History Delayed

The late innings of a developing no-hitter are a study in tension. The pitcher is increasingly isolated from his teammates, who stay away from him for fear of jolting him out of the zone he seems to inhabit. Fans and announcers won’t even mention what he’s accomplishing, an echo of the players’ psychological act that, at this remove, becomes superstition. The pitcher’s offense, if his team has a decent lead, shades toward the superfluous, the at-bats an interruption and a delay of his progress toward a place in the record books.

Indeed, there is a belief that a long and productive offensive inning, while helping the team, will hurt the pitcher’s chances to complete the no-hitter. The rationale is that the long delay will give the pitcher’s arm time to go cold and stiff, rendering him vulnerable the next inning.

An example of this arose on August 1, the night before I submitted this piece to THT. Kansas City’s Danny Duffy threw seven no-hit innings at Tampa Bay. For those first seven innings, the Royals never sent more than four batters to the plate in one inning or saw more than 18 pitches. Then in the top of the eighth, they sent up six batters to see 27 pitches (and knock in two runs to make the score 3-0). The bottom of the eighth opened with Duffy giving up a double to Desmond Jennings.

There is some spillover superstition to this but also rational analysis. It’s the same reason a starting pitcher will be removed from a game after a rain delay despite having few pitches on his arm that day.

A twenty-minute bat-around rally, though, is different from an hour-plus rainstorm. Would the shorter interruption not be harmful? Could it even be just the respite the pitcher needs to get out there refreshed and mow down the batters again? Or does the extra time give him more minutes to think about what he’s doing and psych himself out?

Setting Boundaries

To answer these questions, I looked at 22 seasons worth of games, from 1994 to 2015, in which a starting pitcher took a no-hitter into the seventh inning. There were 561 such games in this study. I counted both plate appearances and pitches seen by his offensive team in the inning before he went out to defend his no-hitter and whether he lost or maintained (or completed) it. These act as my proxies for how long an inning lasts before the pitcher gets back on the mound.

No, this is not a perfect method. It doesn’t count time-outs for injury or warm-up time for a relief pitcher (or pitchers) entering the game, and there’s no hope of adjusting for the pace of the opposing hurler. All those factors can affect the true length of the wait for the no-hitter hopeful. I can only use what I have measured and hope it is enough to give a true picture.

(Okay, technically I could find videos of all the games and view the relevant innings, stopwatch in hand. I’ve used that method once for a Hardball Times article. Once was enough. I also did consider using Tom Tango’s pitch estimation formula but rejected this approach. The formula works well over a season–and tolerably for a game–but for a single inning it would be a dressed-up guess.)

A few potential no-hit games were excluded because the starting pitcher departed before pitching the seventh. The matters of fatigue and looseness are obviously different for relievers and cannot be compared to starters. There was also a 10-inning no-hitter in which the starter went nine and a reliever handled the 10th. I counted this game as far as the starter went but left out the reliever’s frame.

For a few of the earlier games in the sample, pitch counts are not known and are thus not counted when that is part of the analysis. One reason I did not extend my sample to earlier years was that more, and eventually most, games would be lacking pitch counts.

Also, there is one alteration I made to the game data (which was almost two). The records say that Armando Galarraga blew his no-hitter–and perfect game–in the ninth inning on June 2, 2010. Objective evidence states otherwise. As part of my quixotic crusade to have people remember what Galarraga earned and not what he was awarded, I count his ninth inning as a maintained no-hitter, not as a blown one.

In the case of Johan Santana, I was ready to do the reverse. When he pitched his no-hitter for the Mets in June of 2012, I wrote at THT about the Carlos Beltran liner that hit the left-field line chalk but was ruled foul. I said that, if I considered Galarraga’s game perfect, I couldn’t consider Santana’s to be a no-hitter—and invited upon myself the worst Comments section flaming I have ever received as a Hardball Times writer.

Well, I’m stubborn about such things. If I had found that missed call had been in the seventh inning or later, I was going to rule Santana’s game a blown no-hitter for this study and then brace for my second napalm shower. Lucky everyone: It was in the sixth. So I’ll bend enough to include his game, because who wants to throw away data?

