Robert Stephenson looked done. After a rocky 2017 (4.68 ERA, 13.8% walk rate), he pitched poorly enough in 2018 spring training that the Reds sent him down to Triple-A Louisville. A vote of no confidence from the Reds, of all teams, is a bad sign for a pitcher. In 2016, the Reds finished 30th in pitching WAR; in 2017, they finished 29th. As Stephenson toiled in Louisville, Reds pitching wasn’t setting the world on fire — the 2018 team finished 26th in WAR, allowing more home runs than every team in baseball other than the Orioles.

When Stephenson returned to the majors at the tail end of 2018, things looked grim. In four appearances, he compiled a 9.26 ERA with more walks than strikeouts. His control, always a limiting factor, looked like it might be his undoing — even in a serviceable Triple-A season, he’d walked 12.2% of the batters he’d faced. As 2018 came to a close, the Robert Stephenson story seemed nearly written. Stuff-first pitching prospect can’t harness his command and never makes good on his promise? Seen that one before. As 2018 was Stephenson’s last option year, he started 2019 in the majors, but time very much felt short.

To understand why Stephenson’s middling major league career was something more than just a journeyman starter’s struggles, you have to look back to his prospect pedigree. In 2015, Kiley McDaniel rated him as the top Reds prospect. In 2016, Stephenson slipped all the way to second. At each turn, though, he showed every tool imaginable. His fastball touched the upper 90s. His curveball was drool-inducing. His changeup wasn’t quite there yet, but you could dream on it. He scuffled in a September call-up in 2016, but for the most part, he looked the part of a future impact arm.

If that was the whole arc of Stephenson’s career, it would be just another cautionary tale about toolsy high school pitching prospects. Sometimes all the stuff in the world isn’t enough, you could tell yourself. Player evaluation is hard! But fortunately for the narrative, that’s not where the story ends. The Reds had to find a place for Stephenson on their 2019 roster, so they turned to the bullpen. Control-challenged starters, after all, are often just relievers waiting to be discovered. What has Stephenson done with the opportunity? Here are the top five relievers this year when it comes to getting swings and misses.

Swinging strike rates this high mostly just look like random numbers, but stop and think for a minute about what this means. A quarter of the pitches Josh Hader throws result in swinging strikes. Not a quarter of the swings — a quarter of the pitches. Stephenson isn’t far behind with his 21.6% rate, and that’s almost as wild. If Stephenson throws five pitches, one is getting a swing and a miss. Hader is a game-breaking curiosity, a mythical bullpen beast who strikes out half the batters he faces and swings playoff series. Robert Stephenson had a 5.47 career ERA coming into this season, and there he is in second place.

Sometimes, relievers are easy to spot. Take a two-pitch pitcher who needs a little velocity boost. Give them an offseason to work on throwing with maximum effort. There you have it, a reliever in a can. So did Stephenson add three ticks to his fastball and start maxing out that wipeout curveball scouts loved so much? Well, yes and no, but mostly no. Stephenson has added a pinch of velocity this year, but he’s not a completely remade pitcher or anything. In 2017 and 2018, his four-seam averaged 93.1 mph in starting appearances. In 2019, he’s dialed it up to 94.2 mph. Maybe he hasn’t gotten a huge velocity boost from relieving, but it’s still something.

When it comes to a secondary pitch, though, Stephenson has made a change. In his 2016 debut, he threw a fastball two thirds of the time, mixing in changeups and curveballs in roughly equal measure. In 2017, he threw a slider for the first time. The pitch was more of a power curve than anything else, thrown with a curveball grip and wrist action closer to a fastball, and it immediately became Stephenson’s best pitch. Batters whiffed at nearly half of the sliders they swung at; not too shabby for a pitch he’d never thrown before.

By 2018, Bob Steve had made the slider his go-to pitch, and analysts noticed. Though he didn’t record many major league innings in 2018, he threw 40% sliders when he did. Of the 99 sliders he threw, 18 drew swinging strikes, a 40% whiff-per-swing rate that beat anything he’d ever done with his curveball. The fastball/slider combination still didn’t produce great results that season, but the bare bones of an impact reliever were there; a decent-velocity fastball, wipeout secondary stuff, a willingness to throw a ton of secondary pitches.

That fastball, however, it’s fair to say wasn’t ready for prime time. By FanGraphs’ linear-weight pitch values, his fastball has been 38 runs below average in his career. It’s hardly better using Pitch Info classifications, at 34 runs below average. These linear-weight pitch values take balls in play, strikes, and balls into account, but the problem with Stephenson’s fastball is pretty straightforward — when batters swing at it, they destroy it. This isn’t a one-year thing, a small sample artifact, or anything benign like that. Every year he’s been in the majors, his results and expected results on contact have been objectively awful.

