Archive for Research

Hey FanGraphs, Your Math Isn’t Mathing… Or Is It?

Denis Poroy and Cary Edmondson-Imagn Images

If you spend some time poking around the nooks and crannies of FanGraphs, you’ll eventually encounter one weird thing. Go to our Depth Charts Team WAR Totals page, and you’ll see all 30 teams arranged by the amount of WAR we project them to accrue this season. Go to our Projected Standings page, and you’ll see the winning percentage we expect for each team. Sometimes, those two pages seem to be displaying the exact same information. Sometimes, they don’t quite line up.

Take right now, for instance. We project the Padres for 40.8 WAR, the Giants for 38.7 WAR, and the Diamondbacks for 38.2 WAR. Look at the projected standings, however, and we have the Padres down for a .490 winning percentage, the Giants at .504, and the Diamondbacks at .501. That doesn’t feel right. Shouldn’t the team with the most projected WAR also project for the best record? Well, buckle up, because to explain how this works, we’re going to have to do some math.

We’ll break this one down into two parts. First, what does a team WAR projection mean? Most basically, it’s the sum of each player on that team’s WAR projection, but we’ll have to get more specific than that. Our projection systems can spit out a WAR, but that’s not their real output. They project actual on-field baseball results. Manny Machado’s Depth Charts projection is for 644 plate appearances, 28 doubles, 26 homers, 127 strikeouts, and so on. The WAR part of it gets calculated after the fact. Read the rest of this entry »


More Musings on What Teams Are Paying for a Win in Free Agency

Rick Scuteri-Imagn Images

Earlier this week, I wrote about the cost of a win in free agency. I loved seeing the discussion of that article online and in the comments section, so I thought I’d set aside some time to consider a few of the questions readers had. Here are my answers to those questions.

What if We Used More Tiers?
If three tiers is good, would four be better? Five? Six? In my initial analysis, I ran all these variations in the background and decided that three was optimal for presentation and clarity. I also determined that the sample sizes would get vanishingly small as we expanded to more and more tiers. But as several readers asked for more granular looks, why not? Here is a four-tier version:

Dollars Per WAR in Free Agency, 2020-2026
WAR Tier $/WAR Players
0-1 $7.4M 406
1-2 $8.6M 236
2-3 $10.5M 83
3+ $12.3M 62

And a five-tier version:

Dollars Per WAR in Free Agency, 2020-2026
WAR Tier $/WAR Players
0-1 $7.4M 406
1-2 $8.6M 236
2-3 $10.5M 83
3-4 $11.1M 40
4+ $13.2M 22

Read the rest of this entry »


What Are Teams Paying For A Win In Free Agency? 2026 Edition

Mark J. Rebilas-Imagn Images

What are teams paying for a win in free agency? Earlier this month, I answered a FanGraphs Weekly Mailbag question about that very issue, outlining a rule I’ve been using in formulating my contract predictions. I left my explanation loose and vague because it was one of four questions in a mailbag, but to give you the general gist, I think about free agent salaries on a graduated scale, with role players being paid less per win above replacement than superstars. Today, I’d like to back up my argument with a bit more mathematical rigor.

One of the benefits of writing for FanGraphs is that smart baseball thinkers read the site. I woke up last Monday to a direct message from Tom Tango, MLB’s chief data architect. Tango had a few suggestions for further research, a method for adjusting past years of data for current payroll situations, and even a link to a discussion of the cost of a win with Sean Smith. Smith, better known as Rally Monkey, is the creator of Baseball Reference’s calculation of WAR – when you see rWAR, that actually stands for Rally WAR, not Reference WAR. In other words, I got help from some heavy hitters.

