game score 16) five days before pitching a no-hitter in 1990…Allie Reynolds pitched two no-hitters in 1951, with a very different lead-in to each. Five days before his first no-hitter, he was knocked out after giving up six runs in just one inning (game score 18; the next day manager Casey Stengel used Reynolds in relief and Allie gave up two runs while getting just one out). In his start prior to the no-hitter he threw in his last start of the season, Reynolds gave up just one run in a complete game win with a game score of 73…After a start in which he gave up seven runs in three innings in 2011 (game score 19), Francisco Liriano rallied to toss a no-hitter, although with six walks and just two strikeouts, Liriano had a game score of 83 to tie Cliff Chambers for the worst game score in a no-hitter, at least since 1914….In the start prior to the first of his seven career no-hitters in 1973, Nolan Ryan retired just one batter and gave up five runs (game score 22). The next day, manager Bobby Winkles used Ryan to get a two-inning save, the last and longest of the three regular-season saves Ryan is credited with in his career (he also earned one in Game 3 of the 1969 World Series).
And for the worst starts after a no-hitter…Carlos Zambrano was walloped for eight runs in 1-2/3 innings (game score 9) five days after his 2008 no-hitter…Bob Forsch followed his 1978 no-hitter by giving up seven runs in one inning (game score 10)…Tim Lincecum had a 4.61 season ERA prior to his 2013 no-hitter in which he threw 148 pitches, then next time out nine days later gave up eight runs in 3-2/3 innings (game score 12). Lincecum did not pitch a no-hitter in the two seasons in which he won a Cy Young Award, his two no-hitters came in years in which his final ERAs were 4.37 and 4.74…Dave Stewart struck out 12 in his 1990 no-hitter, but five days later he struck out nobody in giving up six runs in 2-1/3 innings (game score 16)…Philip Humber, mentioned here earlier, followed up his 2012 perfect game by giving up nine runs in five innings five days later (game score 17)…Bob Feller pitched baseball’s only Opening Day no-hitter in 1940, then gave up six runs in three innings five days later (game score 22)…Five days after his 1922 no-hitter, Jesse Barnes managed to retire just one of the five batters he faced before getting the hook (his game score was as high as 28 only because he started with 50 and didn’t pitch long enough to do serious damage).
My takeaway from looking at all this? There’s no way of knowing a no-hitter is coming based on a pitcher’s previous start, but (duh) better pitchers have a better chance of pitching one. And, while either might happen, don’t expect either continued greatness or a total collapse in the start after a no-hitter. Most likely the pitcher will go back to being who he is, good, bad or mediocre.
Before I wrap up, a few notes about the distribution of all game scores since 1914. From -5 to 52, game scores rise in an almost perfect progression, that is, there are more game scores of -4 than -5, more of -3 than -4, etc. There are only two exceptions to the steady increase. There’s a decline from 35 (5505) to 36 (5353), but then 37 is higher than 35. There’s also a decline from 43 (6144) to 44 (6138), but then 45 is higher than 43. The totals bounce around a bit from 52 to 55:
52 | 7089 |
53 | 6961 |
54 | 7077 |
55 | 7131 |
But then a steady decline is in effect from 55 to 97, with one exception, from 58 (6877) to 59 (7022), with 60 then lower than 58.
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