As you can see, the fastball has been quite poor, even in 2019. Given how much his fastball has been shelled, though, Stephenson’s 2019 is even more impressive. He has a 3.96 ERA and a 2.56 FIP despite a fastball that essentially turns every batter into Cody Bellinger. How has he pulled off that trick? Well, he stopped throwing fastballs, that’s how. Take a look at the qualified relievers who have thrown the most sliders this year.

Want to limit the damage done on fastballs and leverage your excellent slider? Sometimes the solution is pleasingly straightforward — throw as few fastballs as possible, and replace them one-for-one with your best pitch. This play only works in relief, as you can’t exactly throw 60% sliders as a starter, but his slider is so good that even when batters know it’s coming, they can’t hit hit.

Stephenson’s slider is gorgeous when he throws it out of the zone. Jung Ho Kang surely has sliders on the brain here, but still bends the knee.

Keston Hiura manages to get the bat on the ball, but only barely, and the result is the same.

These are the kinds of sliders that end at-bats, and Stephenson is adept at hunting strikeouts with the pitch. He’s getting whiffs on 56% of swings against his slider, a frankly mind-boggling number. But as well as the slider plays as an out pitch, that’s not the only thing Stephenson uses it for.

When Stephenson first developed his slider in 2017, he used it in the way most pitchers use sliders. It came out late in counts as a hammer, a pitch that looked like a fastball early before falling off the table late. While he dabbled with it early in counts, it was largely a pitch to be used while ahead. This year, that dalliance with early-count sliders has become a full-blown romance. Stephenson is throwing sliders to open at-bats 62% of the time in 2019. If the count gets to 1-0, he still goes to his slider 43% of the time. 2-0? Still 42% sliders. On 2-1 counts, Stephenson throws 70% sliders. He’s using the pitch in every situation, whether it’s a traditional slider count or not.

This adjustment is a stroke of genius for someone who can’t afford to let batters tee off on his fastball. As a batter facing Stephenson, you desperately want to avoid a two-strike count, because a two-strike count against Stephenson’s slider is a sure way to end up in a Pitching Ninja GIF. Best, then, to swing at an early fastball. It’s the pitch you want to hit, after all. The next step in that game theoretical confrontation is for Stephenson to throw sliders in fastball counts, and either throw enough for called strikes or be deceptive enough that batters can’t just leave the bat on their shoulders.

Amazingly enough for a pitcher who came into 2019 with a 13.6% career walk rate, Stephenson has pretty good slider command. He’s locating 45% of his first-pitch sliders in the zone, enough that hitters can’t wait him out. His overall slider zone rate of 46% is comfortably better than average (43% for the big leagues as a whole). When he does miss the zone, he’s missing close — he already has nine swinging strikes on out-of-zone sliders to start at-bats this year, the most of any reliever and only three behind slider factory Patrick Corbin for most in the majors.

Though he throws the slider in the strike zone less often than his fastball, the slider has proven to be more effective at managing counts. For his career, he’s located 52% of his fastballs in the zone to open at-bats, a slim lead over the slider. The pitch generates almost no out-of-zone swings, though, which undoes the edge he gets from having more pitches in the zone, and that’s before we even get to what happens when batters do swing. When batters swing at fastballs, they might hit them, and with Stephenson’s fastball, you don’t want that. Take a look at Stephenson’s first pitch outcomes, both in his career prior to 2019 and in 2019.

Those balls in play are mostly fastballs, and letting batters put first-pitch fastballs into play isn’t where you want to be when your fastball is as flat as Stephenson’s. Emphasizing the slider has moved all three results the way you’d like to see them move, and even if it’s a small sample size, it’s encouraging to see such promising first-pitch numbers. The league as a whole has a .364 wOBA after a 1-0 count and a .267 wOBA after 0-1. Those 13% of plate appearances that Stephenson has moved from the 1-0 or in play bucket to the 0-1 bucket are like facing Brandon Drury instead of Ronald Acuña 13% of the time — that’ll do nicely.

Maybe you’re a skeptic. Maybe you think that anything can happen in 25 innings, that the dead can walk and a minor leaguer can look like an effective reliever, if only briefly. Maybe you’d prefer to point to Stephenson’s 3.96 ERA and say that even if this is a new skill level, a high-3 ERA reliever hardly merits a deep dive. I don’t see that, though. I see a celebrated prospect who was legitimately not good enough to stick in the major leagues by doing what he’d done his whole life. I see that celebrated prospect making up a new pitch on the fly, throwing that pitch 60% of the time, and excelling in the major leagues with it. Robert Stephenson was a cautionary tale, and now he’s an impact reliever with a hellacious put-away pitch he can throw in any count. In what has so far been a frustrating Reds season, it’s great to see a former prospect make good.

