For the past few days, I’d been searching for a baseball topic to write about. It usually takes less time, but we’re in that calm (if not monotonous) period between the All-Star break and the trade deadline. Ideas are scarcer. Maybe I’d settle on an article with a simple premise?

So I committed myself to tackling pitcher BABIP. (Good going, Justin!)

The notion that pitchers have no control over what happens to a ball in play ushered in a golden age of baseball research, and findings from back then still influence how we view the game today. But over time, we realized that exceptions do exist; for example, Clayton Kershaw consistently allows a below-average BABIP, most likely because he’s a phenomenal pitcher. In addition, certain pitchers have a knack for inducing weak contact in the form of pop-ups or grounders. Exactly how those batted balls impacted BABIP remained a mystery, but you could no longer brush off the metric as total noise.

Years later, Statcast data became available for public use. Even so, research on pitcher BABIP remained far and few between; it’s a daunting subject! I did use two articles as inspiration, however. The first is from FanGraphs user rplunkett97 on our community research page. Dating back to 2017, it mainly discusses a linear model with several variables (BB/9, GB%, Team UZR, and more) used to produce an expected BABIP for each pitcher. The second is courtesy of Alex Chamberlain, also from the same year, who used a mixture of Hard-hit and Barrel rate to create his own version of xBABIP.

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One of the great batting lines of the first half was Yasmani Grandal’s .189/.388/.436 slash. Unfortunately, as has been the case for many a hitter on the White Sox, his return to action in ‘21 is in doubt after he underwent surgery to repair a knee ligament. I won’t wax poetic on Grandal; Devan Fink did a great job covering his early-season batting line. But it’s becoming more common to see a hitter with an average that starts with a “1” these days. The common reference to a batting average under .200 is the “Mendoza Line,” which our Ashley MacLennon made a strong case for ditching as a reference earlier this season. I, on the other hand, am going to make the case for why it’s become irrelevant.

Batting average, the prevailing measure of a hitter’s success for most of baseball’s existence, has faded into the background, yet the rate at which a hitter successfully reaches base via a hit is still usually the first statistic reported. Grandal’s batting average is not good, but the selection of .200 as a cutoff point is arbitrary; after all, a batting average of .214 is also not good. What most baseball fans understand now is that because all base hits are not equal in value, batting average is limited in what it says about a hitter. But there is a stigma attached to a poor batting average, which is probably why the Mendoza Line has stuck.

Let’s rewind to last year’s shortened campaign. There was a lot of speculation going into a 60-game season as to whether or not a player would be able to hit .400. That didn’t happen, though Charlie Blackmon was hitting .500 after a couple weeks. We did end up with a handful of qualified hitters with an average below .200 — seven such, to be exact:

This is by far the highest number of qualified hitters with a batting average below .200 for a single season. It is totally a product of the short season, though. None of the hitters on the list above are contact hitters, but their true bat-to-ball skills are probably better than what they showed in ‘20. When the sample is small, there is a greater chance that you get some outliers in your results.

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Last year, Connor Kurcon created dynamic hard-hit rate (DHH%) to add dimension to our typical understanding of Statcast’s hard-hit rate (HardHit%). Whereas HardHit% uses a fixed minimum exit velocity (EV) threshold of 95 mph to determine a hard hit, DHH% uses a — you guessed it — dynamic threshold that changes according to launch angle of the batted ball event (BBE). Kurcon found this orientation of hard-hit rate to be more powerful than its original in terms of describing same-year contact quality (per weighted on-base average on contact, or wOBAcon), predicting next-year contact quality, and predicting itself (year-over-year “stickiness”).

Inspired by a Yermín Mercedes home run off a Willians Astudillo eephus, I borrowed the premise of DHH% and applied it to pitch velocity — that is, the dynamic threshold was based on pitch speed rather than launch angle. Although not as powerful as the original, Pitch DHH% also proved itself superior to HardHit%.

