Last week, I began a series of pieces about team win-loss totals as estimated by BaseRuns, first by taking a broad look at the methodology and its limitations, then by zooming in on the offenses that deviate most notably from their BaseRuns assessment in the run scoring department. Let’s wrap up with a look at the defenses that sit furthest from their runs allowed approximation.

In the offense edition, I used a game show format to evaluate whether the perspective offered by BaseRuns has a point, or if there’s something its methodology is overlooking. We’ll keep that framework going for the defenses as well. Here’s a reminder of how it works:

To determine whether or not BaseRuns knows what it’s talking about with respect to each team, imagine yourself sitting in the audience on a game show set. The person on your left is dressed as Little Bo Peep, while the person on your right has gone to great lengths to look like Beetlejuice. That or Michael Keaton is really hard up for money. On stage there are a series of doors, each labeled with a team name. Behind each door is a flashing neon sign that reads either “Skill Issue!” or “Built Different!” Both can be either complimentary or derogatory depending on whether BaseRuns is more or less optimistic about a team relative to its actual record. For teams that BaseRuns suggests are better than the numbers indicate, the skill issue identified is a good thing — a latent ability not yet apparent in the on-field results. But if BaseRuns thinks a team is worse than the numbers currently imply, then skill issue is used more colloquially to suggest a lack thereof. The teams that are built different buck the norms laid out by BaseRuns and find a way that BaseRuns doesn’t consider to either excel or struggle.

Read the rest of this entry »

I still remember the first time I wondered, What if the colors I see aren’t the same ones that other people see? What if the color I perceive as red looks the same as what you perceive as yellow? I was 10 years old, and I felt like a budding scientist or philosopher, or perhaps a poet. Whichever one, I was already preparing my Nobel Prize acceptance speech.

I’ve since come to realize that my 10-year-old brain wasn’t asking anything that every stoned college freshman hadn’t asked before. I sounded less like a Nobel Laureate and more like John Kruk taking his role as the Phillies’ color commentator a bit too literally. That said, the idea that different human beings perceive colors in different ways isn’t just pot-fueled postulation or Krukian wisdom – it’s the truth. It would have blown my 10-year-old mind to learn the colors I see aren’t necessarily the colors everyone else sees, and it’s not just about rods, cones, and intrinsically photosensitive retinal ganglion cells. Sometimes, it’s a matter of language.

Take a look at the four swatches below. Think about what colors they are. And no, the answers aren’t Steven Kwan’s whiff rate, arm strength, bat speed, and sprint speed: Read the rest of this entry »

You’re probably familiar with the saying, “Happiness equals reality minus expectations.” Maybe because your Aunt Debbie shared a post from her favorite social media influencer. Maybe because you passed the time during a layover at the airport perusing the self-help books in the Hudson News near your gate. Like most self-help tropes, whether or not it hits for you depends a little on your life circumstances and a little on how you choose to apply it. When it comes to sports fandom, emotional hedging can be a useful tool to avoid disappointment, or maybe you prefer projecting confidence to manifest a desired outcome. And if you’re a Phillies fan, you’ve perfected the art of oscillating wildly between the two over the course of a single game. You even have a handy meme with a meter that only ever points to one extreme or the other:

(Please excuse the mismatched needle sizes and logo alignment. These images are precious internet relics that have been downloaded, clumsily edited, re-uploaded, compressed, and decompressed hundreds, if not thousands, of times. The pixelation is earned like callouses on the hands of a skilled laborer.)

But the formula seems to assume that expectations are set and controlled by the person in search of a happy existence. The entire notion is upended when mathematical models based on historical outcomes become the source for baseline expectations. In this scenario, if your team is outperforming expectations, then you can enjoy the banked wins, but you do so in fear of the rainier days that surely lie somewhere in the team’s future forecast. Whereas if your team is underperforming expectations, things might feel dire, but there’s reason to believe sunnier days lie ahead. Read the rest of this entry »

Below are two changeups. Can you tell which one is better?