The Long and Short of It

How often budding no-hitters survive the following inning in an interesting side subject. Zachary Levine looked at the matter in a Baseball Prospectus article two years ago, over a longer sample time, from 1950 into 2014. Readers are encouraged to look that piece over for the added info, but I will take my own quick look at the 22 years I’m covering.

From 1994 to 2015, a six-inning no-hitter had a 39.4 percent chance of surviving the seventh inning. The survival rate rose in the eighth to 42.5 percent and spiked in the ninth to 60.6 percent. (That is including Galarraga as a success. If you count him a failure, it’s 59.6 percent.) Levine shows a rise in success rates as innings pass but not the ninth-inning surge.

The general rise is probably explained by less excellent pitchers faltering and being weeded out. The spike in my more recent numbers may partly be due to the recent spike in perfect games: 10 of the 23 perfectos ever hurled have been since 1994. A pitcher will perforce be facing the bottom of the order in the ninth inning of a perfect game attempt. Even including near-certain pinch-hitters, that’s a milder challenge than the average no-hitter in the ninth will provide. Those 10 perfect games (11 with Galarraga) are a substantial fraction of the 55 (56) no-hitters accomplished in the same timeframe.

That tangent followed, we may now resume looking at the original data. I broke down both batters-faced and pitches-thrown numbers for the frames before no-hitting pitchers threw in the seventh, eighth, and ninth innings. Sample sizes are given for batters faced: They are sometimes slightly smaller for pitches thrown due to gaps in the pitch count records.

I show breakdowns by inning, but those are much less important than the overall numbers, at bottom.

* Included is one 10th inning, by Pedro Martinez on June 3, 1995. He lost the no-hitter (and perfect game) that inning.

There’s next to no difference in batters faced by those who lost or preserved their no-hitters. For pitches thrown, however, those who maintained had almost one pitch more thrown in the preceding half-inning than those who blew the no-hitter. This is the reverse of the hypothesis we brought in, and while it’s not a proof of the reverse, it’s good evidence against the original idea.

But perhaps lumping all those games into a single average isn’t the best way to examine the data. The belief is that a long intervening inning will leave a pitcher less able to continue his no-hitter. It may be better to divide these innings into groups of varying lengths and look for differences there.

I did this by both batters faced and pitches thrown. The latter I divided into several groups: up to 12 pitches, 13 to 20, 21 to 28, 29 to 36, and 37 or more.

I also did a combination category, counting the sum of batters faced and pitches thrown. The time for a batter to come to the plate and get set to swing is roughly the time it takes for the pitcher to set up and deliver one pitch, so I considered them equal in how long they would extend an inning. My groups for this combination were: up to 15, 16 to 25, 26 to 35, 26 to 45, and 46 or more.

The percentages in the following tables show what proportion of all no-hitters maintained–or lost–came with the number of batters, pitches, or combined shown. The parenthetical numbers are the sample sizes.

Some rows do not add up to 100.0 percent due to rounding.

For batters faced, there’s no difference big enough to be considered decisive, or even strongly suggestive. It’s interesting that blown no-hitters happen a little more after one-two-three innings, and maintained no-hitters occur more often after frames of six batters or more, but the margins are not wide enough to bear conclusions.

Look at pitches thrown, and there’s something more. The sustained no-hitters come less often in short innings, by three and a half points for the lowest category, and more often in long ones, by three and a third points in the highest two. It’s not really dispositive, but getting there. In the combined category, though, the margins recede a little. The very long innings still favor the pitchers who maintained their no-hitters, just not quite by enough.

Therefore, I cannot say long rallies by their teams will help pitchers going for no-hitters. I can say the original theory, that those long innings cool off their arms and worsen their chances, is not at all supported by the data.

A Deeper Plunge

At this point, I had intended to factor in the friendliness of the ballparks toward hitting for average. A park that allowed long innings more easily to a pitcher’s offensive teammates naturally would be inimical to his prospects to sustain a no-hitter. If long offensive innings had lowered the chances of a pitcher’s no-no, this was an alternative explanation for how this would happen, one I meant to comb out of the numbers.

Instead, long innings have, if anything, nudged the pitcher’s chances upward. I would be, not mitigating the expected result, but strengthening the unexpected result. That is, if ballpark factors do what I expect them to do. But why should that be more reliable than my original hypothesis?