Friend, you’re a baseball fan. You don’t need me to tell you that the Astros are great, because you already know it. You probably know they’re playing .650 baseball so far this year. If you look at their run differential, you might notice that their Pythagorean record is actually better than their record — they “should” have one more win based on their run differential. Heck, if you look at BaseRuns standings, which look at underlying production rather than runs, they “should” have three more wins. Their offensive and defensive statistics work out to a projected .700 winning percentage. That’s a 113-win pace for a full season, and playing well enough to have a 113-win season with neutral luck is outrageous.

You also don’t need me to tell you that the Astros offense is great. Their team batting line so far this year is .275/.349/.488, good for a 126 wRC+. If the entire Astros offense were a player, they’d be a top-60 hitter in all of baseball. Not the Astros starters. Not qualifying Astros batters. The entire team, backup catchers and minor league call-ups and all, is producing slightly better than Ronald Acuna this year. Ronald Acuna signed a $100 million contract this year and people protested how underpaid he is. Again, the entire Astros team is hitting like that.

The thing is, though, you also already knew that. Astros offense superlatives and near-superlatives are endless. They strike out less than any team but the Angels. They hit for more power than any team other than the Twins. They get on base more than any team in baseball. In a stadium that doesn’t help offense, they’re scoring 5.2 runs a game, with underlying statistics that look like they should be scoring 5.5. They’re hitting for the highest batting average in baseball and simultaneously have the third-most home runs, all without having played the Orioles. Average or power? Porque no los dos?

Yes, finding new and interesting things to say about the Astros offense is challenging. I’m going to try, though. One of the strengths of this Astros team is their incredible star power. George Springer is vying with Mike Trout for the most WAR in the American League, with a 172 wRC+ that’s sixth in baseball. Alex Bregman is replicating his breakout 2018 — a 152 wRC+ with more walks than strikeouts. He’s running a BABIP of .237 despite an xBABIP of .316 — he could actually be due for some positive regression! Michael Brantley has turned the Astros’ one lineup hole from 2018, left field, into a point of strength. He’s striking out a what-are-you-talking-about 9.5% of the time while hitting for power on his way to a 144 wRC+.

Those three players have been worth a combined seven wins above replacement. They have a collective 156 wRC+. The only teams with a better-hitting top three (minimum 100 PA per batter) are the Dodgers and the Cubs (the Pirates are a close fourth). The Astros’ stars, in other words, are the envy of nearly all of baseball. As an aside, the best three Marlins batters have put up a cumulative 99 wRC+. What’s an article about a great offense without a fun fact about the inverse?

That’s all well and good — the cream of the Astro crop is incredible. You probably knew that, because all three players are drawing headlines. Great, cool, amazing. What you might not know, though, is that the rest of the offense is incredible as well. Think of it this way: George Springer just went on the 10-day IL with a hamstring strain. How will the Astros offense fare without him? Well, the rest of their team has combined for a 122 wRC+ this year, which would be the second-best batting team in the majors, behind only the equally hot Twins.

We can take this further. Let’s get rid of Bregman as well. Without Bregman and Springer, the Astros would have a 116 wRC+, good for the fifth-best non-pitcher wRC+. Two MVP candidates down, the Astros are nipping at the Cubs’ heels for fourth-best offense in baseball. Heck, let’s go further and take out Brantley. With all three of the Astros’ top trio removed (and again, they’re one of the best groups in baseball), the remaining Astros have compiled a 112 wRC+ this year. That batting line would be fifth-best in baseball, just ahead of the Braves. The Braves have a dynamic offense, with sensational young talent backed by Freddie Freeman. That’s how good the Astros are after you get rid of three MVP candidates. If that doesn’t make much sense to you, well — good. It’s outrageous!

We can go further. The weighted wRC+ of the Astros’ 4th-6th best hitters (Carlos Correa, Jake Marisnick, and Robinson Chirinos) is 137. Want to replace Marisnick’s small sample with a larger sample of a worse batting line from Josh Reddick? It’s still 133. As you might expect, this group of 4th-6th offensive options is the best such group in baseball. The Rangers’ trio of Logan Forsythe (not as washed up as I expected), Elvis Andrus, and Danny Santana are within striking distance at a 127 wRC+, but no one is particularly close to matching the Astros’ trio. Heck, this Astros group is better than 15 other teams’ top three hitters, even if you use the lower-wRC+ Reddick group. The Astros’ mid-tier guys are simply unlucky — they’d be the best three guys on plenty of teams.