First up is Griffin Jax’s power changeup. He throws it over 92 mph; at two inches of induced vertical break (IVB) and 15 inches of arm-side run, it almost resembles a filthy left-handed slider:

Second is Hunter Gaddis straight change, floating up to the plate with 10 inches of IVB at an average velocity of 78 mph:

So, which one would you take? That’s a bit of a trick question: By whiff rate, these two pitches are virtually identical. Jax’s changeup ranks second in all of baseball with a 57.3% whiff rate; Gaddis’ is right behind him in third. Stylistically, they’re opposites; by the results, they are indistinguishable.

If you were creating the perfect fastball or the perfect slider in a video game, it’d be a straightforward process. Crank up the velocity, max out the vertical break, and those pitches will generally improve in a roughly linear fashion. Not so with changeups. Pitch models struggle to accurately grade these pitches because their quality can’t as easily be captured by velocity and movement in a vacuum. The Cole Ragans changeup, for example, gets a roughly average grade by Stuff+ despite performing like the best changeup in the sport over the last handful of seasons. It’s slow, and it barely moves — what makes it so good?

Thanks to new data from Baseball Savant, I think the answer might soon be clear. Read the rest of this entry »

In the sixth inning of Monday’s game between the Blue Jays and the Cardinals, George Springer got a pitch to hit, a hanging curveball that split the center of the strike zone. He recognized the pitch late and fouled it off:

His post-swing demeanor suggests that he considered it a missed opportunity, and it’s clear to see why. With a pitch like that, he was thinking extra bases; instead, Andre Pallante got a strike for his troubles. Now Springer’s back was against the wall. Pallante came back with a much better pitch on 1-2, but Springer spoiled it:

Unlike the previous miss, this looked like a calculated act to me. Springer was late on the pitch, but it was too close for comfort, so he took a defensive cut, meeting the ball early in his swing and punching it harmlessly away.

Welcome to the confusing world of analyzing foul ball rate. Both of Springer’s swings produced the same result, but the first one was a poor outcome for him and the second a desirable one. You can argue that the second pitch would have been a ball if he hadn’t swung, but he certainly wasn’t sure of that when he committed to swinging; living to fight another day against such a well-located pitch is a good outcome.

You probably wouldn’t be surprised to learn that Luis Arraez, Nick Allen, and Brice Turang are among the leaders in early-count foul ball rate (foul balls per swing). They swing a lot, make a lot of contact, and spray their contact to all fields, including foul territory in every direction. On the other side of the coin, you’ve got sluggers like Bryce Harper, Aaron Judge, Vladimir Guerrero Jr., and yes, Springer. These guys don’t swing as often, which means a few things. First, they swing at better pitches on average, which leads to better contact. Second, they make less contact on average, and less contact means fewer fouls, even for the same rate of fouls-per-contact.

I’d rather be in the second camp than the first there. Early-count foul balls are a waste, literally the same as a swinging strike. They might be worse, even – baserunners can’t steal, catchers can’t block poorly and allow a passed ball. A full 46% of Arraez’s swings – 48% for league leader Wilyer Abreu – end up as foul balls. Sure, contact is great, but when half of it counts as a strike, it’s a lot less enticing.

Things change with two strikes, though. When a foul ball extends the at-bat instead of ending it in a strikeout, it becomes valuable instead of detrimental. Have you ever watched Jake Cronenworth hit? With two strikes, he turns into a lacrosse goalie, trying to redirect everything in the vicinity of the strike zone. He’s not trying to hit a homer unless the pitcher truly grooves him one; he’s specifically looking to avoid a strikeout. Cronenworth sports the highest foul-per-swing rate in baseball with two strikes at 51.2%. It works – he still strikes out a decent amount because of his penchant for running deep counts, but he walks 16% of the time because eventually pitchers miss the zone.

The bottom of the two-strike foul ball rate list, on the other hand, is filled with strikeout-prone types. Javier Báez makes foul contact on just 27% of his two-strike swings. Judge, who still strikes out a ton even as he rewrites the record books, is towards the bottom. So are Jackson Chourio, Shohei Ohtani, Fernando Tatis Jr., Kyle Schwarber, and all nature of excellent sluggers. You can get away with it if you hit like those guys, but Andrew Vaughn, Brenton Doyle, Miguel Andujar, and Michael Toglia are floundering under the weight of their inability to fight pitches off. This isn’t a disqualifying statistic, in other words, but it’s surely a bad thing; it’s directly leading to higher strikeout rates, and unless you have light tower power, many of the pitches you swing at with two strikes aren’t the kind you can hit for extra bases anyway.

