Quantifying Age Relative to Level

Age relative to level is one of the most fundamental concepts on the quantitative side of minor league baseball analysis. The younger a player is, relative to his peers in the league he’s playing in, the more positively we should view his production. It would be a mistake to count a 24-year-old dominating the Low-A level as one of the game’s top prospects, much as it would be wrong to write off his struggling teenage teammate.

Applying an age relative to level (I’m just gonna call it ARL for the rest of this piece) adjustment is thus common practice among talent evaluators, especially statistically-minded ones. But when I went to investigate how exactly it should be quantified, I surprisingly found a lack of in-depth investigations into what the magnitude of ARL adjustments ought to be.* For a concept that’s been out there in minor league discourse since before I became part of this community a decade and a half ago, it’s surprising that ARL has stayed firmly a somewhat vague heuristic rather than at least having some sort of understood baseline value.

*If I’ve missed something, by all means send it my way. I did a few searches and asked some research-oriented folks if they knew of anything that did this, and the consensus seemed to be “I’m sure someone has, but I’ve never seen it.” Which was my thought too!

So here we are: I’m gonna give quantifying ARL a shot, if a crude and initial one. Let me first define the research question(s) here:

First, and most generally: what is the value of a player being a year younger than another at the same level, holding performance constant, in terms of his eventual MLB potential?

Second, is such an adjustment the same at all levels and ages, or does it vary? That is, does the amount we should adjust for a 23-year-old at High-A vs. a 22-year-old equal the amount we should adjust for a 24-year-old vs. a 23-year-old? And is the value of being a year younger than league average the same in, say, Low-A and Double-A?

Data and Limitations

One of the wonderful things I’ve realized about returning to baseball writing now, as I have, is that the FanGraphs minor league statistics pages now are collecting data on their sixteenth season (not counting 2020, since there was no baseball). Those data are downloadable with one click, and thus easy to immediately dive into for large-scale investigations like these. Here’s a good place to start with batter data, and likewise for pitchers (they do require some cleaning for precise use, e.g. removing/combining separate entries for players traded midseason).

Minor league performance data still has a lot of rough edges, even then. We don’t really have much publicly-available data on minor league defense, so I’m not going to try to account for that. Further, there is obviously huge variability in ballparks, league environments, and team and level defenses. For purposes of this analysis, I’m just going to use one number for hitters and one number for pitchers to capture their performance. I chose wRC+ for hitters and FIP for pitchers, since both do some accounting for league effects, at least. Finally, since I’m just working from the FanGraphs data, this analysis will treat age as a whole number (i.e., age as of July 1 of the season) rather than a decimal. That’s not particularly exact or ideal, but the volume of player seasons in the dataset nevertheless will allow trends to appear clearly.

For purposes of these investigations, I’m going to focus on ARL at three particular levels: Low-A, High-A, and Double-A. Rookie-level data is notoriously unpredictive, and FanGraphs doesn’t make a distinction between Rookie levels in these mass exports anyway (plus, Rookie ball was recently contracted significantly). Triple-A is much less of a “prospecty” level and has a much wider distribution of ages, so the way ARL functions there may be very different than at the three levels I’m focusing on here.

Hitters

Let’s begin with offense. What we’re going to work toward here is understanding the relationship of age and performance to predicting future success. So if we control for a hitter’s wRC+ at a given level, how predictive is his age of future success?

I need to define “future success” here. For purposes of this piece, I’m defining it in the most simple way possible: 1) Did the player end up playing in MLB at all?

2) How much MLB playing time (PA or IP) did the player end up getting?

Since we need to give players time to reach MLB, we can’t really do much with seasons from the most immediate past; for this piece, I’ll consider the 2006-2016 seasons. 2016 is a good cutoff because it gives even a 17-year-old in Low-A a decent amount of time to progress to MLB, and if he didn’t, he’d already be hitting minor league free agency this season. With a minimum PA of 100 in a season, this gives us between 5100 and 5200 player seasons to play with in each of the three levels we’re considering. (For pitchers, I used a 30-inning cutoff, which produces a slightly lower but fairly similar volume of player seasons).

Low-A

I’ll get to some slightly more advanced analysis in a moment, but let’s start this with a simple breakdown of what proportion of players of each age in Low-A ended up playing in MLB.

This probably isn’t surprising–sure enough, Low-A teenagers make it to the big leagues at quite high rates, and players 24 and up at this level are extreme longshot types. The distribution of probability is notable, though. If I run this as a linear regression, I get the equation

Probability of playing in MLB = -.087(Age) + 2.089

That equation (R-squared = .119) doesn’t end up modeling the data very well,* because it implies a constant slope of 8.7% per year, which only seems to be close when differentiating 22-year-olds from 23-year-olds. Every year below age 21 seems to move probability by closer to 14% or so, while the drops from age 21 to 22, 23 to 24, and 24 to 25 are much smaller.