Ever since Kurcon unveiled DHH% in 2020, though, I’ve been thinking about how the premise might apply to spray angle (horizontal angle, lateral angle, whatever you want to call it). It seemed intuitive to me that a hitter would generate more power to his pull side and less to the opposite field. I suspect if you were prompted to guess, you might have said the same. Read the rest of this entry »

There is an interesting quote from Greg Maddux about the relative merits (or, if you’re Maddux, demerits) of “wasting” a pitch in a 0-2 count versus continuing to attack the hitter. Throwing a pitch outside of the zone and hoping for a hopeless swing in an 0-2 count is a baseball convention that’s ingrained in pitchers from the time they are adolescents. The idea is to not give the batter the chance to put the ball in play when the pitcher is in a supremely advantageous position. Maddux eschewed this notion. He said, “The hitter is most vulnerable when you get him in an 0-2 bind. My goal is to take him out immediately. I’m going right after him, not fooling around with wasting a pitch up high or throwing one in the dirt.”

Maddux’s impetus for questioning convention was twofold. First, a waste pitch is (wait for it) a waste. It is a waste of a pitcher’s time and energy and gets him out of rhythm. If you believe that on any given day a pitcher has a finite number of effective pitches in him, then throwing a pitch without the singular purpose of using that pitch to get the batter out is foolhardy. Maddux’s second gripe is that batters have the lowest batting average in 0-2 counts, so why would you fear throwing the ball in or around the strike zone? He also mentions the pitch is usually so far away from the strike zone that the hitter will lay off by default, giving the opposition the opportunity to see one more pitch out of the pitcher’s hand. Maddux is seemingly inferring that seeing this extra pitch assists the batter in timing up a pitcher’s motion, allowing them to gain a small edge in being able to better pick up the ball coming out of the hand.

The merits of a 0-2 waste pitch has been explored in the past. Earlier this yeah, Jim Albert used the same Maddux quote as a jumping off point for evaluating 0-2 pitches at his blog Exploring Baseball Data with R (as an aside, Jim is one of the coauthors of a must-have book if you are interested in getting into baseball analysis). Jim noted that pitchers don’t tend to use fastballs as waste pitches; when pitchers do waste pitches, they are more likely to bury breaking balls below the strike zone. He did note that 0-2 fastballs were located higher than fastballs in other counts, but they still were often in and around the strike zone, and thus were not waste pitches. Back in 2011, John Dewan at Bill James Online found that, in terms of the average plate appearance outcome, there was only a 10th of a run difference in favor of the pitcher between throwing in the strike zone versus outside of it, so there was no clear dominant strategy. Read the rest of this entry »

We’re now five years into the Statcast era, and with that has come a good base of knowledge and an understanding of what small sample events are significant or beyond noise. Alex Chamberlain recently provided a wonderful example of this type of analysis; I encourage you to read that to get a feel for what I’m going to be talking about. But where Alex and Connor Kurcon covered the values of hard-hit balls at extreme launch angles and extreme exit velocity at given pitch speeds, I want to cover foul balls and what we can — or maybe can’t — learn at the extremes.

Any quick look at the Statcast leaderboard will show you that Yermín Mercedes has a max exit velocity of 116.8 mph, good for ninth best in baseball this year. That’s an incredible feat for any player, but what criteria do we want to set when determining a max? We’re ultimately seeking to measure raw power output, so maybe we should be more inclusive to all batted ball events. If we include foul balls, Mercedes would suddenly have the sixth-highest max exit velocity in baseball at 117.7 mph.

I encourage you to listen to that clip with sound, because the play-by-play commentary is all we have as to where the ball landed.

That 0.9-mph jump might not mean much, but there’s more to it once you consider both the rarity of the batted ball and the fact that we have a number on it in the first place. There’s a wide acceptance of all stats derived solely from launch angle and exit velocity, but you should consider the importance of spray angle. In the same way that both Alex and Connor talked about abnormal exit velocities in the context of a pitch speed or launch angle, something similar should be noted when thinking about the spray of the ball.

To understand this relationship, it’s important to see the spray angle at which each player generates their max EV:

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In 2018, an article by FanGraphs alum Travis Sawchik came with an ominous title: “Go See the Two-Seamer Before It’s Gone.” His instruction alluded to a still-ongoing trend within MLB, whereby numerous pitchers abandon their two-seamers and sinkers in favor of high-spin four-seamers thrown up in the zone. Its impetus boils down to a couple key developments. For one, teams and pitchers wanted to counter batters who adjusted their swing planes to elevate low pitches. They also realized that high fastballs are useful at inducing whiffs, regardless of batters’ tendencies. Furthermore, those fastballs paired well with the breaking ball shapes and locations teams began to covet around the same time.