I’d posit that high foul ball rates before two strikes are bad, while high foul ball rates with two strikes are good. Early in the count, fouls are a waste, while late in the count, they’re a get out of jail free card. Assuming that these two events are equivalent doesn’t make much sense to me; hitters behave differently, and if we don’t credit them for that different behavior, we’re missing something essential about the act of hitting.

To measure this, I had to put everything on the same scale. I first took every hitter who has swung at 200 or more pitches early in the count, found the average foul ball per swing rate, then normalized each player’s foul ball rate into z-scores. I did the same for every hitter who has swung at 100 or more pitches in two-strike counts. That gave me two scores for every hitter: early-count foul rate and two-strike foul rate. I flipped the sign of the early-count foul rate scores – lower is better – and then summed the two.

This let me separate out the hitters who always have high foul ball rates or always have low foul ball rates – they don’t demonstrate this skill of changing their approach in a measurable way. Arraez, for example, makes foul contact on 46.2% of his early-count swings and 46.3% of his two-strike swings. It’s the same approach, and because the league as a whole cuts down on their swings and makes more foul contact with two strikes, Arraez rates below average in this metric. He’s two standard deviations above average in his early-count foul rate and only 1.6 above average in two-strike foul ball rate, a net of -0.4 for his “foul score.” Allen is even worse – he makes foul contact on 47.1% of early-count swings, but only 39.3% of two-strike swings. When pitchers try to throw the ball past him, they succeed. His foul score is a woeful -2.15.

That’s among the worst marks in the majors, but the actual worst hitter is doing a lot worse than that. That would be Andujar, who is making a ton of foul contact early (44.6%) but almost never when he needs it to stay alive (27.4%). The result is a foul score of -4.2. If you’re wondering why a guy with his skills – solid bat speed, elite contact rate – has never taken off in the majors, it might be related to this. Likewise, if you’re trying to puzzle out what’s ailing Xander Bogaerts this year, it can’t help that he makes foul contact 39% of the time early but only 30% of the time late, for a foul score of -2.2.

Most big leaguers aren’t outliers to this degree. More than 60% of the league has a foul score between -1 and 1, and 93% fall between -2 and 2. The top 10 hitters by this metric have an aggregate wRC+ 20 points higher than the bottom 10, but most players fall into the broad, undifferentiated middle. I’m not saying that this is a skill that everyone in baseball has or should use, but I do think that it’s measuring a real ability.

That brings us back to Springer, a paragon of adaptability. Early in the count, he’s allergic to foul balls, fouling the ball off just 30.6% of the time. Put him in a two-strike count, however, and he goes into protect mode, fouling off the ball with 42% of his hacks. He’s demonstrated some version of this skill throughout his career, in fact. His worst two years for modulating his foul ball rate were 2023 and 2024 – perhaps not coincidentally, those were the two worst offensive years of his career.

Another standout in the field? Springer’s erstwhile teammate, Carlos Correa, who is roughly Springer’s equal in foul score this year and has been even better over the course of his career. Was this part of the Astros’ famed no-strikeouts transformation? I obviously can’t say with any certainty, and they might have been doing a few other things to tilt things in their favor, but a solid approach like this can’t hurt.

It’s not all former Astros. Harper has learned this skill over time. During his Nationals tenure, he didn’t change his approach much at all when reaching two strikes. Since joining the Phillies, however, he’s running one of the largest differences between early-count foul rate and two-strike foul rate in the entire major leagues. And hey, would you look at that, he has a huge foul score this year, too – his 28% early-count foul rate and 37% two-strike foul rate land him fourth in the majors in foul score.

When fans and analysts talk about smart hitters with bat control, I’d argue that they’re implicitly describing this skill. The ability to take different swings depending on the context – prioritizing loud, fair contact early, then choking up and defending late – thrills old-school and new-school fans alike. That ability to adapt is more valuable than always slapping at the ball or always trying to hit it out of the park.

If you’re like me, you have one big question: Is this a sustainable skill, or does it flicker in and out from one year to the next, introducing noise into hitters’ production? The outliers here clearly seem to have an edge – Harper, Springer, and Correa do it consistently. Allen and Andujar have always made more foul contact with two strikes than early in the count; they’ve never possessed this skill. Still, I wanted to check whether it’s a talent (or hinderance) held by only a few.