*We can bump the R-squared up to about .128 or so with quartic modeling, mostly because it handles age 24-27 better and doesn’t zero it out, but the pattern itself is pretty intricate and hard to model much better than that in one function.

Part of this is the inherently asymptotic nature of ARL and MLB probability, but the 21-to-22 gap reflects a different elephant in the room: player origin. Many players are drafted out of college and then sent to Low-A for their first full seasons at age 22, whereas most 20-year-olds at the level are either high schoolers in their second full season or international signees who could be in their third or even fourth full season. Comparing 21-year-olds to 22-year-olds is thus a bit more apples-to-oranges, and so age doesn’t have as strong of an effect. We’ll try to account for this more directly a bit later.

So that’s our starting point. I did want to note, before proceeding, that age and wRC+ at this level historically have a positive correlation, though it’s a slight one: a regression analysis pegs it at about 1.8 points of wRC+ per year, so the average 24-year-old in Low-A would be expected to post a wRC+ about 10 points higher than the average 18-year-old assigned to the level.

There are a few ways to try to attack the relationship between ARL, statistical production, and future outcome. I know we just established that a straight linear relationship between age and MLB probability isn’t ideal, but let’s begin by just throwing age and wRC+ into a blender and try to predict MLB probability. We get:

Probability of playing in MLB = -.094(Age) + .004(wRC+) + 1.877. (R-squared = .195)

Adding statistical production helped explain a good bit more of the variance in players ascending from Low-A to MLB, and was indeed a very significant predictor. Interestingly, though, it didn’t take away any of the slope of age: that actually increased a bit here. And here we also get a glimpse of the relative value of a year: it’s .094/.004, or 23.5 points of wRC+. So a player with an age of x and a wRC+ of 100 in Low-A would have an equal chance of making it to the majors as a player of age x + 1 year and a wRC+ of 123.5.

We can also try this with the dependent variable of MLB plate appearances (through 5/12/22):

MLB PA = -140.1(Age) + 5.43(wRC+) + 2713.06. (R-squared = .123)

This equation values a year of age as being about equivalent to 25.8 wRC+ points, so again we see a similar magnitude of effect. If these analyses are accurate, then that would mean that a 23-year-old with a 150 wRC+ in Low-A should be considered about the same quality of prospect as a 19-year-old with a 50 wRC+. Defense aside, then, Lucas Dunn and Austin Gauthier ought to be considered similarly likely to make it in MLB as Arol Vera and Robert Puason.

But let’s come back to the divide between college draftees and players who start their pro careers at a much younger age. I thought maybe we should include another term for what (full) year of the player’s career the season represents. Since the FanGraphs data just abruptly starts in 2006, I omitted players who started in 2006 and 2007 from this analysis, so this part is just 2008-2016 (sample size: 3,473 seasons). If we add professional year as a term in this model, we get:

Probability of playing in MLB = -.101(Age) + .004(wRC+) - .029(Years Pro) + 2.078 (R-squared = .219)

MLB PA = -143.84(Age) + 5.23(wRC+) - 49.99(Years Pro) + 2870.66 (R-squared = .154)

Two things emerge here. First, a year of age is still about as meaningful as 25 wRC+ points or so, and second, the years pro term indeed plays a role here, and is about a third as substantive as age itself. So a 22-year-old in Low-A in his first full season would be about the same grade of prospect as a 21-year-old in Low-A in his fourth full season, holding all else equal. This term helps bring us closer to the distribution in the first table earlier.

Let’s do a sanity check here. Let’s compare 23-year-olds in Low-A who excelled with 19-year-olds who struggled and see if these cases–which will twist the linearity a bit–at least come close to the equations, or if they present a different valuation of age vs. performance. There were 122 seasons between 2008 and 2016 where a 23-year-old posted a wRC+ between 125 and 150 in Low-A (the average was just 131.5), and 98 seasons where a 19-year-old posted a wRC+ below 75 in Low-A (average 54.5). The 19-year-olds actually had slightly more pro experience, on average, than the 23-year-olds, by .15 seasons. If we plug these two populations into the above equations, we would expect 33.9% of the 19-year-olds and 24.5% of the 23-year-olds to make the major leagues, and for the 19-year-olds to average about 357 MLB plate appearances* to date to the 23-year-olds’ 189.

*This is counting players who did not make the majors as having 0 PA, not excluding them from the sample.

The equations actually just about nail the former group, but actually overstate the success of the latter significantly. In fact, 33 of the 98 struggling 19-year-olds ended up making the big leagues, and they averaged 282 plate appearances, but only 15 of the 122 23-year-olds made it up (12.3%), and they only got 102 plate appearances on average. So for the 23-year-old group, both values were only around half of what the equations predicted. This serves to drive home two lessons: 1) not everything is linear! 2) Clearly, ARL matters a ton here.