Let’s get really crazy now. Let’s exclude the six best hitters from the Astro lineup. I’m cutting Reddick out here in the interest of making the remaining lineup score as poorly as possible. With none of their top six hitters, the Astros have a remaining team wRC+ of 98. The back half of the team, the part that is largely comprised of fifth outfielders and utility infielders and backup catchers, is almost as good at batting as the league as a whole.

If that sounds absurd, it’s because it is. There’s an MVP candidate having a so-so year in this group (Jose Altuve and his 117 wRC+), which is only notable because it’s not one of the best eight batting lines on the team. Aledmys Diaz has a 118 wRC+, which would rank among the top 10 second basemen in baseball if he could get on the field enough to qualify. Heck, even Tony Kemp’s 86 wRC+ isn’t too bad — it’s certifiably great for a fifth outfielder, but it’s not even embarrassing for the worst regular starter on a team, which Kemp most emphatically is not.

How stacked is this Astros team? If the top six Astros weren’t allowed to bat and instead of replacing them with minor leaguers, the team filled in the missing plate appearances with the remaining players’ 2019 lines, the team would project to score roughly 4.5 runs a game after accounting for park factors. With the team’s great pitching (3.53 runs per game allowed), their Pythagorean winning percentage would be .611. The hobbled Astros would have the fifth-best Pythagorean winning percentage in baseball. Want it in BaseRuns? That still works out to a .610 expected winning percentage, fourth-best in baseball.

Now, in reality, this is more of a fun fact about the Astros pitching staff than one about their hitters. Replace the historically dominant Astros offense with a sub-100 wRC+ bunch, and the team would still be one of the best in baseball. Their pitching is just that good. But it’s also an Astros offense fun fact because that 100-ish wRC+ team just so happens to be the Astros’ offense after subtracting out their six best hitters in 2019.

Just to drive the point home, here’s a table of the Astros offense, only subtracting out their x best hitters. The distance you have to go down the line to make a bad team is staggering. The Astros minus their top nine hitters would have the same wRC+ as the Indians this year!

The 2019 Astros are an exercise in baseball absurdity. Their best hitters are as good as any team’s best hitters. Their mid-tier hitters are better than a bunch of other teams’ best hitters. Their worst hitters are league average. If it’s hard to wrap your head around how good this team is, that’s reasonable. Teams don’t bat this well for full seasons. Since 1900, the only team with a better league-adjusted full-season line is the 1927 Yankees, who were literally nicknamed Murderer’s Row. Teams that hit like the Astros are dimly remembered myths, not flesh-and-blood modern concerns. That’s not a comparison you can make in your head, most likely, because it isn’t one I can make in mine.

Getting rid of the good players makes a comparison a little more mentally reasonable. Remove three MVP candidates, and the Astros are still one of the best-hitting teams in baseball. Remove three more of the best hitters in baseball, and the dregs of the team still hit like the A’s or the Nationals. So don’t focus on the aggregate line, the pure statistical absurdity of the 2019 Astros. Focus on how well every part of the Astros lineup is hitting, how their utility infielder hits like your All-Star second baseman. This performance almost certainly won’t keep up, but it’s still amazing to marvel at the extent of their excellence in 2019.

The height of fashion in baseball analysis three years ago was finding a reliever who could pitch multiple innings. Some people called it the Andrew Miller role, though Miller was never a perfect example of it — aside from the memorable 2016 playoffs, Miller was more of a setup man who occasionally threw the seventh in his tenure on the Indians. Chris Devenski and Chad Green were trendy examples in 2017, and Mets swingmen Seth Lugo and Robert Gsellman both performed admirably in long relief in 2018.

Whichever example you turn to, the value of having a reliever who can perform over multiple innings of work is clear to see. As starters throw fewer innings across baseball, having relievers who can handle larger workloads is increasingly important. A two-inning reliever might have been a luxury in 2009, when a seven-man bullpen would cover two or three innings a night, but 2019 bullpens go eight deep and pick up nearly four innings a game. Using relievers to cover more innings naturally results in weaker relievers getting into games, so getting extra frames out of good relievers has never been more valuable.

That’s the theory, anyway. In practice, the role isn’t easy to fill. If you’re looking for someone to throw a few innings of relief, they have to be a decent pitcher. There’s not really much point in filling bulk innings with replacement-level stuff — you could just use the back of the bullpen for that. There’s just one problem with that: a good pitcher who can throw multiple innings mostly describes a starter, and getting rid of a good starter to create a good reliever doesn’t make that much sense. Blake Snell, for example, would probably make a great reliever, but that would be a waste of his talent. Read the rest of this entry »

The book on Luke Weaver was written before he had played a game of professional baseball. Great changeup, good fastball, no third pitch. I mean “the book” metaphorically here, but I also mean it literally. Here’s Eric Longenhagen on Weaver before the 2017 season:

“Those who have questioned Weaver’s upside (myself included) did so because, in college, he lacked a good breaking ball. Weaver’s fringey curveball remains so today, but he’s a good athlete who has developed plus command and added an average cutter to his repertoire in pro ball.”

