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.
Read the rest of this entry »

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 »

When a meteoroid strikes the top of the Earth’s atmosphere, it’s traveling at an unthinkable speed — something like 30 miles per second. Though it’s initially as cold as the void of space, the friction of striking the atmosphere creates intense heat. The thermal energy is sufficient to vaporize it, layer by layer. If the meteoroid survives long enough to strike the Earth’s surface as a meteorite, its outer layer will be blackened beyond recognition. I learned all this on Wikipedia today, because I wanted to understand what it must be like to face Tyler Glasnow.

Tyler Glasnow is a singular pitcher. He stands 6-foot-8, one of only three current major league pitchers that tall. He throws a 97.4 mph fastball. Among starters, only Noah Syndergaard throws harder. It’s not so much that Glasnow releases the ball tremendously high in the air; he’s a long strider, which lowers his release point. It’s more that there’s no one in baseball who throws quite like Glasnow throws — at extreme velocity, with extremely long levers, from a unique release point. Glasnow’s perceived velocity is second only to Jordan Hicks — his fastball explodes towards batters.

As if that weren’t enough, Glasnow’s curve has long been above-average. Want to know how long this has been the scouting report on Glasnow? Take a look at what Eric Longenhagen had to say about him before the 2017 season: “Glasnow’s scouting report has read the same way for the last four years. He throws hard, has touched 100 in the past (I have him maxing out at 97 this year) and spins one hell of a curveball — a potential plus-plus curve, in fact.”

The knock against Glasnow has always been control. In the minor leagues, he often ran double-digit walk rates, and when he got his first extended playing time in the majors in 2017 he walked 14.4% of the batters he faced. Glasnow was a project — and there was hope that his command would come. Here’s Longenhagen again: “That said, there are reasons for patience with the command. Glasnow’s velocity exploded in pro ball, and it’s not easy for someone to quickly learn how how to harness and command that kind of newfound arm speed — and even more difficult when the prospect in question is built like a giant whooping crane.” Read the rest of this entry »

Take a look at a 2019 WAR leaderboard and you’ll see some familiar names at the top. Cody Bellinger is having a whale of a season. Christian Yelich is hitting like Barry Bonds and is somehow second in the majors in baserunning runs as well. Mike Trout — well, you know Mike Trout. Look a little closer though, and you might notice something strange. There are four shortstops in the top 10 for WAR this year, and they’re not the usual suspects. Paul DeJong, Elvis Andrus, Jorge Polanco, and Javier Báez are all having great seasons so far, and if you had them as the four best shortstops in baseball this year, you’re a better prognosticator than I am.

Cast your eyes a little further down the board and you might see an interesting trend. Marcus Semien is 11th in WAR. Tim Anderson, Trevor Story, Xander Bogaerts, and Adalberto Mondesi are in the top 25, and Fernando Tatis Jr. isn’t far behind. Perennial stalwarts Andrelton Simmons, Corey Seager, and Carlos Correa are off to good starts. Shortstop, in fact, has produced more WAR than any other position this year.

Now, to some extent, that’s a referendum on how important shortstop is defensively. Only catcher has a higher positional adjustment than shortstop, and as a result only catchers have been worth more defensive runs this year. However, dismissing the prevalence of shortstops atop the WAR leaderboard as a defense-based illusion sells this current crop short. We could very well be looking at the best-hitting shortstop season of all time.

Let’s start at the very top with wRC+. This year’s shortstop class has produced a 107 wRC+ so far. That isn’t the actual best in baseball history, but it’s second only to 1874, and hoo boy are stats from 1874 weird. In that season, shortstops walked .9% of the time, struck out 1.2% of the time, and delivered a batting line of .305/.311/.372 in only 660 games. Let’s be reasonable here and throw out everything before the turn of the century. Cut those out, and the leaderboard looks like this:

2019 shortstops are on top, and it isn’t particularly close. Strip out everything pre-integration, and the recent rise of slugging shortstops jumps out even more:

Ask most baseball fans for the best shortstop-hitting season in history, and they’ll point to 2002. This was indeed a year of great shortstop hitters — Alex Rodriguez hit .300/.392/.623 on his way to a 10-WAR season, and Derek Jeter, Nomar Garciaparra, and Miguel Tejada all had sterling years. That’s all well and good — it was a top 10 season on the above leaderboard, after all — but 2002 also had 585 plate appearances of Neifi Perez’s .236/.260/.303 line, as well as a shockingly low-offense season from Rockies shortstop Juan Uribe, who hit .240/.286/.341 while playing half of his games at Coors.

This season has its fair share of laggards (Brandon Crawford is slugging .212), but it also has 16 shortstops with a batting line at or above league average. Freddy Galvis is hitting .297/.317/.485 and is the 14th-best-hitting shortstop this year. That 114 wRC+ would have been sixth-best in 2002. The depth of shortstop right now is simply stunning. Read the rest of this entry »

2018 wasn’t supposed to be the year of Juan Soto in Washington. It was supposed to be the year of Victor Robles. Robles, the consensus No. 1 outfield prospect in the Nats system and probably the No. 2 outfield prospect in all of baseball behind Ronald Acuña, was ready for the majors. Only a hyperextended elbow kept Robles from making an impact in the majors last year, but in abbreviated playing time in August and September, he looked like he was making up for lost time (.288/.348/.525, 131 wRC+).

Robles’ 2019 hasn’t been quite as impressive, but you can see in his performance why he’s such an exciting talent. Even while running a 30.5% strikeout rate and walking only 4.8% of the time, Robles has put up a league-average batting line (.265/.308/.480, 102 wRC+). Watch Robles play, and you can immediately see what the hype is about. He’s electric both at the plate and in the field. With all that said, I’m not here today to talk to you about Robles’ tremendous potential or his jaw-dropping athleticism. I’m here for the bunts.

Victor Robles leads the major leagues in bunt singles this year (he’s actually tied for the lead with teammate Adam Eaton). It’s a good thing, too, because he’s also first in bunts (fair balls that were bunted — it’s hard to get a good count of foul bunt attempts). If that seems weird to you, you’re not alone. We’re talking about a guy with non-negligible power — the FanGraphs prospect team graded him at 50 raw power this offseason. He has four home runs so far this year, and he ran a .157 ISO in the minor leagues, which isn’t Joey Gallo level or anything, but is certainly not poor.

Take a look at this list of players with the most bunts per plate appearance since 2017, Robles’ first playing time in the majors. I liberally filtered out pitchers and people with less playing time than Robles:

Robles sticks out like a sore thumb on this list. Magneuris Sierra literally had a zero ISO in 64 plate appearances in 2017. He’s never hit more than four home runs in a season, minors or majors. Delino DeShields hit six home runs in 440 plate appearances in the bigs — once. Robles has four this year already. Depth Charts projects him for another 11 over the balance of the year. Heck, he had three homers in 66 PA last year when he was called up. Maybe he’s not a power hitter, but he’s certainly not a slap hitter either. What’s up with the love for bunts? Read the rest of this entry »