If everything is so age-specific, I’ll try one last technique to give us a sense of how this works: multilevel modeling. In multilevel modeling, we treat the slopes and intercepts of one equation as dependent variables in a different equation. We know that minor league performance (here, wRC+) has some predictive utility on whether a player makes it to MLB or not. What if we generated separate functions for every age that modeled this relationship?

NOTE: The slope is the amount that 1 Low-A wRC+ point would change the player's probability of making it to MLB.

What this does is it shows that not only does age affect the probability a player makes it to MLB (the intercept), it also changes the relationship between current performance and chance of future MLB time (the slope). This actually makes a lot more immediate sense. Age dramatically moves the likelihood a player with a given wRC+ in Low-A makes it to MLB, but it also increasingly flattens the effect of wRC+ for older players. Unlike the earlier functions, each of these can be modeled fairly effectively, here with quadratics:*

*The slope function is maybe a little conservative at the top end, because the 25-year-old group is thrown off a bit by only having two future MLBers, both of whom (Eddy Alvarez and Ryan Court) had very high wRC+s.

This setup produces more accurate results on the 23-year-old sample that the earlier functions overrated, pegging a 23-year-old at a 131 wRC+ for a 13.8% chance of playing in MLB. We’ll leave it here for purposes of this piece: I’ve got two more levels and pitching to talk about, after all.

High-A

So we’ve looked through the data at one level, but that doesn’t mean ARL translates equally to other levels. The dynamics of Low-A, where a lot of college draftees are in their first full season and a lot of earlier signees are much deeper into their pro careers, are flattened out a bit when we get to High-A, a level that players only reach if they either have enjoyed past success or have a reasonably high pedigree. As we did with Low-A, let’s start by examining a simple table of age of High-A hitters vs. their probability of ascending to MLB.

Indeed, this seems to straighten out a lot of the Low-A weirdness with first-year college guys. Every year up through age 23 is a pretty similar decline (in the 14-16% range), and then it tapers off asymptotically (other than the weird age-27 blip). I also want to note that our baseline chance of making it to MLB has increased from about one in five Low-A batters to one in four, here. If I run this is a basic age vs. MLB probability regression, I get:

Probability of playing in MLB = -.102(Age) + 2.593. (R-squared = .144)

So as a baseline, this means not only does age follow a more normal pattern of effect on prospect outcomes here (hence the higher R-squared than in Low-A), it also has a bigger effect by default (the slope on this initial equation in Low-A was -.087). I’m not sure I’ve found anything surprising so far, but I’m not sure I would’ve intuitively expected this, since High-A has a wider distribution of player ages.

Our basic linear regressions in Low-A yielded something like one year = 25 wRC+ points as a basis for converting age to performance value. Does a similar picture emerge at this level? Let’s take a look:

Probability of playing in MLB = -.102(Age) + .004(wRC+) + 2.18. (R-squared = .224)

MLB PA = -171(Age) + 6.55(wRC+) + 3538.45 (R-squared = .148)

Sure looks like it. Again, this proved more predictable than Low-A, explaining about 2.5% more variance in these outcomes.

So, since it’s more predictable with just age, and the pattern seems to be more regular, does that mean we don’t need to account for previous pro experience like we did with Low-A?

Probability of playing in MLB = -.109(Age) + .004(wRC+) - .022(Years Pro) + 2.37 (R-squared = .25)

MLB PA = -174.98(Age) + 7.12(wRC+) - 58.72(Years Pro) + 3681.4 (R-squared = .186)

No, it still does help to account for amount of prior experience. There’s maybe a hint that it’s slightly reduced in importance in the first equation, which assigns it about ⅕ the importance of raw age rather than the ⅓ we saw in Low-A, but that ⅓ ratio is there again in the second equation, so we can’t say it’s much less important. Adding it to these models significantly improves our R-squareds as well, like it did in Low-A.

Finally, let’s see what happens when we approach this from a multilevel modeling perspective like we did with Low-A.

If we take out the weird age-19 blip, we get the same sort of quadratic shape on the intercept, but the slope here is actually modeled well with a simple linear relationship, reflecting the more regular nature of the distribution at this level relative to High-A:

What’s up with age 19, though? It might just be that it’s a small sample of 75 players, 58 of whom made MLB. If it’s not, it probably says something about the fact that unlike 18-year-olds in Low-A, 19-year-olds in High-A not only are young for the level, they generally have to have performed well in their careers to get there, at which point whether they manage to immediately master High-A has a little less bearing on their ultimate future. People weren’t freaking out about Corey Seager’s struggles in 2013 the way they were about Robert Puason’s issues in 2021, for good reason.

