When baseball fans quibble with sabermetrics, one of the arguments I hear is, “If we can already predict everything that will happen, then why isn’t baseball just played on a computer?” It’s a funny stance to me for two reasons. First, statistics can’t predict everything; they can only tell you the odds of an event occurring. And, second, the randomness of baseball — and, really, sports in general — is something that even the most devout statisticians can marvel at.

Mike Fiers threw the second no-hitter of his career last week. Rachael McDaniel did a brilliant job of explaining how unlikely it was for Fiers, the individual, to have the fortunate of joining the group of 35 pitchers to throw two no-hitters in the big leagues. I just want to borrow a few lines from McDaniel’s prose, but you should really read the whole thing. It’s great:

That’s the wonderful thing about pitching achievements, the no-hitter and the perfect game. With their length and intensity, with the level of collaboration and the sprinkling of luck that is necessary to sustain that nine-inning walk along the knife’s edge, there is so much room for serendipity. In the annals of the no-hitter, you can just as easily find the greatest of all time proving why they’re the greatest as you can a roster of unlikely heroes — rookies, journeymen, washed-up veterans — who, for those few hours, reach out and find perfection.

I want to take a second crack of explaining how unlikely Fiers’ second no-hitter was, but with a different angle: math. 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 »

Is it premature to call Michael Brantley the best free agent signing of the 2018-19 offseason? Probably, but that depends on how one defines “best.” Also important are the words “so far,” which are admittedly not in the initial question, but are still significant nonetheless. If we are trying to determine a total return on investment, we’d need to evaluate the impact of many factors, including those not specifically seen on the field.

By this process, one could argue that Bryce Harper has been the “best” free agent so far, generating increased interest in baseball in Philadelphia (attendance numbers are an indication of this) and setting the professional sports record for most jersey sales in the first 24 hours of a launch. Those are certainly positive numbers for the Phillies’ brass, but that’s not what I’m looking at here.

Narrowing our focus down to on-field production alone, no 2018-19 free agent signee has been better so far than the Astros’ new outfielder. Though 37 games, Brantley has produced 1.7 WAR, putting himself in first by a 0.4-win gap over the next closest player, Charlie Morton. He’s half a win ahead of the next position player, with Eduardo Escobar and DJ LeMahieu each having been worth 1.2 wins. Read the rest of this entry »

Even after losing Bryce Harper to free agency, the Nationals were projected to win the NL East, but for the second year in a row, things are going awry. At 14-22, they’re actually five games worse than they were last year at this point; they currently own the worst record in the NL this side of the Marlins, who at least have the excuse of being bad by design (not that they haven’t been designed badly). With Wednesday’s sweep-culminating loss to Milwaukee, Washington has lost four games in a row, and 14 out of 19; they’ve dropped six straight series. They’re underperforming in virtually every phase of their game, and while injuries have been a part of the story, they’re hardly alone in that regard. Everybody hurts.

When the season began, the Nationals were projected for a .555 winning percentage, a 53.2% chance of winning the division, and a 25.9% chance at claiming a Wild Card spot, resulting in a 79.1% chance at a playoff spot overall. Through Wednesday, they’re down to 28.6% for the division, 16.8% for the Wild Card, and 45.4% for any playoff spot.

Those are still better odds than recent history suggests. While a sub-.500 start through 36 games isn’t fatal to a team’s playoff hopes, in the era of two Wild Card teams per league (since 2012), no team has dug itself out of a hole this deep at this particular point. Of the 70 playoff teams in that span, only seven were even below .500 at this point before recovering to claim a spot: the 2013 Dodgers (15-21); 2014 Pirates (16-20) and Royals (17-19); 2015 Rangers (15-21), Blue Jays (17-19), and Pirates (17-19); and 2018 Dodgers (16-20). It’s been 10 years since a playoff-bound team started 14-22, namely the 2009 Rockies.

Relative to our preseason projections as of March 21, the Nationals are the majors’ top underachievers by a wide margin: 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.

Big expectations — and building anticipation — can bring out the need for immediate results. Vladimir Guerrero, Jr. had humongous expectations given his lineage, his prospect status, and the utter destruction he wrought on minor league pitching. His name made him known earlier than other prospects without Hall of Fame fathers, but his play declared him ready for the majors last year, with some desiring a May call-up and the player’s union mentioning him by name last September when he remained in the minors. Through 10 games, Vladimir Guerrero, Jr. has not produced, but then, even super-duper prospects who are almost completely unlikely to bust sometimes don’t hit well for 10 games.