All in all, the stage was set for a league-wide revolution. You’ve read the stories of how Gerrit Cole and Tyler Glasnow blossomed into superstars using high fastballs. Conversely, you’ve heard the story of how forcing the sinker upon Chris Archer aggravated his struggles. You might have also encountered stories connecting this trend to the recent uptick in strikeouts. The validity of these reports aside, they helped cement a narrative: the four-seamer was in, and the sinker was out.

Three years later, the league doesn’t seem to have veered away from it. Pitchers have located 20% of four-seam fastballs in the upper-third of the zone this season, the highest rate of the Pitch Tracking era (2008 onwards). Meanwhile, two-seamer/sinker usage is the lowest it’s ever been.

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On May 17, Chicago White Sox legend Yermín Mercedes hit the sixth home run of his stellar, albeit wilting, nevertheless unlikely, rookie campaign. A mammoth blast over the center field wall of Target Field, the home run sparked — in equal parts, seemingly — awe and controversy.

? THE YERMINATOR JUST HOMERED OFF OF LA TORTUGA! ? pic.twitter.com/pHacUxXtdF

— MLB (@MLB) May 18, 2021

The controversy? Mercedes teed off on a 3-0 count with one out to spare in a 15-4 blowout, off a beloved Position Player Pitching^TM no less. He did so in the home park of a sputtering rival, one expected to compete for their division’s title but, at the time, had instead won half as many games (13) as it had lost (26). Naturally, a lengthy and unpleasant discourse about the game’s unwritten rules ensued. Retribution, however juvenile, was had.

At the time, the sheer amount of baggage on the home run did not register with me. My brain is so moldy and soggy that I reacted somewhat primitively. Good lord, Yermín Mercedes absolutely mashed possibly the slowest pitch I’ve ever seen.

Indeed, Mercedes’ home run is the hardest-hit batted ball (109.3 mph) against a pitch 60 mph or slower (47.1 mph) in the Statcast era. Only Christian Walker (seen here) and Ryan McMahon (seen here) come close, and their batted balls came against pitches thrown more than 53 mph. That’s, like, light speed in comparison. Read the rest of this entry »

Swing decisions are generally evaluated with limited nuance. We consider whether the pitch was in the strike zone (as defined by your data provider of choice) and whether the batter swung. Over the course of hundreds or thousands of pitches, this provides an easy-to-comprehend method of effectively evaluating a player’s approach. With a sufficient sample, these binary classifications give us insight into how players approach their plate appearances relative to their peers, which hitters are better at discerning the strike zone and which are more aggressive.

I have a bone to pick, though: there is often no differentiation between pitches that just miss the defined strike zone versus those that miss by multiple feet, or pitches that just nick the strike zone as opposed to pitches right down the middle. A lot of swing decision analysis is done in the binary, but as many analysts have shown, looking at the gradations in the strike zone can be revealing. Granted, this distinction lacks meaning over many pitches; selective hitters with elite batting eyes will separate from their less fastidious peers with respect to chase rate over time. But in smaller samples, the lack of distinction between pitches and their proximity to the strike zone makes judging a player’s swing decisions difficult.

One method we can use is to group pitches by their probability of being called a strike. Similar to how pitches are evaluated for the purpose of studying catcher framing, I created a general additive model for gauging the probability that a given pitch would be called a strike. My model was trivial (relative to the research I linked above) in that I just considered pitch location and pitch movement; for the purpose of this exercise, I thought that would be enough to get the idea across. The model was trained on 80% of pitches called a ball or strike from the 2020 season, with the remaining 20% used as the test set. For the test set, the model was about 92.5% accurate, in that it correctly predicted whether a pitch was called strike 92.5% of the time.

I applied the model to all pitches from the 2019 and ’20 regular seasons, which yielded the probability of a called strike on every pitch. Pitches with higher probabilities of being a called strike if taken are toward the heart of the zone. Pitches at the edges of the zone have anywhere from a 40–60% chance of being called a strike. And pitches with expected probabilities closer to zero are nowhere near the strike zone.

I binned every pitch in increments of 10% of called strike probability. The following represents the swing rates in each of those bins:

As one would imagine, the league as a whole swings at pitches that have higher called strike probabilities; the closer the pitch is to the heart of the zone, the higher that probability. Break those probabilities down even further, and you can see that the chance of a swing increases steadily with called strike probability.