With Smith’s excellent article on free agency as a guide, I built my own methodology for examining the deals that free agents receive and turning them into a mathematical rule. I took every starting pitcher and position player (relievers are weird and should be modeled differently due to leverage concerns) and noted their projected WAR in the subsequent season, as well as the length and terms of their contract. I excluded players who signed minor league deals, were projected for negative WAR, or whose contract details were undisclosed. To give you a sense, applying this approach to the 2025-26 offseason leaves us with 89 players, from Kyle Tucker all the way down to Jorge Mateo. Read the rest of this entry »


The Relationship Between Framing and Blocking

Geoff Burke-Imagn Images

On Monday, Michael Rosen wrote a fun article about catcher blocking. He didn’t just write about it; he created his own blocking metric from scratch in order to grade every catcher in the game and to understand how much value a single block or passed ball can carry. The whole article is excellent, but one piece in particular caught my eye. Michael put together a supercut of Agustín Ramírez’s passed balls, all of which shared a theme. They weren’t the pitches in the dirt that you’d expect to end up as passed balls. They were normal pitches on the edges of the zone, ones that Ramírez tried so hard to frame them that he ended up missing them entirely. Michael drew the obvious inference: His framing focus, I believe, may have led to some of these inexcusable passed balls. At the risk of piling on, here are the pitches in question:

I’m so sorry, Agustín. This is brutal, and it makes Michael’s point very bluntly. It also makes me wonder about the relationship between the framing skill and the blocking skill. Does selling out to be a better framer hurt your blocking? Clearly, it can and at least sometimes does for Ramírez, but it still doesn’t strike me as a particularly likely hypothesis overall. Moreover, even if framing does hurt your blocking, the trade-off would certainly be worth it. Read the rest of this entry »


Catcher Blocking Is Still The Wild West

Dan Hamilton-Imagn Images

The doldrums of the offseason induce fascinating research. Look no further than Ben Clemens’ post “They Don’t Make Barrels Like They Used To,” or Davy Andrews’ follow-up, “They Don’t Make Pitch Models Like They Used To.” When the free agent signings dry up, baseball writers must get real creative. And so they write about stuff like the Competitive Advantage Life Cycle.

In his pitch models piece, Davy outlined in four bullet points what happens when one team gains an edge over the others:

  • Teams realize the immense value of a skill.
  • An arms race ensues as they scramble to cultivate it.
  • The skill becomes widespread across the league.
  • Since the skill is more evenly distributed, it loses much of its value.

“The second we gained the ability to calculate the value of catcher framing, everybody started working on it,” he wrote. No longer was Ryan Doumit allowed to work behind the plate once it became clear he was capable of leaking 60 runs of value in a single season. Davy produced this helpful plot to demonstrate this convergence of catcher framing value, the Competitive Advantage Life Cycle in action:

All the teams are smart now. Even the Rockies might be smart! Even in areas that ostensibly look like pockets of inefficiency — reliever contracts, for example — there is likely some sort of internal justification for the behavior. Once something can be quantified, the serious outliers disappear. Right?

Maybe not quite. Three years ago, catcher blocking statistics surfaced on Baseball Savant, though teams surely were measuring this skill internally for years prior to its public introduction. Has there been a general convergence in the years since? To some degree, yes. Here is the blocking equivalent of Davy’s plot, with Savant’s “blocks above average” metric on the y-axis. There isn’t a clear clustering trend like in the framing case, but the middle of the pack appears a touch tighter.

Measured as the standard deviation between teams, the trend is a little clearer. Slowly but surely, teams are beginning to converge.

But the catcher blocking revolution is a tentative one. While it’s moving in the right direction, it’s too soon to say the arms race is fully on. To wit: Last year was the worst catcher blocking season in recorded history.

Though Savant introduced the metric publicly in 2023, they have in the years since provided data going back to 2018. Between 2018 and 2025, there were 538 qualifying catcher seasons. Agustín Ramírez’s -28 blocks below average last year ranked 538th among that cohort. It should noted that blocks above average is not a rate stat; he did all that in just 73 games behind the dish.

The slower convergence on blocking is, I think, understandable. Of all the things a catcher does, it’s among the least sexy. Framing, naturally, has received most of the attention from analysts over the last decade or so; it tends to comprise the plurality of catcher defensive value, even in this phase of the Competitive Advantage Life Cycle. Throwing runners out, meanwhile, gets the most love on broadcasts, and it’s the easiest to spot.