Double-A

Before we dive back into more data, permit me a moment to editorialize. As I’ve talked about in previous posts on here, when I initially started doing prospect analysis in my college days, age relative to level was one of the biggest factors I considered. People talked about it seemingly even more in the late 2000s than they do now, back when more folks were in the post-Moneyball “who needs scouts?” mindset, and studies like Rany Jazayerli’s landmark draft-age piece seemed to indicate that even half a year or so of age was a huge deal. When I started doing my analysis mostly via actually going to games in 2012-2015, age obviously became less important in my evaluations (because I had much better context for the players than just age, a statline, and whatever mainstream reports were out there), but I still thought ARL was a very significant thing–if anything, I worried I was kind of losing track of it, since it’s tough to see a player dominate in front of you and keep focused on he’s 24, so he’s a longshot, or vice versa with struggling teenagers.

Over my long absence from baseball writing, though, one of the changes in my thinking was I thought maybe we’re a little too focused on ARL. Granted, since we don’t have accepted values of ARL, maybe this “too much” idea is entirely my own projection, and everyone’s been treating it right (or even underrating it!) all along, but over the last few years, I’ve watched from the sidelines and seen all sorts of guys ascend from seemingly nowhere into viable MLB contributors without ever even appearing on a deep org-specific prospect list.

As my interest level in baseball ticked up last year, I thought about this more, and something occurred to me. Right now, these are the average ages of players at each of the four full-season minor league levels:*

Low-A: 21.5

High-A: 22.8

Double-A: 24.4

Triple-A: 27.0

*This is batters and pitchers combined. Pitchers tend to be a bit older than batters, as we’ll see in a bit.

I think if I were to ask most of you “What’s a reasonable amount of time to give a player to master a level?”* you’d probably say something like “a year.” I would too: there’s obviously some convenient rounding in there, but it intuitively seems to track pretty well with who at least gets within sight of the big leagues versus who flames out, especially since repeaters don’t perform as well as we might intuitively think anyway. But if a 24-year-old Low-A player actually manages to do this from Low-A to Triple-A, he’d actually go from initially being 2 ½ years older than his peers to merely an average-age player for his level. Along the way, we would start to take his performance more and more seriously.

*By this I mean, in order to more or less maintain his stock. Obviously, younger guys will remain prospects even if they take two years or more–in the piece just linked above, I just wrote two weeks ago about how Austin Beck is still on the map even though he’s been at High-A since 2019–but Jasson Dominguez isn’t going to be treated like a generational phenom again even if he slugs .600 the rest of the way this season, nor is anybody arguing for Beck to vault back into Oakland’s top ten prospects again. They’d have to prove themselves quickly at the next level, at least, to regain that amount of traction.

This kind of thing does happen. Players like Stephen Vogt, Kevan Smith, David Peralta, Robinson Chirinos, and Jose Martinez have snuck onto the scene with something akin to this start-old-but-just-keep progressing kind of path, all save perhaps Smith well outdoing what was ever expected of them as prospects.*

*Admittedly, for every Vogt, there are a lot of Zach Zaneskis. I’m not saying this is an underrated group, but rather that the sort of steady progress we look for will eventually erode ARL to a large extent.

As you can see from the above chart, where we really start to diverge from this one-year-per-level idea is Double-A, where there is a higher volume of repeaters, veterans demoted from Triple-A, minor league free agent signees, and even the occasional independent league acquisition. Racing across the gauntlet of those opponents in a year actually moves a player’s ARL by 2.2 years: a 24-year-old in High-A, almost certainly one of the older players on his team, would become one of the younger, more “prospecty” names on his Triple-A team two years later if he solves Double-A in between.

There are a couple of other important things about Double-A in particular that have affected my thinking about ARL. One is that, unlike the A-ball levels, it’s within striking distance of the major leagues, and so performance really starts to matter. Even at age 30, Yadiel Hernandez’s showing at the Double-A level had potential MLB implications* that simply aren’t there for an older A-ball guy: you see a statline like Hernandez’s, or even one that didn’t come to fruition like Travis Denker’s 2016, and you think “This guy might be one of the two or three best bats in this organization right now.”**

*I know that there are extenuating circumstances here that don’t apply to a lot of the 30-year-old retread types who hang around in Double-A, but Hernandez hadn’t been great there at age 29 and wasn’t great in Triple-A at 30, yet he’s had a career now.

**In terms of immediate MLB ability, not prospect status, of course.

The second is that, as reflected by the presence of some 30+ year old guys, Double-A isn’t a level at which age is an outright disqualifier. If you’re older than about 25 (maybe 26 for pitchers), you pretty much can’t be in Low-A barring some special circumstances. Add a year to those numbers for High-A. All of a sudden, though, there are some 31-year-olds in Double-A. If you get there even at age 25, you might just have an additional half-decade to try to Andres Torres your way to a career. The Nationals, with a generally barren system in the mid-to-late-’10s, have had some good recent examples of what happens if you just give players forever to figure stuff out: not just Hernandez, who they stuck with for a couple years after signing him at 29, but also Adrian Sanchez and Dakota Bacus, who both made it to the big leagues (albeit briefly) despite not really figuring out the upper minors until their late twenties. Even guys like David Masters, Alec Keller, and Khayyan Norfork managed to at least become solid Double-A hitters eventually.