Swing rates increase rapidly as the called strike probability approaches 0 and 100%. For the more competitive pitches, the changes in swing rate are much smaller. Intuitively, you would expect this relationship to be linear throughout the probability interval; for every 1% increase in called strike probability, the swing rate would also increase by some corresponding percent described by the slope of a line regardless of where you are along this interval. This is not the case.

My hunch is that once a pitch reaches a certain threshold of competitiveness (in terms of challenging the hitter to swing), the swing decision is not as tethered to the chance of the pitch being called a strike. Instead, the choice depends on the pitch type and what the hitter is guessing or picks up out of the pitcher’s hand. Addressing the rapid increase in swing rate on the lower end of the spectrum, I would imagine that many of these pitches are thrown in advantageous counts from the perspective of the pitcher — two-strike counts. While the lack of stigma surrounding strikeouts has been talked about ad nauseam in baseball circles, hitters still do not want to strike out. So if these less competitive pitches are often being thrown with two strikes, the swing rate increases are going to be more sensitive to any marginal change in called strike probability. Break it down by count, and you can see that that’s the case:

For the sharp increase on the higher end of the range, my theory is the same as the other end of the spectrum: Pitches approaching a 100% called strike probability are so enticing to swing at that batters will disregard the count to attack them. Murkier pitches will not really be swung at in 2–0, 3–0 or 3–1 counts, but if the pitch is close to an automatic strike, it must be toward the heart of the plate; a batter who has the green light will want to swing.

For context, league-wide swing rates have oscillated between 45–47% over the past decade. Swing rates on pitches with a called strike probability between 40–60% generally fell in this range in 2019 and ’20. It’s the extreme ends of the spectrum where hitter behavior changes most rapidly. We also saw that the count has a significant effect on the swing rates for any given pitch, especially those that were most and least competitive. So, we know the general league-wide trends and we understand why this is a more nuanced method in evaluating swing decisions. What about at the player level? I found a couple of interesting quirks. When you look at the players who are most aggressive on the pitches that are the most advantageous to swing at (those with a called strike probability of at least 90%), you get a mix of players who we think of as having good plate discipline and those who are more free swingers:

Freddie Freeman, Luke Voit, Brandon Lowe, and Corey Seager are all examples of players we generally understand as having good plate discipline. They lay off pitches that have very little chance of resulting in a called strike and attack pitches that can result in positive outcomes on contact. This list also includes Jeff McNeil, Jay Bruce, and Jorge Alfaro, all of whom swing at pitchers at rates higher than league average no matter the location. This type of strategy can work for a player like McNeill, who has displayed throughout his career he is among the league’s best at making contact. For players like Bruce and Alfaro, this is a recipe for either falling out of the league (in the case of Bruce) or finding more time on the bench as time goes on (in the case of Alfaro). On the other end of the spectrum, the analysis is more cut and dry:

Here we have a list of players who we consider either disciplined or passive. These players do a good job of avoiding swinging at bad pitches, but it seems to be more of a product of just not swinging at all. It could also mean that these players are zeroing in on “their pitches to hit,” and can lead to very good seasons (see: Yasmani Grandal, Mitch Garver, and until this season David Fletcher, Brett Gardner, and Eric Sogard) but passing up good pitches can be problematic without either elite power or contact ability (see: Greg Garcia, Harrison Bader before 2021, and Josh VanMeter). This extreme passivity is a fine line to walk; as you can see after great combined 2019-20 seasons, Fletcher, Gardner, and Sogard have fallen off this season after posting very good lines previously. Fletcher especially is one of the best at putting the bat-head on the baseball, but his passivity may be catching up to him as the league has collected more data on his swing patterns.

Finally, here were the most aggressive and passive swingers on pitches with very little chance of becoming a strike:

Unsurprisingly, batters who avoid swinging at the worst pitches tend to post good results. The other end is a bit of a mixed bag. Tim Anderson has gotten away with what we would consider poor swing decisions because of his demonstrated ability to post high-end BABIPs the past few years, a combination of hitting the ball at angles that result in singles and his foot speed. Javier Báez has posted excellent lines (2020 notwithstanding) by slugging his way to success. Without outlier skills, this sort of approach leads to lackluster performance. Before 2020, José Iglesias was not a good hitter in the majors. Kevin Pillar and Hanser Alberto have mostly posted middling results, and I talked about Alfaro’s issues above.