Given the expectations, it’s easy to call a .162/.244/.189 slash line with a 23 wRC+ disappointing. It is disappointing. Just like the 29 wRC+ Paul Goldschmidt has put up over the last 14 days. Or the 35 wRC+ from Corey Seager during the same time period. Mitch Haniger’s wRC+ over the last two weeks is a measly 49. Ronald Acuña Jr.’s is barely better at 51, with Jose Altuve just ahead at 56. It’s possible the latter numbers have escaped your attention. It’s okay to have missed them or to even have known about them and ignored them because we know they aren’t an accurate representation of the talent level these players possess. But when a player comes up from the minors for the first time and doesn’t break out immediately, second thoughts can creep into the backs of our minds about can’t-miss prospects who missed.

Read the rest of this entry »

As beef goes, the Chris Paddack–Pete Alonso back-and-forth wouldn’t make the grade for even the sketchiest ballpark hot dog; Monday night’s Petco Park matchup between Paddack and Jacob deGrom was of a choicer cut. In just his seventh big league start, the 23-year-old rookie dominated a flailing Mets lineup and out-dueled the reigning NL Cy Young winner, continuing a run that has produced some eye-opening numbers.

Paddack and deGrom matched zeroes until the bottom of the fifth inning, with the former, consistently attacking high in the zone, having struck out eight to that point while allowing just a pair of singles, and the latter punching out four while allowing just one single. In the bottom of the fifth, Hunter Renfroe — still basking in the glow of Sunday’s walk-off grand slam against the Dodgers’ Kenley Jansen — hit a solo homer. The Mets put two on base in the top of the sixth to no avail, and the slim margin continued until the bottom of the seventh when the Padres scored again on an Eric Hosmer single, a Renfroe double, and a Ty France sacrifice fly. That was deGrom’s last inning, while Paddack continued until yielding a two-out single to Jeff McNeil in the eighth. He departed having struck out a career-high 11 while allowing just four hits and a walk; he went to a three-ball count just twice. The Padres cruised to a 4-0 win. Read the rest of this entry »

Last night, Mike Fiers threw his second no-hitter. He no-hit the Reds on 131 pitches, with three batters reaching against him on two walks and an error. It was the 300th no-hitter in major league history, and Fiers became the 35th pitcher in major league history to throw multiple no-hitters.

“You almost get emotional,” he said after the game.

***

The lights were out. Three panels of them out of five on the tower were non-functioning, looming barren above left field at the Oakland-Alameda County Coliseum. Where usually there were rows of bright lights, a series of illuminations hanging above the names of Jackson, Henderson, Eckersley, there were instead the unimpressive shadows of bare bulbs.

The problem was unanticipated, and clearly not easily fixed. I was watching when the lights went out at Dodger Stadium last year, and that technical issue certainly looked more impressive — one moment I saw a ballpark where a baseball game was happening; the next, a panicky wave of cell phone flashlights cresting a sea of darkness. But while play resumed for the Dodgers in just 20 minutes, it took almost two hours for the scheduled game between the Reds and the A’s to begin. Fifteen more minutes and the game wouldn’t have happened at all. Even as Fiers took the field to begin warming up, the lights still flickered, unsure. Read the rest of this entry »

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 »

Madison Bumgarner’s reputation as a pitcher wasn’t burnished during the regular season. Bumgarner has been mostly very good as a starter prior to October. From 2011 through 2016, he averaged 212 innings and 3.9 WAR per year. During that time his 23.3 WAR places him ninth among major league starters, which is more a low-level ace than a dominator in the form of a Clayton Kershaw or Max Scherzer. No, it was in three postseasons that Bumgarner forged his reputation, pitching another 100 innings across three playoff seasons and three championships, including earning NLCS and World Series MVP honors in 2014. With the Giants unlikely to contend this season, Bumgarner’s value to the club more likely lies as a trade chip than a bringer of championships. After struggling the last two seasons, Bumgarner is pitching better in 2019, but whether he’s back to his old level of success remains to be seen.

We are still just seven Bumgarner starts into the season, but there is a bit of optimism. In his last start, Bumgarner threw the ball harder than he has in some time on the way to six innings of one-run ball against the Dodgers during which he struck eight against just two walks. The velocity wasn’t just encouraging, it was harder than he’s thrown in years.

Other than a few starts in early 2017 before he was hurt, Bumgarner hasn’t thrown the ball with as much velocity as he did the other night on a regular basis since the 2015 season. And it wasn’t just the last start that Bumgarner has pitched well. While the velocity against the Dodgers was new, in his last four starts, Bumgarner has struck out 27 batters against just three walks in 24.2 innings for a 1.84 FIP. That four-game FIP is the best Bumgarner has put together since the 2015 season and nearly a full run lower than any stretch last year.

Bumgarner is pitching better than the last few seasons, but to get some idea about how much better, let’s take a baseline and compare Bumgarner over three different periods, plus the last four starts as a bonus. First, let’s look at some numbers most readers at FanGraphs should be familiar with. Read the rest of this entry »