Cardinals fans got two years of data to back up that assessment — a scintillating 2017 (3.17 FIP, 28.6% K-rate) and a frustrating 2018 (4.45 FIP, fewer strikeouts and more walks) were worth a combined 2.7 WAR, but between underperforming his FIP and losing his rotation spot in the second half of 2018, Weaver felt like a surplus arm. The changeup and sneaky good fastball were as good as advertised, but batters consistently teed off on his curve. When Weaver and top catching prospect Carson Kelly were sent to the Diamondbacks in exchange for Paul Goldschmidt, it felt like a needed change of scenery for both of them.

If the book on Weaver was written while he was still in college, it’s a safe bet that he’s had time to read that book. He has worked towards developing a better breaking ball more or less every offseason of his pro career, and 2019 was no exception. This time, though, he had technological help. He bought a Rapsodo, a portable pitch-tracking camera, and used it to work on his curve. He took his cutter (or is it a slider?) out of mothballs, telling David Laurila he was picking up the hybrid pitch after years of being mainly fastball/change/curve.
Read the rest of this entry »

Freeze baseball at the end of last year, and Josh Bell fit into an ignominious archetype. A former top prospect, he’d fallen into the power-light first base role previously occupied by the likes of James Loney and Sean Casey. The good power vibes from a homer-happy 2017 (26 dingers, .211 ISO) had faded after his slap-hitting 2018 (12 home runs and a .150 ISO). FanGraphs’ Depth Charts projections penciled him in for a .172 ISO and a wRC+ around 113 — roughly average offensive production for a first baseman.

If that projection was surprising, it was only because Bell looks the part of a slugger. At 6-foot-4 and 235 pounds, he’s an imposing presence at the plate. His minor league numbers had never showed great thump — his best showing was a credible .173 ISO with 14 homers in 2016. After that 2016 season, Eric Longenhagen graded him as having 50 game power — dead average, with the chance to improve to a 55 eventually. Bell’s frame always carried the promise of greater power numbers, but neither scouts nor projection systems thought it was a likely outcome.

That’s all well and good, but uh, have you seen Josh Bell’s 2019? He’s recorded a ludicrous .364 ISO, fifth-best in the majors. He already has 14 home runs and 14 doubles (and, perplexingly, two triples), besting last year’s home run output in only 188 plate appearances. This prodigious power, along with a .366 BABIP, has propelled him to a 185 wRC+, third-best in baseball. The power that was promised by Bell’s physical gifts has finally come in, and it’s come in all at once.

When someone puts up a line like Bell’s (an ISO that looks like a BABIP, a season-long wRC+ higher than any previous month of his career), my natural inclination as an analyst is to look for flukes. Maybe he’s hitting an unsustainable number of line drives, or 75% of his fly balls are turning into home runs. Perhaps he’s faced abysmal pitching in hitters’ parks. Surely any of those explanations is more likely than a sudden, real power spike that dwarfs his previous career. Read the rest of this entry »

Last week, I investigated the changing performance of starters relative to relievers. There’s nothing too crazy about that — FanGraphs is a baseball analysis website, after all, and the starter/reliever divide is a rich topic for analysis. I have to confess, though, that the reception of the article was pretty exciting for me. You see, I got into baseball statistics when a friend recommended The Book to me, and there was Tom Tango, writing about my piece.

Aside from making me feel validated, Tango went over a few methodological improvements I could make to strip a little more noise out of the data. That, in essence, is what all of this analysis is doing — removing noise piece by piece, hoping to find the sweet, sweet signal underneath it all. In my initial article, I covered three topics: pitchers the first time through the order, starters vs. relievers but only using good pitchers, and swingmen. Today, I’d like to look at each of the three with a slightly different aim.

First, let’s talk about performance the first time through the order. Focusing on this consistent set of data (first time through the order, batters 1-7) for both starters and relievers lets us strip out distributional effects from starter workload changes. Merely looking at these splits, however, left out one key factor: home vs. away performance. Mitchel Lichtman has found that home field advantage isn’t a constant — it’s highest in the first inning. Road batters have a pronounced disadvantage relative to home batters in the first inning, which fades away somewhat afterwards. Credit it to having to hit cold, or go the other way and say that road starters are off their game in the first inning, but it’s worth exploring home and away splits to see if there’s anything there. Read the rest of this entry »

The title gives the suspense of this one away, I know. I thought about leaving it as a mystery, a tease. “Five great MLB relievers — you won’t believe number four!” After thinking about it for a bit, though, I decided suspense was overrated. Kirby Yates has been great the past two years. Like, really great. Even if you think that Kirby Yates has been great, you probably are underestimating just how great he’s been. Here, guess the top five relievers of the past two years by FanGraphs’ WAR.