There is not a one-size-fits-all method of approaching plate appearances. A player’s ability to make contact and his power are the driving forces behind how often he should swing and which pitches he should choose to offer at. This conclusion is nothing revelatory but distinguishing swing decisions based on its chance of being a strike if taken gives additional insight into certain players’ plate discipline profiles. Freddie Freeman or Juan Soto, how swing clearly can track the ball very well and we know they have great discipline. But their plate discipline is different than a player like Yasmani Grandal, who has also displayed discipline throughout his career, though that discipline manifests itself in a much more passive approach. When parsing swing decisions by the quality of a pitch on a granular level, players can get by either through aggression or selectivity. This also shows that free-swingers are free-swingers, no matter the pitch. Baseball players and their skills contain multitudes. When we deal with samples in terms of pitches faced, it helps to further parse the information at hand to get a better understanding of how players struggle or perform well.

With the continual increases in league-wide fastball velocity each year, we’re beginning to understand that pitcher aging curves are going to change dramatically. As Jeff Zimmerman’s work makes clear, older pitchers are holding onto more of their fastball velocity and shedding usage at the same time. There’s a survivor’s bias in studying the pitchers who have accrued the most innings, but there’s something to be learned about the limits of maintaining velocity from pitchers who exemplify the modern game.

Max Scherzer is an archetype of the modern pitcher: someone who has been all gas and punchouts. But as he ages, he appears to be entering into a slow decline. He’s boosted his K-BB% rate from 23.4% last season to 30.9%, but his fastball has lost 0.6 mph (94.9 to 94.3 mph) off its average and 0.8 mph (97.9 to 97.1 mph) off its max. And while we can argue about averages, what might be most important for measuring arm health is max velocity.

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About a month ago, I wrote about Jack Flaherty and looked at his increased reliance on both his fastball and his slider. I posited that through his first seven starts, Flaherty had effectively been a two-pitch pitcher, with the aforementioned combination of pitches making up about 80% of his total pitches. (His curveball was his third-most used pitch, thrown sparingly at about a 13% clip.)

To investigate if this constituted a negative development and could account for Flaherty’s reduction in strikeouts relative to his career norms, I conducted a series of analyses. I grouped pitcher seasons from 2010-20 and looked at the number of pitches each pitcher had with a usage over 15%. This was somewhat arbitrary; I chose the 15% cutoff so pitchers with mixes like Flaherty’s in 2021 would appear in the bucket with two pitches. I then took each bucket and looked at the group’s strikeout rate, walk rate, FIP-, and WAR per 180 innings pitched. I found that between two, three, and four pitches, there was virtually no difference in any of the measures; the strikeout and walk rates were within a percentage point, as were the FIP- figures, while the prorated WAR numbers were within hundredths of a win. Next, I calculated the third time through the order (TTO) effect for pitchers in each bucket. To my surprise, there again was little difference between the pitcher buckets. My hypothesis was that two-pitch pitchers would struggle to get through the order as effectively as their peers who utilized more pitches. But based on my cutoffs for a relevant pitch (15% usage), this did not seem to be the case.

From there I concluded that Flaherty leaning on his fastball and slider more was not inherently bad; there seemed to be no evidence that being a two-pitch starter was inherently detrimental to striking out batters, preventing runs, and turning over a lineup on more than one, two, or three occasions.

But upon further reflection, I was dissatisfied with my process in arriving at this conclusion. The basis for my dissatisfaction was that my criteria for determining whether a pitcher was a two-pitch pitcher or a pitcher with three to four credible offerings. I chose the criteria, as I explained above, based on the tendencies of a single player I was interested in and in a way that would fit the narrative I was trying to tell. I also felt (anecdotally) there had been an influx of pitchers in the majors who have found success by primarily relying on two pitches; some of those pitchers happened to represent clubs the public deems “smart.” Thus, two-pitch starters were not actually more flawed than their peers with more diverse repertoires.

