Evaluating managers from a quantitative standpoint is no small feat. There have certainly been attempts and discussions in the past, but no such framework has ever taken hold of the analytical community and forced its way into our vernacular. It can be easy to suggest that the job consists of little more than penciling names onto a card to hand the umpires or lift tired starting pitchers to insert more effective relievers. These are areas that could potentially be quantified, but they're not the sole responsibilities of a skipper. Even so, sometimes the second of those two aspects of managing can become tricky and less clear-cut.

Back on April 10, CC Sabathia took a no-hitter into the eighth inning against the Rays—the Rays? No hit? Say what!?—before giving up a base hit to Kelly Shoppach. Sabathia had thrown 110 pitches prior to surrendering the hit, and as Shoppach made his turn at first base, Yankees manager Joe Girardi essentially transformed into Michael Johnson and sprinted to the mound to pull his workhorse from the ballgame. The quick hook suggested that Girardi had allowed Sabathia to pitch that long in an attempt to achieve a rare feat. As soon as that feat was no longer attainable, there was no point in keeping Sabathia in what would end up a 10-0 victory, especially with the lefty having thrown so many pitches at such an early point of the season.

Fast forward to last Friday and Diamondbacks manager A.J. Hinch found himself in a very similar situation: off-season acquisition Edwin Jackson was in the midst of no-hitting the very same Rays, with an escalating pitch count as the game entered its later stages. Fortunately or unfortunately, Hinch was not as lucky as Girardi in the sense of not having to make a decision, as Jackson completed the no-hitter, marking the fourth no-no of the young season. In total, Jackson threw 149 pitches and walked a Burnett-esque eight batters.

My reaction to the no-hitter spanned the emotional spectrum, ranging from excited to curious to angry to flabbergasted. My goal here is not to turn into Buzz Killington by any means, but rather to use the questionable non-move of Hinch to highlight a few different points: managing to a feat and not necessarily to health, a discussion of pitch counts, and a look at the worst no-hitters of the last 60 years given that, well, walking eight batters in a game is never positive, regardless of whether or not the pitcher in question uses up all of his strand rate magic bar in the same game.

Managing the Feat

I’ll be the first to admit that, while I may be very critical of Hinch’s decision to let Jackson throw 149 pitches, I can certainly empathize with the man. Though I would have been inclined to yank Jackson earlier in the game when he was struggling so mightily, it is always easier to be an armchair quarterback. Who knows how I might have felt in that moment? Perhaps my standard thought process would go out the window and emotions would take over. Regardless, I disagree with the condition, but it is interesting to discuss Hinch's choices.

The dilemma reminds me of “the train problem,” which is a reasoning test of sorts taught in introductory psychology courses. The premise, though grim, is quite simple: you're standing in a railway yard and you see a runaway train coming down the line. You see that if it keeps going, it’s going to run over five people and most certainly kill them. You also notice that you are standing next to a switch that would turn the runaway train to another track, on which it would run over just one person. Do you throw the switch? The majority of responders reply with an affirmative, reasoning that one death is certainly better than five deaths. However, it should be fairly obvious that both result in death, which is not a positive outcome.

Relating the scenario back to the baseball game, Hinch could not have made the right decision in this situation, and I might go so far as to argue that the most awkward decision a manager may face is what to do with a starting pitcher on the verge of an historic feat, but who also has an escalating pitch count that could hinder his effectiveness or lead to an injury down the road. If Hinch kept Jackson in the game, as he did, many are left to wonder how a team could let a pitcher throw so many pitches just to achieve something rare, especially when the hurler in question is considered to be a key piece of their potential success puzzle.

If Hinch removed Jackson, the opposite occurs. Most fans and many analysts spew vitriol in his direction for messing with history. these same people would then likely shift their anger towards pitch counts in general and how Hooks Dauss or other similar funnily named players from the days of yore could unleash 175 pitches in a game and come back the next day. Simply put, Hinch could not have won, but why was it a big deal in the first place?