Blocking sort of falls between those two catcher activities. It’s somewhat visible, but the difficult blocks happen relatively infrequently. And the value is muted: Savant estimates each block above (or below) average grades out to a quarter of a run. Even Ramírez’s record-breaking season, then, only resulted in -7 runs of blocking value. By comparison, it isn’t all that remarkable to lose seven or more framing runs; eight catchers bested (worsted?) that mark in 2025 alone.

Additionally, there is not much blocking discourse. What distinguishes a good block from a great block? How much is a block worth? Who is the best at this skill? I don’t think there is a common consensus on these questions.

Defined as it is by Savant, blocking is, in some sense, the fundamental task of catching. Only a subset of all pitches are potentially “framable.” Catching a runner stealing is even less common. But on nearly every single pitch, the catcher must catch the ball. It’s right there in the name! Catcher!

For a full-time catcher, that comes out to tens of thousands of pitches in a single season. Perhaps you are saying, ‘OK, how many of those are actually hard to catch?’ I submit that they all are; professional catchers just make it look easy. Imagine a moderately athletic young person was thrown into a game to catch for nine innings. They’d miss hundreds of pitches. To catch in the major leagues, you cannot miss hundreds of pitches. You need to catch them all.

Compared to the general population, Ramírez is an amazing catcher. He saw thousands of pitches with crazy velocity and mind-bending spin and caught nearly every one. But he did not catch them all. In fact, he made a mess of many catchable pitches in the 2025 season. On Savant, the “blocks above average” statistic is described thusly:

Every pitch is assigned a probability of being a passed ball or wild pitch based upon several inputs, most notably: pitch location, pitch speed, pitch movement, catcher location, and batter/pitcher handedness. Based on that knowledge, each pitch a catcher receives (or fails to) is credited or debited with the appropriate amount of difficulty. For example, if a catcher blocks a pitch that is a PB + WP 10% of the time, he will receive +0.10. If he blocks a pitch that is a PB + WP 90% of the time, he will receive +0.90.

I wanted to better understand what this looked like in practice, so I tried to recreate the Statcast model from scratch and apply it to all the pitches in the 2025 season. I was not privy to some of the inputs of the Statcast model, such as the positioning of the catcher, and my physics knowledge was not robust enough to calculate where a spiked pitch intercepted the ground, as Tom Tango did in this explainer post.

What I do have access to, however, is Python, and a just-good-enough knowledge of machine learning techniques. I started with pitch location, release position, pitch movement, and velocity as my predictor variables. At first, it was terrible. But after some trial and error, I landed on a CatBoost framework, and the resulting model came surprisingly close to reproducing Tango’s model. While it slightly underrated the likelihood of wild pitches, it nonetheless correlated nearly identically with the Savant leaderboard at the individual catcher level (0.9 r-squared).

Once I had a good-enough approximation, I set out to better understand the spectrum of wild pitch/passed ball probabilities. Out of nearly 200,000 pitches with runners on base in the sample, just 198 graded out as both a) having a less than 1% chance of being a wild pitch or passed ball, and b) ultimately becoming a wild pitch or passed ball. Here is the general distribution:

Of those 198 extremely unlikely passed balls/wild pitches, 12 can be attributed to Ramírez himself. Funnily enough, he actually graded out as a roughly average framer. But his framing focus, I believe, may have led to some of these inexcusable passed balls. Apologies to the man, but I compiled a reel of his lowlights that can be seen below:

(There is hope yet for Ramírez. Shea Langeliers finished with -26 BAA in 2024; his framing declined in 2025, but his blocking graded out as bang-on average.)