I will address the latter part of this line of thinking later (spoiler: it is extremely flawed) but this is just how I was trying to rationalize my findings. I have seen the performances of Luis Patiño and Shane McClanahan in 2021 and Tyler Glasnow last year (he added a slider this season) in Tampa with two pitches and thought the Rays may be on to something. Same for the Astros and Framber Valdez, Cristian Javier, and Lance McCullers Jr. (until this year, when he also added a slider). Two of the most surprising break-through pitchers of the past two-plus seasons have been Kevin Gausman and Lucas Giolito, both of whom rely primarily on a fastball/offspeed combination (for Gausman, the pitch is a splitter; for Giolito, it is a changeup). Dinelson Lamet is another pitcher with exceptional results (when healthy) relying only on a four-seamer and slider. As I mentioned above, this is all anecdotal evidence backing up a potentially faulty conclusion. There is no empirical support here. This is not the most rigorous approach to research.

That led me to redo my analysis, this time with more rigor in classifying the “two-pitchedness” of a player. Before I get into my methodology for this determination, I would be remiss if I did not at least introduce the main concept I am trying to measure: the third time through the order effect (which I will denote as TTO for the remainder of this piece). This is a phenomenon that has played a massive part in determining pitching roles and deployment in this era of major league baseball. It consists of the degradation of pitcher performance as he moves through the opposing lineup. No matter how you measure it — wOBA allowed, RA9, ERA — the pitcher population pitches worse the second time through the order compared to the first and the third time through the order versus the second. Generally, the effect is measured relative to the first time through the order. Since I will be using wOBA allowed in this piece, that means the second time through the order effect is the difference in wOBA allowed for the second and first time through the order and the third time through the order effect is the difference in wOBA allowed between the third and first time through the order. For some more background on the subject, I would recommend this piece at Baseball Prospectus by Mitchell Lichtman, which was my introduction to the phenomenon. More recently, Rob Mains did a multi-part series on the TTO penalty for BP. I would also recommend these two articles from Chris Teeter at Beyond the Boxscore; the first link measures the TTO for groundball versus fly ball pitchers and the second gauges the TTO by the type of secondaries a pitcher employs.

Now, onto to my analysis. First, let’s walk through how I grouped pitcher seasons this time around. For every pitcher season from 2010-19 (I threw out the shortened 2020 season) where the pitcher in question threw at least 100 innings, I looked at the percentage of pitches he threw for each pitch type. All the pitches were ranked in descending order based on their usage. I pulled the top two most used pitches for each pitcher and added their usage together. The sum of the usage of the top two pitches was my gauge of the “two-pitchedness” of that pitcher season. To give an example, Walker Buehler’s two most used pitches in 2019 were his fastball and slider. The former he threw 53.2% of the time and the latter he threw 14.2% of the time. Add those two figures together and you get 67.4%. That combined number was the figure I was concerned with for each pitcher season. A pitcher who only has two credible offerings will have a value close to 90%. Pitchers with the most egalitarian mixes will be down towards 50%. So instead of using an arbitrary cutoff to gauge whether a pitcher was a two-pitch pitcher, I used a continuous number that gives us a spectrum that’s not biased in any way (unlike my analysis in the Flaherty piece).

I bucketed the combined usage of the top two pitches in increments of 10 percentage points. All players with a combined usage of their top two pitches greater than 50% and at most 60% were grouped together, then greater than 60% and at most 70%, etc. Note that we are dealing with pitchers who threw at least 100 innings in a season. This means we are considering starters and, in recent seasons, “bulk” guys or pitchers who appear after openers and are tasked with starter-level workloads without the designation of pitching as a starter.

With the pitchers bucketed I went to pitch-by-pitch data from Baseball Savant. Each plate appearance in each regular season game was given the designation of how many times that pitcher faced that spot in the batting order. I appended the information about the pitch usage bucket the pitcher fell into and then collected the data for each bucket.

Before I get to the TTO figures, let me show you the information I described towards the beginning of this article about the performance of pitchers in each bucket, now with the refined pitcher designations:

For the rest of the piece, I am going to neglect the bins with so few players because the generalized results in those bins lack any signal given the size of the sample of pitchers in those buckets. Interestingly, it seems pitchers up to 90% combined usage of their top two pitchers performed best. They tied for the highest strikeout rates and posted the lowest walk rates, lowest park and league adjusted FIPs, and the highest WAR accumulation rates of all the relevant bins. All of these figures steadily decrease as the pitch mixes become less concentrated in the top two pitches.