To sum this up, the way I like to think about Double-A is that (most of) its players are “in the conversation.” This is especially true when they first reach the level. For instance, as somebody who follows the A’s system, last year I thought Max Schuemann, Will Simoneit, and Shane Selman, who all had strong seasons at High-A Lansing at age 24, “put themselves in the conversation.” As in, they earned promotions to Double-A, where they all of a sudden aren’t that old for the level anymore, and if they succeed there too, all of a sudden they’ll be youngish Triple-A guys with multiyear records of performance.* Further, since players can sometimes hang around in the upper minors into their thirties, they’ve bought themselves more time to figure things out.**

*This doesn’t necessarily make them prospects, but it at least makes them interesting organizational players who could find their way somewhere if they keep it up. Nobody’s paying any attention to Selman even now, for instance, but there’s really very little separating him from where Seth Brown was in 2018.

**Not everyone gets this chance, of course. It depends on the organization, the player’s prospect status, and his off-the-field contributions, among other things. I’m just saying a 25-year-old in AA has more potential time in front of him than a 24-year-old in High-A does.

That’s where I’ve gotten in theory, but how does this actually play out quantitatively? Here’s our chart of Double-A hitter age vs. chance of making it to MLB:

An important note here: in the raw Double-A data we run up against an issue not present in A-ball, that being that some players make it to MLB and later come back down to AA. I went through and hand-coded everybody back to their MLB results after the Double-A season in question, so if somebody made it back to MLB, they get credit for making it, and whatever plate appearances amassed after that point, but if not, they’re coded equivalent to someone who never made it up.

As Double-A has better players than the A levels and is more proximal to MLB, naturally we have a significant increase in the overall percentage of players that make it to the majors, old for the level or not.* But it’s still a familiar picture: there’s that same 14%-ish drop through age 25, then things taper off slowly from there. Of note is just how slowly: whereas the A-ball levels basically taper to zero, this bottoms out still above ten percent, with 13 (11.2%) of the 116 players 30 or older finding a way to see some MLB time. Since most of the players we’re really thinking about in prospect terms are 27 or younger, I’ll restrict my initial analyses to them. Again, let’s go through accounting for performance. Does a year equal 25 points of wRC+ here too?

*Of note: every single Double-A teenager made it to MLB. The worst careers of them were Fernando Martinez and Jesus Montero.

Probability of playing in MLB = -.112(Age) +.005(wRC+) + 2.617. (R-squared = .262)

MLB PA = -241.67(Age) + 8.4(wRC+) + 5376.25. (R-squared = .225)

It’s 22 and 28, so…pretty much. The shrinking a touch on predicting whether the player will make it to MLB at all might fit my “in the conversation” narrative–26-year-olds in Double-A are more likely to make it to the big leagues than 22-year-olds in Low-A, even though their ARL is a full year higher, so there is something to the idea that the categorical dismissal of those guys is mistaken. But we start to see age come up in a more restrictive way when it comes to MLB plate appearances: a 26-year-old Double-A guy who ends up making it to the major leagues is much less likely to have a long career than a 23-year-old, because he’s probably getting to the majors in his late twenties.* When A.J. Ellis, David Peralta, and Stephen Vogt are the absolute right-tail outcomes, that says something. So overall, the relative value of age vs. performance stays more or less the same here. Notice also how the slopes on both variables have increased relative to A-ball–since MLB is so much more viable for this player set, there’s a lot more at stake, and distinguishing yourself by either being young (buying yourself time) or performing well is extremely impactful for these players’ careers.

*This is true to some extent with, e.g., 24-year-olds in High-A as well, but they could at least hypothetically speed to the majors the next season and get to MLB in their mid-twenties. David Freese, Matt Carpenter, and Brian Dozier are three prominent examples, and while they’re not Hall of Famers or anything, they had around twice the career plate appearances of guys like Vogt and Ellis.

Does years of experience still have an effect on this picture?

Probability of playing in MLB = -.118(Age) + .005(wRC+) - .013(Years Pro) + 2.76 (R-squared = .301)

MLB PA = -223.1(Age) + 9.2(wRC+) - 79.75(Years Pro) + 5068.5 (R-squared = .284)

Yes and no; interestingly, we see a dramatic split here between our two outcomes. Years of experience barely even achieved statistical significance at predicting whether a player made MLB or not, and was only about a ninth as important as age itself. However, when it came to predicting ultimate MLB playing time, it maintained the weight it had in A-ball, where you’d consider a 26-year-old in his third pro year functionally as “young” as a 25-year-old in his sixth.