Now, I don’t know about you, but I got four of the five names. Given that you’re reading an article about Kirby Yates, you presumably didn’t make the same mistake that I did. Context clues and all. Maybe you read Matthew Trueblood’s article about him at Baseball Prospectus yesterday and had him on the brain. Still, though, even FIP can be fluky. How about the best K-BB rates over the last two years?

Hey Nick Anderson, looking good. And there, again, is Yates, striking out the world and walking no one. Read the rest of this entry »

Take one look at the numbers, and Yu Darvish is having a pretty rough 2019. A 5.40 ERA is bad enough, but he’s actually outperforming his FIP, which sits at a grisly 6.49. While it’s only eight starts, a small enough sample that I’d normally counsel patience, Cubs fans surely don’t feel that way — 16 games into his Cubs career after an injury-shortened 2018, Darvish has compiled a 5.16 ERA (5.64 FIP) and been worth -0.1 fWAR. A closer look at Darvish, however, makes the picture far more muddled. Despite his undeniably rough start, silver linings abound in his underlying statistics.

The story with Darvish has to start with walks. No one would ever call him a control pitcher (he’s had a walk rate higher than league average in five of his seven seasons), but he’s veered from effectively wild to caricature this year. His 19.3% walk rate is not only first in baseball, it’s first in baseball by a comical margin — among pitchers with 30 IP, he’s as far ahead of second-place Brad Keller as Keller is ahead of 54th-place James Paxton. It’s early in the season to start considering Darvish’s place in history, but full-season walk rates like these haven’t been seen since young Randy Johnson.

Let’s leave aside the walks for a moment, though. Take those out of the picture, and you might struggle to differentiate Darvish’s 2019 from the rest of his spectacular career. Here are Darvish’s groundball/fly ball ratio and hard-hit rate for every year of his career.

Darvish has not only amassed an average-ish hard-hit rate, he’s getting grounders like he never has in his career. Those are hardly the numbers of a pitcher with a 5-handle ERA. What gives? Read the rest of this entry »

If you read about baseball on the internet these days, it’s tough to miss pieces on the changing relative skill levels of relievers and starting pitchers. As Sam Miller pointed out on Effectively Wild, relievers have a higher ERA this year than starters. Not only that, but the strikeout rate advantage relievers have traditionally had over starters is plummeting. Look at almost any statistic, and the historical edge relievers have had over those in the rotation has diminished.

At the same time, relievers are setting volume records left and right. For five straight years, relievers have set a new record for largest share of pitches thrown. In 2012, Rockies relievers struck out more batters than Rockies starters for the first time in baseball history, and you could convince yourself that it was a Coors field oddity. In the next six years, however, four more teams did it. From a bulk perspective, relievers are pitching more and more innings, carrying ever more of baseball’s pitching workload.

Clearly, these two effects are correlated. You’ve undoubtedly heard of the times-through-the-order penalty, the concept that starters fare worse each time through the batting order. In tandem with the innings spike by relievers, the number of pitches starters throw their third time through the order is plummeting. It’s not rocket science — the third time through the order is the time when starters are weakest, and those weak points are disappearing. Of course starters’ stats look better!

Given the changing roles of starters and relievers, it’s probably not right to look at unmodified splits to figure out whether starters are actually getting better relative to relievers. Even if the talent level of every pitcher remained exactly the same, cutting out a chunk of third-time-through plate appearances from starters’ cumulative totals will change their statistics. To actually see whether relievers are getting better relative to starters, we’ll need to do something a little fancier. Read the rest of this entry »

On May 17, 2018, Paul DeJong stepped to the plate in a tense situation. The Cardinals were down 4-0 in the eighth, but were rallying — two on, nobody out. On a 2-2 pitch, DeJong saw a pitch inside, and he didn’t exactly get out of the way:

After a replay review, DeJong went to first base. Then, he went to the doctor. The diagnosis: a broken hand. DeJong sat out nearly two months, and when he came back, his power lagged. At the time of his injury, he’d slugged his way to a 125 wRC+ and .213 ISO. The balance of the year, he compiled a 90 wRC+ and a .182 ISO, and the first month back was particularly dire: 59 wRC+ and a Hamiltonian .090 ISO.