Pitch Count Concentrations

Jackson’s no-hitter, as we will explore below and already mentioned above, was not your ordinary no-no. The 149 pitches rings alarm bells because, well, that high of a pitch count just does not happen anymore. Since 2000, there have only been five instances of a starter throwing 146 or more pitches: Livan Hernandez (150 on June 3, 2005), Ron Villone (150 on September 29, 2000), Jackson’s 149, Randy Johnson (149 on July 31, 2002), and Kevin Appier (146 on July 3, 2000). Making matters worse was that Jackson threw a high concentration of these pitches in a brief, early span of innings: he threw 27 in the first frame, 18 in the second, and 22 the inning after that, totaling 67 through three innings.

Jackson managed to settle down for the middle three innings, before throwing 51 more pitches over the final three frames. Nothing came easy, and he labored for most of the game. A quick glance at his inning-by-inning totals don’t look like they sum to almost 150 pitches, primarily because he didn’t have too many 20-plus pitch innings, but his distribution was still cause for concern.

Back when I first started writing at Baseball Prospectus I ran a two-part study looking at the effects on velocity and movement, broken into subsets based on average velocity, of tallying a high number of pitches in an inning. The results were intuitive in that throwing 100 pitches in a game while staying fairly consistent in the number of pitches thrown per inning was much less problematic than throwing 35 in the first inning and reaching 100 by the fifth frame. The results were also more drastic for pitchers in the 94-plus mph range, as they were throwing with less movement to begin with, and lost the velocity that served as a counteracting force over the course of the same game, as well as their next start. The study likely needs a bit of a refresher with all of the added data over the last couple of years, but intuition will likely win out given that pitching a baseball is a very unnatural motion.

The underlying rationale for the higher concentrations of pitches within a very few innings becoming a problem deals with just how unnatural the motion is on the body. Consider going to the gym and doing 25 or more reps on the bench press of approximately 90 percent of your maximum benchable weight, without proper rest in between each rep. Placing that amount of stress on the body without the proper recuperation period can be very damaging, because the muscles and tendons need time to recoup the lost energy. This is why not all pitch counts are the same, even if they happen to consist of the same number. For Jackson, the 149 raised a red flag because it was high in nature but also because he did not have many easy innings.

Where Does the No-Hitter Rank?

Upon hearing of his no-hitter and the eight walks I began to wonder where it would rank in the annals of no-hit history, in terms of the Game Score, a Bill James invention. While flawed a bit, is convenient and tells a very decent story of the game, where a score of 50 is average, and above is better. Jackson recorded an 85 on his no-hitter, which is certainly very good, but only one point better than a complete game/shutout he threw a couple of weeks earlier that isn’t going into the history books anytime soon.

Since 1995, there have been 71,394 starts, only 1,911 of which have featured game scores of 84 or higher, a minuscule rate of 2.6 percent. So while Jackson’s game might not be impressive relative to no-hitters, it still ended up being a great effort from a results standpoint. Of the no-hitters thrown since 1954, the average game score is 92, with a range of 84-101. The 84 belongs to George Culver in 1968, Ken Holtzman in 1969, and Joe Cowley in 1986. Jackson’s certainly falls into the lower quintile of no-hitters, but it was not the worst.

But then I got to thinking about those eight walks, as it seemed like such a rare occurrence in its own right. Sure enough, since 1995, just 87 of the aforementioned 71,394 starts have seen the starting pitcher walk eight or more batters. Those 87 games averaged a game score of 41, with a range of 13-85. Put both of these factoids together and Jackson simultaneously tied the highest game score for one involving eight or more walks while coming oh so close to achieving the lowest game score for a no-hitter. If Hinch had taken him out, we would have missed out on gold like that!

To reiterate my earlier point, I am not trying in any way to diminish Jackson’s effort, because he is now in the history book with the achievement. My concern is that the Diamondbacks risked the short-term and long-term health of a pitcher they have under contract through next season, just to see if he could prevent the opposing team from registering a base hit. The decision to leave him in had to be gut-wrenching for a young manager like Hinch, but the skipper's job description includes helping the team win now and into the future, not doing what he can to immortalize an athlete or help Jackson do something that was rare.

 If Jackson remains healthy for the entire season and the rest of his career, it doesn’t render this argument moot. I'm a decision-based organism and not one who thrives on results or outcomes all the time. For the sake of pitcher health, though, I sincerely hope that opposing teams register hits like in the Girardi-Sabathia game, so the decision is taken out of the hands of potentially unsure managers.