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.
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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.

If you don’t look too closely, it’s easy to see Brad Hand at the top of the ERA and WAR leaderboards for relievers and shrug. He’s an excellent reliever, of course; he hasn’t had an ERA above three since adding a slider after the 2015 season. When Cleveland traded Francisco Mejia for him (and Adam Cimber) last summer, they weren’t adding two generic middle relievers; Hand was the hottest commodity on the relief-pitching market for a reason.

There’s nothing too surprising about a good reliever continuing to be good. Hand struck out 35% of the batters he faced last year; he’s up to 39% this year, which is better but not obscenely so. If you don’t look at Hand’s batted ball data, in fact, you might think nothing has changed. The fact that I wrote that, though, means that you should look at his batted ball data; something jumps out immediately there. Take a look at this graph of Hand’s groundball rate by year:

What the… Brad Hand has the lowest GB% in baseball this year, and it’s the lowest by a lot. His 9.7% mark is less than half the next-lowest rate. The distance between Hand and second-place Jeffrey Springs is the same as that between Springs and 23rd-place Roenis Elias. That’s quite a change for a pitcher who had run a higher-than-average groundball rate the last three years.

The first thing to ask when seeing a split as extreme as this is “Is it April?” Now, while it’s not April, it’s still early in the season, particularly for a reliever. Hand has appeared in 16 games this year, so let’s take a look at his groundball rate over every 16-game stretch since 2016:

Yeah, okay, something’s up.
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It’s amazing to write about baseball through the lens of a singular player like Mike Trout. The sheer totality of his excellence is fun in a way that just wouldn’t be true if you looked at all of his skills individually. Trout is an above-average outfielder, sure, but that isn’t all that fun by itself. He has great plate discipline — so too, though, does 2019 Jason Heyward, and he doesn’t spark the same kind of joy as Trout. No, the fun is that there’s basically no category you can come up with where Mike Trout isn’t good.

This got me to thinking: would it be fun to have a player who was like Trout, except not to quite the same degree? I don’t mean in the broad player value sense — in a way, every player in baseball is just a worse version of Trout. No, I mean someone who’s good at everything across the board in the same way that Trout is — just, a little less.

Trout hits for power, so our mystery player will need to hit for good (but sub-Troutian) power. Scratch both Joey Gallo and Jose Altuve from the list. They have to have an excellent eye at the plate and be judicious with their swings; sorry, Javier Baez, but the ride ends for you here. They need to be an above average baserunner, but not the best of the best — J.D. Martinez and Trea Turner both fall at this hurdle.

To work out this highly unscientific study, I started with stats from 2017-present for everyone who qualified for the batting title in at least one of the three years. This lets me cast a wide net without picking up someone whose prime isn’t happening now. First, I looked for players who were worse than Trout in a few categories: ISO, OBP, SLG, BsR/PA, BB%, and K%. (At this point in the search, I learned that Trout has a higher ISO than Aaron Judge, and I mean, wow.) Read the rest of this entry »