Finally, let’s do another slope and intercept chart. I’ll include guys up through age 30 this time.

So, first, the intercept again fits a quadratic equation very neatly.

The slope, when graphed out, has a weird pattern, though.

I guess you can sorta model it this way?

I’m not going to sweat the intricacies too much here, especially with respect to the older players. I do want to point out two things, though. First, in High-A, we saw that 19-year-olds had a very low slope–a small relationship between wRC+ and making MLB–and here that trend exists with players 21 and younger. These struggles in Double-A have some significance,* but players are usually only in that position to fail because they’ve succeeded quickly at lower levels, so they’re often just blips. Secondly, the slope peaks lower than it does at either A level, but it is equally strong for players of ages 22-24, so there isn’t one exact age of players for whom performance is as pivotal as 18-year-olds in Low-A or 20-year-olds in High-A, but those three ages–almost half the sample here!–sees a stronger correlation between their performance and eventual MLB fate than most players at lower levels.

*For space reasons, I’m not showing you separate calculations on predicting MLB plate appearances at every year (I can, upon request), but a point of wRC+ for a 20-21 year old in AA seems to be worth about 18 future MLB plate appearances (probably a bit more, actually, since many of these’ players careers haven’t concluded). So 30 points or so of wRC+ equals an extra full season of MLB time–that’s not nothing.

Overall Thoughts on Batters

Whew, that was a lot of math, and we’ve still got to talk about pitchers. Before we do, I want to pause for a moment, summarize where we are, and run through a quick example to show how this can be applied.

What I’ve learned from running these analyses is that:

1. A year of age is, in a basic sense, worth about 25 points of wRC+ for batters.

2. A year of experience is something like ⅓ of a year of age, so a player drafted after his junior year of college is functionally only around two years “older” than a high school draftee born three years earlier.

3. The multilevel modeling framework I’ve used here generates age-specific equations you can use for calculating a sort of “generic” percentage chance a player makes it to MLB, and these seem to set helpful default expectations.

Just to give an illustrative example of this, in High-A Lansing, the A’s have 24-year-old Brett Harris, who has a 186 wRC+ as I’m writing this, and 20-year-old Brayan Buelvas, who is down at 62. Who projects to have the better chance of playing in MLB based on those numbers–the guy beating up on younger competition, or the guy struggling against pitchers three years his senior? Our 25-wRC+-to-a-year heuristic would favor Harris a bit, especially since it’s his first full season and Buelvas’ “third” (counting the 2020 non-season as a season). The linear equations give Harris a 47.6% chance of playing in MLB and Buelvas a 37.2% chance. The multilevel approach is more rigorous and historically accurate, though it doesn’t account for professional experience, and it generates a 34.6% chance for Buelvas and 40.1% for Harris. If we want to add the 4.4% bump for professional experience that the linear model suggested, we’re again in the realm of a 10-11% advantage for Harris.*

I want to stress, in this brief respite from 10,000 words of statistical analysis, that I would never look at the data in the above paragraph and run out into the prospect world shouting “HARRIS IS A BETTER PROSPECT THAN BUELVAS!!!” None of this takes into account defense, or swing mechanics, or pitch recognition, etc., or even the way the player is generating his wRC+ (Walks? Contact? BABIP? Power?). None of this preempts the need for an eyeball evaluation of the player in any way. It’s not a shortcut.

What it is is a sanity check and a grounding. I don’t know about you, but by default, I look at situations like Buelvas’ and Harris’ and don’t know exactly how those performances compare to each other. Obviously we know Buelvas is struggling, Harris is dominating, and Buelvas has time on his side while Harris definitively doesn’t, but how much of an equalizer is that time advantage, exactly? This analysis says it’s a very significant one, but isn’t enough by itself to make Buelvas as good a prospect as Harris if everything about the two players is equal.* So if one were to rate them as equally valuable defensive players with equal physical projection (relative to their ages) whose production is well-represented by their wRC+s (i.e., no weird luck, injury issues, etc.), one’s default orientation should probably be to rank Harris a touch higher on an A’s prospect list. Of course, if any of those other factors tip Buelvas’ way–and at least one clearly does, as we’re early in the season and he sports a .203 BABIP that’s bound to regress upward–then one could still potentially make a convincing case that he is the player more likely to have MLB value. The analysis does indicate that “Harris is 24, so he’s got no shot” and “Buelvas is hitting terribly, so he’s got no shot” are pretty clearly bad takes, but mostly, it just helps us make intelligent adjustments in cases similar to those of Harris and Buelvas. In contextualizing both ARL and performance, this modeling should help us avoid overreacting to players more than a standard deviation away from the mean in either of those variables.

*Gosh, I feel like I’m walking into some sort of sabermetric version of the “spherical chickens in a vacuum” joke.