To do so, I took data from 2023 and 2024. I identified the top 10% and bottom 10% of hitters in 2023, then compared their performance to 2024. The top 10% of hitters averaged a score of 1.7 in 2023 and 0.6 in 2024. The bottom 10% of hitters averaged -2 in 2023 and -0.4 in 2024. Expand it to the top 25%, and you get a similar result: 1.2 in 2023 and 0.3 in 2024 for the top 25%, -1.6 in 2023 and -0.4 in 2024 for the bottom 25%. There was a 0.3 correlation between year-one foul score and year-two foul score. It’s a real skill – not as strong as, say, home run rate or swinging strike rate, but nevertheless something where hitters who are good at it in one year tend to be good at it in the next.

So the next time you see George Springer foul off an early hanging breaking ball, you’ll know: That’s a rare event. And next time you see Bryce Harper turn an 0-2 count into an all-out foul ball battle, yep, that’s years of training showing through. These guys are good at what they do, and it’s a thing that you, the fan, implicitly know is a good thing. Isn’t baseball cool?

There’s a war going on across major league baseball. It’s been waged over decades, in fact, between two opposing factions of the game. Pitchers, at times aided by their catchers, want to own the top of the strike zone, the place where their fastballs have the easiest time missing bats. Hitters want to hit home runs, and the top of the zone is an ideal launching pad. But while both sides would dearly love to own the territory, they can’t both win at once. What follows are some dispatches from the front, the latest moves and counter-moves by some of the game’s best in this contested space.

Chad Patrick lives at the top of the zone. No pitcher in baseball throws upstairs fastballs more frequently. He might not seem like the type. He’s a soft tosser in the context of the modern major leagues, sitting in the low 90s with his four-seamer and sinker, and the high 80s with his cutter. But for Patrick, shape is more important than velocity.

As Alex Chamberlain has extensively explained, the plane of a pitch when it reaches home plate is a key determinant of its success. That’s most true at the top of the zone for four-seamers. Pitches that come in high and flat act like optical illusions – the average fastball thrown to that area falls more, because it’s falling at a steeper angle. Read the rest of this entry »

This is a public service post of sorts. If you’re like me, when you type “Run Ex” into Google, it will auto-complete to “Run Expectancy Matrix.” It knows what I want – a mathematical description of how likely teams are to score in a given situation, in aggregate. I use this extensively in analysis, and I also use it in my head when I’m watching a game. First and third, down a run? That’s pretty good with no outs, but isn’t amazing with two.

There’s just one problem with that Google search: It’s all old data. Oh, you can find tables from The Book. You can find charts that are current through 2019. There’s a Pitcher List article that I use a lot — shout out to Dylan Drummey, great work — but that’s only current through 2022. And baseball is changing so dang much. Rather than keep using old information, I thought I’d update it for 2025 and give you some charts from past years while I’m at it, so that you can understand the changing run environment and use them for your own purposes if you so desire.

First things first: Let’s talk methodology. I downloaded play-by-play logs for all regular season games played between 2021 and 2025. For each play, I noted the runners on base, the number of outs, and then how many runs scored between that moment and the end of the inning. I did this for the first eight innings of each game, excluding the ninth and extras, because those innings don’t offer unbiased estimates of how many runs might score. Teams sometimes play to the score, and the home team stops scoring after the winning run. If you have the bases loaded and no one out in the bottom of the ninth, one run will usually end it, and that provides an inaccurate picture of run scoring. That’s also why I skipped 2020; the seven-inning doubleheaders and new extra innings rules produced a pile of crazy results, and the season was quite short anyway. No point in trying to wade through that maze. Read the rest of this entry »

Home teams don’t win enough in extra innings. It’s one of the most persistent mysteries of the last five years of baseball. Before the 2020 season, MLB changed the extra innings rules to start each half of each extra frame with a runner on second base. (This only occurs during the regular season, which means the 18-inning ALDS tilt between the Mariners and the Astros in the picture above didn’t actually feature zombie runners, but the shot was too good to pass up.) They did so to lessen the wear and tear on pitchers, and keep games to a manageable length. Almost certainly, though, they weren’t planning on diminishing home field advantage while they were at it.