So I am going ahead with the correction to see what actually happens rather than to assume it. I’ll work in not just the ballparks but the offensive ability of both teams playing in each game.

(Home or away matters because, as a rule, teams hit better at home and worse on the road. Of the 561 no-hitters through six innings I included in the study, 327 of them, over 58 percent, were done by pitchers on their home fields.)

For the lead-in half-innings, I’ll generate a stat I’ll call Batters Faced Plus (BF+). This will be, on a scale of 1.0 (rather than 100) being average, the number of plate appearances completed by the offense measured against the mean number we would expect them to have. This will be based on the season on-base percentage of that team, for home or away as the case may be, modified by the venue in which they’re playing. A home team batting would be gauged by season OBP at home; a visitor by season road OBP, adjusted by visitors’ park factor at the field in question.

For the pitchers’ half-innings, I’ll generate an Expected Hold Probability estimating the likelihood they would maintain their no-hitters through that inning. This will be the inverse of the opponents’ expected batting average, with home or road figures and park factors taken into account, raised to the third power (for three outs). This won’t be exact, but as errors (0-for-1 with no outs) and double plays (0-for-1 with two outs) should roughly balance out, it ought to serve.

I looked only at batters faced for this study even though the more interesting basic findings were with the pitch counts. The same problem with estimating pitches I encountered before kept me from trying it here.

So did longer lead-in innings point to tougher roads for the potential no-hitter? It certainly doesn’t look that way. The effect of home fields doesn’t add up to much. Look at how BF+ and Hold Probability relate to each other (for blown chances). The clumpiness of the data is due to average on-base percentages staying within fairly confined ranges, along with the granularity of batters faced.

The graph for maintained no-hitters looks virtually the same, so I have not included it. As the pitcher’s teammates hit better, his opponents do better against him, but by a tiny amount. For every full point of BF+, representing roughly four and a half batters, his expected chance of holding the no-hitter through the next inning drops by two-tenths of one percent. (For maintained no-nos, it’s a bit smaller.) That tiny increment, combined with a microscopic r-squared value, means there is effectively no relationship.

Looking at blown versus maintained no-hitters shows the opposite of the relationship we would expect.

The half-innings before blown no-hitters have the lower BF+ rating: they’re shorter than those for maintained no-hitters. If this were a general park effect, we’d see lower batting averages and thus higher Hold Probabilities for the blown no-nos. Instead we see lower Hold Probabilities. Park effects are not influencing the equation in any meaningful way.

We also see the maintained no-hitters had marginally higher probabilities than the blown ones. By “marginal,” I mean that opponents’ expected batting averages against were roughly two and a half points lower for the sustained no-nos. That’s not nothing, but it’s awfully close to it. Pitchers extending their no-hitters aren’t doing it just by beating up on the creampuffs.

Within all that ancillary stuff, though, is the core finding. The maintained no-hitters see slightly longer half-innings before them than the blown no-hitters, measured against expectations of how long those innings should last. They are not suffering a penalty from longer innings stiffening their arms or tying their guts into knots.

Conclusion

Another unexamined baseball idea—whether you call it superstition or a reasonable assumption based on physiology and psychology—melts in the sunlight. There is no evidence that a long offensive inning renders a pitcher throwing a no-hitter vulnerable when he returns to the mound. What weak evidence there is points instead the other way, saying he’s a bit more likely to continue or complete the feat after a long and productive frame by his teammates. But that evidence is weak, and my preferred conclusion is that there is no influence either way.

Much as I’d quietly hoped to find this bit of received baseball wisdom borne out by the facts, I actually like what the results say about these pitchers. In one of the most tense situations they’ll ever face in their careers, with a chance at fame and the history books starting them in the face, they hold up. The physical stresses and mental anguishes of a long wait to step back into the crucible do not affect them. They are, physically and mentally, tough.

In an era when starting pitchers are coddled and cosseted and fretted over to unprecedented degrees, and with uncertain benefits, it’s refreshing to see there’s a bit of steel in their makeups. At least, when things are going really well, which is admittedly the easiest time to look your toughest.

References and Resources

• Effusive thanks go to Paul Golba, who parsed even more years of Retrosheet data than I ended up using. This article would have been next to impossible without his skills.
• Retrosheet for its pay-by-play records.
• Baseball-Reference for pitch counts.