Hopefully, that clarifies where we are with hitters. Let’s turn to the mound now.

Pitchers

One piece of conventional wisdom about ARL is that it’s less important for pitchers than it is for batters. It’s easy to look around and find anecdotal support for this idea. For one thing, young phenom types can flame out on the mound in a way that’s clearly quite uncommon for teenage dynamos on the position player side. Conversely, there are stories of pitchers suddenly going from the fringe of relevance to MLB domination–think Nestor Cortes or Corey Kluber. Further, the fact that there are so many successful conversions from the plate to the mound–Sean Doolittle, Anthony Gose, Rowan Wick, and so forth–and very few the other way around. It’s just a lot more possible for pitchers to rapidly gain or lose skill than it is for batters, so age appears less relevant.

Let’s take a look through the three levels in question and see how that idea holds up. We’ll use FIP as our performance-measuring statistic, as I mentioned earlier.

Low-A

We will again start with Low-A, and with a basic table of pitchers at each age and whether they made it to MLB eventually. Remember, these data (as with all the rest of the pitching data) require a minimum of 30 innings at the level in a given season.

Well, that’s definitely different from what we saw with position players. Instead of each year of age subtracting about a 14% chance of making MLB until you get to ages that are old for the level, we see a dramatic drop from teenagers (collectively 56.8%) to 20-year-olds, but all subsequent years are 10% or below. Interestingly, despite all the chatter in baseball circles about how There Is No Such Thing As A Pitching Prospect, Low-A pitchers of every age except 18 were more likely to make the big leagues than their position player counterparts.

So that’s our initial landscape. Let’s see how FIP factors into this picture relative to age:

Probability of making MLB = -.083(Age) - .089(FIP) + 2.37. (R-squared = .108)

MLB IP = -26.47(Age) - 23.95(FIP) + 713.6. (R-squared = .085)

Two things jump out to me here. The first is that we’ve got a year of age being worth somewhere between .9 and 1.6 runs of FIP, which is going to be somewhere in the range of 30 points or so of FIP-, so not all that dissimilar from what we had with wRC+ with hitters. Perhaps even more important. By contrast, though, is the second notable outcome, which is that these equations don’t explain the outcomes well at all–their R-squareds are significantly weaker than we had with Low-A hitters earlier (.195 and .123). TINSTAPP is wrong, but maybe it should just be rebranded as TINSTAAPPP: There Is No Such Thing As A Predictable Pitching Prospect.

Does adding pro experience in alleviate this problem?

Probability of making MLB = -.091(Age) - .099(FIP) - .007(Years Pro) + 2.63. (R-squared = .119)

MLB IP = -26.56(Age) - 23.22(FIP) - 6.47(Years Pro) + 719.82. (R-squared = .088)

Not really. In fact, pro experience isn’t even a statistically significant predictor of whether Low-A pitchers will make it to MLB. This is particularly notable since this is the level we might expect pro experience to be the most significant, since we have a lot of first-year guys and even the occasional same-year draftee* competing alongside international signees and high schoolers who might be in their fourth or fifth full seasons.

*Of course a lot of same-year draftees do go to Low-A, but not many get to 30 innings, so there wouldn’t be a ton in this sample.

Inscrutable indeed. Does that mean the slopes and intercepts are going to be in a weird pattern? Let’s see.

Not really, apart from the weirdness with 18-year-olds, which is easy to write off to the sample size of 33. Both of these fit simple quadratic patterns, more or less:

For some context as to the magnitude of this distribution, a 20-year-old pitcher with a FIP of 5 would have an equal chance at making the big leagues as a 21-year-old with a FIP of 4.1, a 22-year-old with a FIP of 3, a 23-year-old with a FIP of 1.76, and a 24-year-old with a FIP of 0.54 (a 28.05% chance, in this case). So if we wanted to say “it’s about a run of FIP,” that’s not a terrible heuristic to go by.

High-A

I’m writing this article as I’m conducting the analysis. Maybe I shouldn’t do that–it probably makes my articles even longer than they would otherwise be, and since I don’t know what the analysis is going to show, I can’t cleverly foreshadow something that’s going to happen here with something I said 3,000 words ago. Inherently, that makes the piece looser and less artful than it otherwise would be, and often makes me feel like I’m underperforming my capabilities as a writer. But I kind of like doing it this way, because I write a paragraph that calls for some analysis, then I do the analysis, and then I react to the analysis, just as you’re doing as you read it. I feel like there’s a sort of weird honesty to that–you know I’m not sitting down to write this from some sort of smug “I have the answers, and now…I shall reveal them!” vantage point. Instead, I’m asking some questions, getting some hints of which direction the answers may lie in, and then trying to make sense of that new knowledge with you.