In recent years, Rob Mains of Baseball Prospectus has extensively documented the plight of the home team. Connelly Doan measured the incidence of bunts in extra innings and compared the observed rate to a theoretical optimum. Earlier this month, Jay Jaffe dove into the details and noted that strikeouts and walks are a key point of difference between regulation frames and bonus baseball. These all explain the differing dynamics present in extras. But there’s one question I haven’t seen answered: How exactly does this work in practice? Are home teams scoring too little? Are away teams scoring too much? Do home teams play the situations improperly? I set out to answer these questions empirically, using all the data we have on extra innings, to get a sense of where theory and practice diverge.

The theory of extra inning scoring is relatively simple. I laid it out in 2020, and the math still works. You can take a run expectancy chart, start with a runner on second and no one out, and figure out how many runs teams score in that situation in general. If you want to get fancy, you can even find a distribution: how often they score one run, two runs, no runs, and so on. For example, I can tell you that from 2020 to 2025, excluding the ninth inning and extra innings, teams that put a runner on second base with no one out went on to score 0.99 runs per inning. Read the rest of this entry »

Yesterday, I wrote an introduction to Statcast’s latest round of bat tracking metrics. MLB.com’s Mike Petriello wrote a real primer, so I tried to build on that by analyzing how the different metrics work together using a couple common pitch types. We’re still figuring out how to use these new toys, but today I’d like to explain how my first dive into the bat tracking metrics led me to one particular player who is doing something weird, which led me to learn something small about the way swings work. After all, that’s why we’re here exploring all these strange new numbers in the first place.

In my first shot at playing with the metrics, I tried to establish something simple. I pulled the overall bat tracking data for all qualified players, and I focused on Attack Direction, which tells you the horizontal angle of the bat at the moment of contact (or, in the case of a whiff, at the moment when the bat is closest to the ball). That seemed pretty straightforward to me. As with most bat tracking metrics, it’s also a timing and location metric. You generally need to meet inside pitches further out in front of home plate. If you’re behind the pitch, your bat will be angled toward the opposite field, and you won’t pull the ball. If you’re out in front of the pitch, your bat will be angled toward the pull side, and you’ll pull it. A player’s average Attack Direction should correlate pretty well with their pull rate, and the numbers pretty much bear that out. Attack Direction and pull rate have a .60 correlation coefficient:

Most of the dots are clustered around that very clear trendline. Players who pull the ball more tend to have their bats angled toward the pull side just as you’d expect. What interested me was that green dot way at the bottom. It belongs to Leody Taveras. I guess it is Leody Taveras, if we really believe in our graphs, which we probably should at this particular website.

Taveras has a moderately low Attack Direction, four degrees to the pull side, but he’s got the third-lowest pull rate of any player on this chart. I couldn’t help wondering how exactly he was doing that. Before I dug into it too deeply, I was reminded that the fact that he’s a switch-hitter might have something to do with it. So I pulled the data again, this time separating out all players by handedness. On the chart below, switch-hitters will appear twice:

The correlation isn’t quite as strong, because switch-hitters are now broken into two different players with two smaller samples (that’s how small-sample right-handed Patrick Bailey got way down at the bottom). But there are two green dots now! And they’re both Leody Taveras! From both sides of the plate, Taveras looks like he should have a pull rate that’s a bit above average, and instead has one of the very lowest pull rates in the game. At this point, I was officially curious, so I started poking around.

First, I specifically looked at Attack Direction on balls hit to the opposite field. Since the start of bat tracking midway through the 2023 season, when Taveras hits the ball the other way, his average Attack Direction is three degrees toward the opposite field. Only four players in baseball have an average Attack Direction that’s less oriented toward the opposite field. Oddly, they’re all sluggers. Salvador Perez, Yordan Alvarez, Aaron Judge, and José Ramírez are all at two degrees toward the opposite field, and Austin Riley is tied with Taveras at three degrees. Taveras is definitely not a slugger. He could not be more different from these five guys. So not only is he doing something way different from most hitters when he goes the opposite way, but the only players out on that ledge with him have completely different swings than he does. There really is something weird about him.