Case closed! We shouldn’t care if a pitcher throws a useful third and/or fourth pitch, right? I will point out that I made this point in my Flaherty piece. But this is the incorrect conclusion. The pitchers in the 80% and up to 90% bucket faced the fewest batters per appearance, followed by the pitchers in the next lowest bucket. This means that these pitchers are being pulled earlier and do not have to combat the second or TTO penalty as often as the rest of their peers and suffer a degradation in performance. Managers and front offices have realized this effect and naturally have made a conscious effort to pull these types of pitchers before the opposition gets too comfortable in the batter’s box.

So pitchers with only two heavily used pitches post better results than those who leverage more offerings, but we know those performance indicators are biased in favor of those two-pitch pitchers. This performance bias presents itself with the TTO effect, which I calculated for the buckets in the table above.

The second time penalty is the wOBA allowed difference between the first and second time through the order and the last column is the TTO penalty. From the pitcher’s perspective, positive wOBA figures are disadvantageous because this indicates hitters are performing better.

The results here are stark. There seems to be no signal in how well a pitcher performs the second time he pitches through a lineup based on his propensity to throw his top two pitches. The TTO penalty, on the other hand, steadily increases from the lowest bucket in this set to the highest bucket. For pitchers who only use their top two pitches up to 50% of the time, the TTO penalty is worth just 18 points of wOBA. By the time we get to pitchers who are effectively throwing two pitches, the TTO penalty almost doubles relative to the lowest bucket, ballooning to 33 points of wOBA. The magnitude of the TTO penalty increases steadily among the buckets. The penalty for the second bucket (more than 50%, at most 60%) is four points higher than the lowest. The third is three points higher than that, while the fourth is four points higher than the third, and finally the last bucket is four points higher than the third. This is almost a perfectly linear trend. Adding pitches clearly gives pitchers more viable options to eat up innings and go deeper into games. That is not to say pitchers with broader repertoires do not suffer the consequence of the TTO penalty; instead the magnitude of the penalty is muted relative to their peers with arsenals concentrated in just a couple of pitches.

Along these lines and with the TTO penalty results on hand, I tried to determine if adding a pitch in a given season would improve a pitcher’s ability to get through a lineup by dampening the TTO penalty. I took two approaches. The first was more restrictive, where the new pitch in question could not be thrown at all in the season prior. This meant that I took every pitcher season from 2010-19 (with the same 100 innings minimum restriction as before) and for every pitch that pitcher threw, I cross-checked with their prior season and noted if they threw the pitch at all. If the answer to that query was yes, then the pitcher was not marked with utilizing a new pitch. Correspondingly, if the answer to the query was no, I marked the pitcher as having a new pitch. The restrictive nature of this querying and flagging of pitchers and pitches made me skeptical that the results would be relevant on account of the small group of pitchers who add a completely new pitch after not using it the prior year. My skepticism was borne out in the results (Note: a previous version of this table was the exact same as the table you will see later in the article. That mistake has been rectified and the following has the updated results).

In the cases of the second time through the order penalty and the TTO penalty, there is basically no change across seasons when adding a new pitch from scratch, with changes on the scale of single points of wOBA, which is noise. There is also no discernible difference between those who add a new pitch and those who do not, based on this criterion. However, the population of pitchers who truly add a new pitch, one they did not throw prior to the season at hand, is very small.

So I changed the definition of what constituted a new pitch. For the second go around, a new pitch was one the pitcher threw at least 10 percentage points more than the season prior. Yes, 10 percentage points is arbitrary and yes, I talked about arbitrary cutoffs at the start of this piece. But I would offer that the cutoff had to be set somewhere and my choosing of the cutoff was not influenced by the pool of pitchers I was analyzing. Also, I realize that my new criterion does not technically denote a “new” pitch like the first. But the spirit of this portion of the investigation is to flag pitchers who add a pitch the opposing hitter must account for differently in a plate appearance compared to how they would have approached the pitcher in a prior season. So, if a pitcher goes from throwing a pitch 5% of the time in year n-1 to 20% of the time in year n, that is a fundamental change in their repertoire that will have massive ripple effects on how they are scouted and what a hitter is looking for in any count.

The results of my second query were more promising but hardly groundbreaking.