One way to lose lots of blocking value is to whiff on these sorts of catchable offerings, but catchers can make up ground by smothering difficult pitches. Here’s the best block of the year, according to my model, which gave Austin Wells just a 14% chance of corralling this splitter. Leverage isn’t considered here, but it must be noted that this block literally saved the game; the Yankees went on to win in 11 innings:

Wells is a decent blocker, but he is far from the best. That honor goes to Alejandro Kirk, who excels not just at limiting mistakes, but also wrangling unruly breaking balls in the dirt. As this plot shows, the highest probability wild pitches/passed balls live down there:

Kirk is able to smother these types of pitches better than anyone in the league. Watch him make easy work of this 89-mph knuckle-curve in the dirt:

One thing to know about Kirk: He’s short (for a baseball player, anyway.) He’s got a low center of gravity, and he gets down to block those pitches. Does being short help you succeed at blocking? It seems like there’s at least some evidence that’s the case:

For now, Kirk is the reigning king of blocking, and Ramírez its court jester. Give it a few years — say, by 2030 — and blocking will likely find itself in the same place as framing, eliminating itself of Doumit-y characters, anything that reeks of serious lost value. All the mess gets filtered out eventually. As of now, we find ourselves in a purgatorial phase of the Competitive Advantage Life Cycle. Enjoy the imperfections while they last.

Thanks to Stephen Sutton-Brown for technical assistance.


Fun with WAR Math

Brett Davis-Imagn Images

How much WAR does FanGraphs project Ronald Acuña Jr. for in 2026? It’s a really straightforward question. It should be especially straightforward now that all of our projections are out. But as it turns out, it’s less clear cut than it sounds at first, and clarifying it has two benefits. First, it’ll help you better understand our projections. Second, it’s fun to play with math. So buckle up: We’re doing arithmetic.

First, let’s settle on what the “FanGraphs projection” even is. Here’s the relevant section of Acuña player page:

Eight projections, each with tons of numbers. That’s a lot! But when I say the “FanGraphs projection,” I’m referring to the first green row, the FanGraphs Depth Charts projection or FGDC. That’s the top-line projection we use anywhere on the website that pulls in projections to make predictions. When you see “2026 (Proj),” it’s using that number unless otherwise stated.

That’s settled then, right? We’re projecting Acuña for 5.4 WAR. Why did I have to waste your time with an article about it? It has to do with how we make that projection, a process you’re about to learn about, probably in more detail than you wanted. Read the rest of this entry »


They Don’t Make Pitch Models Like They Used To

Paul Rutherford-Imagn Images

Before we get started, I need you to promise to hold on until the end here. I have buried the lede. The crux of this article is in the last two graphs, all the way at the bottom. I put them there on purpose because I want the data to tell you a story, so I need you to see this story through to the end. I think it’s worth it.

Last Tuesday, Ben Clemens wrote an article titled, “They Don’t Make Barrels Like They Used To.” Sadly, it was not a scathing takedown aimed at the shoddy craftsmanship of modern-day coopers. It documented the steady decrease in the value of barrels over the course of the Statcast era. In 2025, barrels were worth roughly 250 fewer points of wOBA than they were in 2015. That’s a staggering loss – the entire career wOBA of Pepe Frias up in smoke – and Ben broke down several culprits for the theft, along with one other factor: intention. “Tell hitters that barrels get them paid,” Ben wrote, “and they might start to change their behavior in a way that produces less valuable barrels, squared up to center field or in other ways that are easier to produce but less likely to land safely.” He attributed this to Goodhart’s Law: “When a measure becomes a target, it ceases to become a good measure.”

This law has a sports-specific corollary that you’re probably familiar with. I’ve previously referred to it as the Competitive Advantage Life Cycle in the context of catcher framing:

  • Teams realize the immense value of a skill.
  • An arms race ensues as they scramble to cultivate it.
  • The skill becomes widespread across the league.
  • Since the skill is more evenly distributed, it loses much of its value.

The second we gained the ability to calculate the value of catcher framing, everybody started working on it. The terrible framers either got better or got run out of the sport. Players who were excellent at framing but worse at other parts of the game suddenly found more playing time because their skills were appreciated. Lastly, as the average framing level rose, the rest of the league started catching up to the very best framers. This graph is three years old now, but it shows that convergence very clearly.