Next, I tried looking specifically for balls hit to the opposite field even though the bat was angled toward the pull side at the moment. Just 21% of balls hit to the opposite field have the bat angled toward the pull side at all. I ran a Baseball Savant search, setting the minimum Attack Direction at seven degrees toward the pull side. Since bat tracking started, 5.5% of Taveras’s batted balls have fallen into this category. Among the 375 players with at least 200 BIP over that period, that’s the 11th-highest rate. Elehuris Montero is the champion at a shocking 10.5%, but no player who has put as many balls in play as Taveras has run as high a rate as he has.

At that point, I decided to look at individual balls that fell into this category: balls that go to the opposite field even though the bat is angled toward the pull side at contact. How exactly does this happen? Try to picture it in your mind. If the bat is angled toward the pull side, and it’s being swung in that direction anyway, how does the ball end up going in the opposite direction? There are two main answers. Here’s the less common way:

That’s Taveras way, way out in front of a curveball, hitting it off the very end of his bat. He cued it up so perfectly that if the end of his bat were cupped, the ball might have just gotten stuck in there. So that’s one way to do it. In fact, 21% of the balls we’re looking at, hit to the opposite field even though the Attack Direction is seven or more degrees to the pull side, are squibbers hit off the end of the bat below 80 mph. That’s one way to do it.

The other way is much more common, and it looks like this:

Of those same balls, hit to the opposite field even though the Attack Direction is seven or more degrees to the pull side, 50% are classified as popups, and 65% have a launch angle above 38 degrees. Basically, when you hit a ball in that weird manner, it’s almost always going to be either a cue shot or a popup. Leody Taveras taught me that.

This has a lot to do with Attack Angle. If your bat were perfectly parallel to the ground, but angled toward the pull side, it would be pretty much impossible to hit the ball the other way. But when you pop the ball up, you’re not hitting it flush. You’re getting under it. And regardless of the situation, your bat is almost never parallel to the ground. According to Statcast, the bat is angled downward on more than 80% of swings. If you just look at popups, that number is up above 90%. About half of popups come on four-seamers and cutters, where the batter has trouble catching up and swings just under the pitch. The rest come on softer stuff, and those pitches are usually low in the zone. I need you to do some 3D visualization in your head here, because my diagram is not very good:

On the left is a perfectly level bat, parallel with the front of the plate. Now imagine you’re angling your bat downward and you get just underneath the ball. If your bat is angled toward the opposite field or, as in the middle example, straight toward center field, you’ll likely just foul the ball off behind you or into the opposite field stands. Once you angle it toward the pull side, however, it can stay fair, bouncing up and toward the opposite field. Please imagine that the bat on the right looks so funky because it’s foreshortened, pointed out toward the first baseman. Taveras can show us what that looks like in the real world:

If his Attack Direction were zero, he would’ve fouled the ball up and into the stands down the third base line. He only kept it fair because of his Attack Direction of 18 degrees.

Look, I don’t have a big takeaway here. I just think this interesting. I think it highlights the way that the angle of the bat informs even the most mundane batted balls. If you’d asked me yesterday whether it’s possible to go the opposite way while your bat was angled toward the pull side, I would’ve had to think about it, but my first reaction would’ve been to say no. The bat and ball move through space so quickly that they can be hard to track, but the bat tracking metrics help explain why exactly Taveras pops out so very, very often, and how it’s even possible to hit a ball like that in the first place.

Aaron Nola is having a truly awful season: Through nine starts, he’s 1-7 with a 6.16 ERA, which is bad for any pitcher. For the putative no. 2 starter on a big-market team whose fans are getting pretty tetchy about not having won a World Series in a while, it’s disastrous. Especially when said pitcher is in year two of a seven-year, $172 million contract. In fact, you’d have to say Nola has been surpassed in the pecking order by Cristopher Sánchez at the very least, and possibly by newcomer Jesús Luzardo.

Everyone’s got their theories as to what’s gone wrong. Davy Andrews tried to figure out Nola’s deal last month. Timothy Jackson of Baseball Prospectus speculated earlier this week that there’s something off with his fastball, and that lefty-heavy opposing lineups might be to blame. The Phillies, for their part, just put Nola on the (non-COVID) IL for the first time in almost eight years. The stated reason is an ankle injury Nola says is messing up his mechanics, but a player in a slump this bad can almost always use some time off to clear his head as well. Read the rest of this entry »