Clearly, getting hit by that pitch wasn’t worth it. DeJong is one of the best players in baseball this year, and he was off to a solid start last year before getting hit. If it weren’t for that power-sapping injury, we might be talking about him as a consistent star rather than an out-of-nowhere surprise. At the time, though, it surely made sense to take one for the team. Reaching base there was huge — it increased the Cardinals’ chances of winning the game by almost 10%.

In a full season, a league-average baseball player (think Kevin Pillar or DJ LeMahieu’s 2018) is worth around two wins above replacement. That’s over 600 plate appearances — each trip to the plate adds infinitesimal value. DeJong had a chance to get 1/20th of that value in a single plate appearance, and he didn’t even have to do anything. As the saying goes, “We got ice.” Accepting a hit by pitch to get on base is a time-honored tradition. But is it worth it?

While this question seems pretty straightforward, it’s a thornier problem than it first appears. For example, if a career minor-leaguer, who is only up for the day, is at the plate, it almost doesn’t matter how likely it is that he’ll be injured; it probably makes sense to lean into one. If Mike Trout is at the plate, on the other hand, he should probably be exceedingly cautious. I don’t have all the answers. I do, however, have a theoretical model that should help you know how to feel about any given player taking one for the team.

To start, we’ll need an idea of the likelihood of injury. Anecdotes are great and all, but to judge the likelihood of injury we’ll need more. The DeJong example above is great, but he’s been hit by 18 pitches in his career. Cherry-picking one or two is no way to study this. Luckily, The American Journal of Sports Medicine published an excellent study on HBP injuries last year, and we can use their data.

Between 2011 and 2015, the study counts 361 HBP’s that caused injury in MLB, averaging 11.7 days missed per injury. That gives us a rough baseline for days missed per injury, averaging over the bruised ribs that might result in a precautionary day of rest and the broken hands that linger. Add in the total number of HBP’s from 2011-2015 (7838), and we can work out how likely an injury is to occur each time a batter is hit.

Armed with this data, let’s take our first naive pass at estimating the net benefit of letting yourself get hit. For this example, we’ll use Trout. Trout’s projected 2019 wOBA is .432, while being hit by a pitch clocks in at .720. Through the magic of wOBA, we can work out the run value of that single event — in this case, about a quarter of a run. In other words, every time Trout gets hit by a pitch, that plate appearance is worth .25 runs more to the Angels than a random Trout plate appearance. Not bad!

Next, let’s turn to the dark side. In the study data, about 5% of HBP’s resulted in injury. The average time missed per injury was roughly 11.7 days. In all, getting hit by a pitch costs around half a day lost due to injury, though most HBP’s have no lasting ill effects. For ease of calculation, we’ll assume Trout gets replaced by a replacement-level player and gets 4.5 plate appearances a day, basically his career average.

Sticking with projections, Trout is worth about 8.4 WAR per 600 PA. Do the math, and a half-day absence costs Trout just under a twentieth of a win above replacement. By substituting in this year’s run value for a win, we get that Trout’s absence costs the Angels a third of a run. Whoops! Given that the initial event was worth about a quarter of a run, every time Trout gets hit, the Angels lose expected value.

Well, we’ve established one extreme. Mike Trout shouldn’t lean into a pitch — his continued health is too valuable. Let’s run this again for a 100 wRC+, league-average WAR player. Joe Average has a .316 wOBA, so getting hit by a pitch is more valuable to him — he picks up a full third of a run by hanging an elbow out there. At the same time, Joe’s team doesn’t miss his absence nearly as much — he costs them a tiny fraction of a win through his expected absence. That said, that still works out to .12 runs. Joe Average should lean in, but he doesn’t benefit his team all that much by doing so.

To find a player who should really consider stocking up on body armor and going full Brandon Guyer, we need to get into the fringes of a major league roster. A perfectly average player is a valuable commodity, after all. How about a utility infielder, though? Consider Hernan Perez, the do-everything Brewer who played every position except catcher last year, but hit quite poorly while doing so.

Perez has a .288 career wOBA, so let’s use that in our equation. He projects to be worth about 1 WAR in a full season of games, but he doesn’t play every game. In fact, he has averaged about two-thirds the plate appearances of a regular, so we can ignore one-third of the plate appearances he misses as times when the team already wasn’t planning on using him. Perez’s lean grants him .36 runs over his normal output, a significant upgrade. He then misses fewer at-bats, and his value is easier to replace — in all, his absence costs the team only .03 runs. We’re slicing things thin here, but if Hernan Perez has a chance to get hit, it looks like he should take it.

These examples lack context, though. Trout might pick up .25 context-neutral runs every time he’s hit, but plate appearances don’t come without context. If the Angels are up 10, those runs are meaningless. If they’re in a tie game, they’re incredibly valuable. Let’s redo the analysis, but this time consider how many expected wins being hit adds, rather than how many runs.