Pitchers who added a new pitch by this criterion shave about two points of wOBA from their TTO penalty while the rest of the population adds about five points year-over-year. One possible explanation for this seven-point wOBA discrepancy is that without making a fundamental shift to your repertoire, major league hitters can get a better handle on you the following season, yielding a more substantial TTO penalty. Another explanation, which goes hand in hand with the fact that pitchers who do not meaningfully add a new pitch actually perform slightly better the second time through the order, is that the population of pitchers who did not add a new pitch includes pitchers who decreased their usage of certain pitches. So this population includes pitchers who became more of a two-pitch pitcher season over season, thus choosing to lean into their best pitches more.

As I said at the top, these two-pitch pitchers perform better on a rate basis but do not pitch as deep into games and suffer harsher TTO penalties. This, at least to me, is the most likely explanation for pitchers who would fall under the designation of the first row of the table improving the second time they go through the order but feel the effects of a more robust TTO penalty. On the flip side, pitchers who make a pitch a more substantial part of their arsenals worsen when they go through the order the second time but make up for it by dampening the TTO penalty.

Is this a worthwhile tradeoff? Would you rather have a pitcher more dominant on a per plate appearance level but who taxes your bullpen more? Or would you want your starter/bulk guy to go deeper into the game? It obviously depends on your roster construction and how often your bullpen has been used leading up to a game, but this is a question front offices and field staff constantly juggle throughout the season and in the offseason when building their teams.

Close to 3,000 words later, what have we learned? First and foremost, when attempting to measure anything or test a hypothesis, upon the conclusion of the research it is important to reflect and ask critical questions of how you approached the problem at hand. After my initial study into the viability of two-pitch starting pitchers centered around Jack Flaherty, I concluded that two-pitch pitchers were just as effective on a per pitch basis and that they suffer no additional TTO penalty. Therefore, I surmised, rostering these types of starting pitchers should have no detrimental effects on how you build your roster and are not a reason to be skeptical of a pitcher as a viable option to churn through an opposing lineup. The issue I found was that my definition of a two-pitch pitcher was flawed, based on an arbitrary cutoff to try to diagnose Flaherty’s lack of strikeouts in the early going.

When I eliminated the arbitrary cutoff and used a more continuous definition of how much a pitcher relies on his top two pitchers, I found that pitchers with more limited repertoires were a little more effective than the rest of their peers, but did not go as deep into games. Furthermore, they suffered a much harsher TTO penalty, which is most likely the explanation for those pitchers not facing as many opposing hitters.

The idea that pitchers with only two viable pitches are better suited for short starts, bulk work, or high leverage innings is not a groundbreaking finding, but I hope putting some empirical justification behind this idea is useful and this approach relatively new (at least on the public side). This confirmation of what many evaluators believed to be true should help us ask critical questions about how players should be deployed and developed, and what sorts of pitchers a roster requires. If the Rays invest in pitchers like Shane McClanahan and Luis Patiño, how should they be used and how does that affect Tampa’s roster? Well, it seems they are following what the research demonstrates: roster a deep bullpen and use these pitchers in three to five inning stints. The same concept holds true for the Astros and Cristian Javier and Framber Valdez or the Padres with Adrian Morejon, Ryan Weathers, and Dinelson Lamet.

Another essential part of this calculus is how we should be evaluating players in the minor leagues or amateurs in the draft. The starting viability of players like Garrett Crochet and Max Meyer has been called into question in recent draft classes; the same goes for Sam Bachman in this upcoming draft. Binning these types of pitchers — with high-end fastball velocity, wipe-out breaking pitches, and a history of starting — as starters or relievers seems foolhardy. Instead, we know pitchers with this skillset can effectively get through a lineup twice but more than that and the manager is playing with fire. Given this breed of pitcher’s effectiveness per plate appearance, actively avoiding acquiring pitchers with only two viable pitches is narrow-minded. Instead, if they make it to the major leagues, teams should be trying to supplement these elite talents with other pitchers who mesh with the roles required to maximize the skills of a Max Meyer or Garrett Crochet type pitcher.

I do not believe this is lost on much of the league. I am merely suggesting two-pitch starting pitchers can be excellent players in the correct environment. But given a TTO penalty almost twice that of starting pitchers with more diverse arsenals, two-pitch pitchers need to be monitored closely. If the league allows teams to carry as many pitchers as they would like, two-pitchedness and flame throwing bullpens are here to stay. Until the rules on pitcher limit take affect, with the correct usage limited pitch mixes will continue to be valuable assets to major league clubs, provided those two pitches are high-end offerings.