The terrible framers are gone, and the great framers don’t stand out as much as they used to. Everybody’s a bit closer to the new, tougher standard, so framing is more important than it’s ever been, but also less valuable. All this got me thinking about one of the oddest measurement tools we have these days: pitch modeling. Read the rest of this entry »


Reliever Contracts Make Plenty of Sense

Dale Zanine-Imagn Images

Most free agent contracts are relatively easy to predict. Calculate the going rate for a single win, multiply it by the player’s projected wins above replacement over the length of the deal, and the result will come pretty close to the actual contract. This generally holds true for every type of player save one: the humble relief pitcher.

The Mets gave Luke Weaver $22 million for two years. The Tigers gave Kenley Jansen $11 million for his age-38 season. The Reds gave Emilio Pagán two years and $20 million, with the second year a player option. Run all of the reliever contracts signed this offseason through a dollars per win calculation, and they’re almost uniformly going to come out looking like terrible deals.

The sport appears to be smarter than ever, and yet teams keep shelling out gobs of guaranteed money on bullpen arms who hardly ever top 2 WAR. What’s their problem? Well, maybe teams have collectively decided to behave irrationally in one specific market, but I don’t think it’s that. I think teams are behaving as rationally in the reliever market as any other, but they happen to be using a different metric for evaluating reliever deals. The relevant metric, I think, isn’t dollars per win, but something like championship win probability added. Read the rest of this entry »


Analyzing Kauffman Stadium’s New Dimensions

Jay Biggerstaff-Imagn Images

Yesterday, the Royals made a big announcement. Kauffman Stadium, long one of the most cavernous venues in the majors, is going to be a little less warehouse-like this year. The walls are moving in nine or 10 feet more or less across the board, and getting shorter by a foot and a half to boot. That’s a meaningful change for a stadium where home runs generally go to die. How massive? Time to crank up the old computer and find out.

I plugged the new dimensions from Kansas City’s press release into an equation describing a rough arc. I fit those points to a cubic spline so that it could more closely resemble the actual stadium, with its pinched-in corners. I made a few approximations as well; for instance, the wall is moving to a height of eight and a half feet “in most places,” so I just applied that across the board. I also modeled the old dimensions the same way. That way, I had two different virtual walls built to compare some batted ball data against.

Notably, my approximation isn’t a perfect replica of the stadium. I don’t have a millimeter-scale, or even a yard-scale, map of the place. I can’t account for outfielders robbing home runs, which is definitely going to be more common with the lowered walls, though still quite rare overall. But by running it through both the old and new wall dimensions, I think that this unavoidable error can be minimized. It’s pretty clear that no balls that were home runs with the old outfield parameters will suddenly not be home runs with the new ones, so the thing we’re looking for is the difference, assuming that my approximation is close enough to reality. And it is: My modeling says that over the last three years respectively, 205, 162, and 159 batted balls hit in Kansas City should have turned into homers. In reality, it’s been 186, 147, and 151. Read the rest of this entry »


They Don’t Make Barrels Like They Used To

James A. Pittman-Imagn Images

Here’s a weird chart:

If you’re like me, you’re struggling to make sense of it. The value of a barrel? But aren’t barrels a measure of value themselves? That’s like asking how many dollars a ten dollar bill is worth, or how you’d rate The Lion King on a scale of one to The Lion King. But that’s not actually how it works. Barrels are defined based on exit velocity and launch angle pairs that, according to the dataset MLB used in their creation, were extremely likely to result in extra-base hits. Those cutoffs have remained the same. The results on barrels haven’t.

What gives? Well, some of it is the ball, of course. I’m not breaking new news in the long-running ball aerodynamics debate; you can read some good recent entries into tracking drag coefficients and the like here and here. Indeed, if you’re measuring barrels that way, you can see a pretty straightforward decline. Here are home runs per barrel over the years:

Read the rest of this entry »