To start, consider an extreme situation. It’s the bottom of the ninth, and the Angels are locked in a tie game. The bases are loaded, with two outs, when Trout steps to the plate. Get on base, and the game ends. Make an out, and we’re headed to extras. This is the situation where getting hit is most valuable — if you get hit, you literally win the game.

In a normal plate appearance, Trout is already a great player to have at the plate in this situation. His OBP projection for the balance of the year is .446. Thus, you can think of the chances of the Angels winning the game as .446*1 (he gets on base, they win) plus .554*.5 (he makes an out, the game goes to extra innings and the Angels are 50% to win). This makes the Angels 72.3% likely to win the game at the moment Trout steps into the box. Getting hit increases the chances of a win to, well, 100% — a 27.7% pickup.

In the Trout section above, we worked out that Trout’s expected absence costs the Angels about a twentieth of a win. It looks like it might make sense for any hitter, even Mike Trout, to accept a HBP in the highest-possible-leverage situation. We’ve defined the boundaries — in a normal plate appearance, you need to be a below-average backup for accepting a base to make sense. In the most dramatic possible situation, everyone should do it. What about the spaces in between, though?

Well, this section is going to veer into bad math, but given the speculative nature of this article, I think I’m okay with that. Rather than work out the exact win probability change for each outcome, as we did for the Trout example, let’s just use leverage index. In essence, leverage index measures how important a plate appearance is in terms of swinging the outcome of the game. Average is 1.0, so a plate appearance with a leverage index of 2.0 means that the result of this plate appearance will, on average, change win expectancy twice as much as a random at-bat.

Now, leverage index isn’t perfect. In some situations (like my hypothetical above), a home run is the same as a walk. In others, say second and third with two outs when your team is down by two runs, hits are incredibly valuable and free passes much less so. Still, it gives us a template. Let’s revisit Joe Average using LI.

Joe steps up to the plate to start the bottom of the ninth inning, down 2-0 (LI 1.97). Rather than compute the exact change in win probabilities for each outcome, let’s just multiply his run value by the leverage index. From above, being hit is worth .34 runs. Multiply that by the leverage of the situation, and it’s the equivalent of .68 runs in a context-neutral situation. Since his absence costs his team about .12 runs, the calculus is clear — in high leverage spots, Joe Average should accept a hit by pitch if he wants to help his team win.

Let’s rewrite this as a formula. If you want to know whether it makes sense for any player to take one for the team, you can roughly use this:

(.720- wOBA) / 1.194 * LI – 10.026 * PA/Game * .54 * WAR/PA

A quick breakdown: .720 minus the player’s wOBA gives the extra wOBA accrued by being hit, and dividing it by 1.194 (wOBA scale) puts it into run terms, where it can be multiplied by the leverage of the situation. At 10.026 runs a win and .54 days of expected absence per hit-by-pitch, you can work out the expected run cost of an injury by plugging in the hitter’s playing time and skill level.

There’s still one thing left to cover. Should Paul DeJong have been trying to get hit? Let’s plug it into the formula and find out. When DeJong got hit, the Leverage Index was exactly 2.0. ZiPS projected his 2018 wOBA as .320 before the season (2.1 WAR/600 PA), so we’ve got all the values we need. DeJong earned .67 context-neutral runs by being hit, and his expected absence cost the team a mere .09 context-neutral runs. It was worth it, ex ante, to get hit there.

Now, all of this said, this model isn’t the last word on the subject. It’s extremely approximate, for one. It doesn’t cover any reduced effectiveness that doesn’t involve missing games, a notoriously difficult problem to study. Lastly, it treats getting hit as a binary act that doesn’t interact with the rest of the game. Anthony Rizzo needs to get hit to be Anthony Rizzo — he’s made a career out of standing with two-thirds of his body hanging over the plate to hit outside pitches. Accepting a hit by pitch might sometimes be optional and independent of the rest of the game, but sometimes you can’t disentangle it.

Still, having a rough guess of the benefits and costs of a free trip to first base beats having no idea. Should you get hit by a pitch? Maybe! It depends who you are, and it depends on the game state. The next time you hear an announcer say “We got ice,” know that it’s not that simple. It might be a baseball truism, but without knowing the context, you can never say for sure. There are situations where Mike Trout should get hit by a pitch, and situations where a below-average player should shy away from contact. Nothing in baseball is ever black and white.

Note: The initial version of this article incorrectly included instance of hit by pitch in both the major and minor leagues; is has been updated to correctly reflect the likelihood of injury due to being hit by a pitch.