I’d be lying, though, if I’m not at this point in the article thinking “Maybe I should’ve just gone back and tightened the whole thing up, and said ‘Hey, it’s 25 points of wRC+,’ *show graphs of each level*, and ‘Hey, it’s a run of FIP,’ *show graphs of each level*, ‘and it’s like, 14% chance of making MLB per year for batters and it’s probably something similar at every level for pitchers too.” The analysis of each level of batters had some important nuances, but they were definitely quite similar in a lot of important ways. But I’m sticking with the format I’m now 7,000 words into, because this is weird:

As with position players, High-A pitchers make the major leagues about 5% more often than their Low-A counterparts. But unlike the previous four tables of this sort that we’ve looked at, this doesn’t really break down on a year-to-year age basis. There seem instead to be four age tiers of some sort: 20 and younger, 21-22, 23, and 24+. Remarkably, while even 24-year-old position players at the High-A level historically make the big leagues at less than a 10 percent rate, even pitchers 27 and up exceed that mark. That fits the typical narrative of late bloomers, conversion guys, and so forth, so there’s a reason for it, but I’m at a loss in trying to make sense of age 21 and 22 pitchers at this level converging so tightly and both being so distinct from 20- and 23-year-olds. Maybe average innings pitched by age will yield something more linear?

Maybe a bit, but the tiers that appear in the previous table still manifest in something like a 50% cut in projected innings from the previous tier, whereas it only declines by 21% from age 21 to 22. Since this is so odd, I’m just gonna skip past the first set of linear regressions I’ve been doing–with just age and FIP in them–and cut to the age/FIP/years pro thing. Professional experience didn’t make much of a difference in Low-A, but does it show up here and explain this weirdness at all?

Probability of playing in MLB = -.093(Age) - .123(FIP) - .012(Years Pro) + 2.943. (R-squared = .161)

MLB IP = -30.29(Age) - 28.73(FIP) - 10.02(Years Pro) + 886.21. (R-squared = .101)

No, although despite the relative oddity of the tables above, these data were actually more predictable than the Low-A data (in this linear framework). And hey, years pro was actually a statistically significant predictor of whether the player would pitch in MLB or not! (Barely). FIP also takes on a bit bigger of a role in these equations than those in Low-A, which made me wonder: is FIP at this level correlated with age at all? We saw older players have slightly better wRC+s than younger ones in some of the earlier analyses…but nope, actually age and FIP were not correlated to a statistically significant amount here. They were, slightly, in Low-A (older pitchers were better; in High-A, if anything, they were worse).

So let’s turn to the multilevel model to see if that helps make sense of the patterning here. If the intercepts follow this same sort of tiered pattern, then indeed the ages would cluster together in this odd way, but they could be more evenly spaced but counteracted by some unusual slopes. Let’s see.

This continues the pattern we’ve seen where the youngest players have a smaller slope than players who are a more normal age–they’re so advanced by being in the level in the first place that their performance matters less. But then the slope plateaus, not just across age 21 and 22, but age 20 as well–a run of FIP in High-A at any of those ages moves the player’s chance of making MLB about 16%. Then there’s a huge drop to age 23 that holds steady through age 24, and then it tapers off. The intercepts simply mirror the tiers we saw earlier.

So, for whatever reason, age 21 and 22 pitchers in High-A seem to blur together, but age 23 is really different from 22 and quite different from 24. Also, the slopes here indicate that, as we might expect, performance at this level is significantly more determinative of MLB futures than performance in Low-A is. However, if I use the same example I ran through in Low-A–what is a 5 FIP pitcher equal to at other ages in terms of making MLB?–I get a 4.17 FIP at age 21, 3.36 at 22, 2.48 at 23, and 1.40 at 24. Overall, a bit less than a run, on average.*

*These are using the smoothed-out regression equations. If I run it from the raw age-specific regressions, I get 3.82 at 21, 3.60 at 22, 2.03 at 23, and 0.79 at 24, reflecting the similarity between 21 and 22 more dramatically. Practically speaking, I’d probably use the smoothed-out equations in individual player cases because you’d want to use their decimal age, not just the as-of-July-1 whole number, but given how weird the patterns are in the particular High-A pitching dataset, the age-by-age equations might actually be more reflective (and they’ve got the difference between age 20 and 23 at about exactly three runs, so there it is again). In any case, we’re at something like a 1±.3 runs per year so far for most level-appropriate ages, other than this weird age 21-23 stuff in High-A, which at least averages out into that realm.

Double-A

Finally, we come to Double-A pitchers. Here’s how they break down by age:

After the weird stratification of High-A, this is surprisingly regular-looking. It actually looks a lot like what we saw with a lot of the initial position player tables, with each year prompting a similar amount of decline (in this case, around 12%) until it starts to taper off as you get into ages that are relatively old for the level. As with the other levels, about 5% more Double-A pitchers get to MLB than do Double-A position players, and everyone does seem to be “in the conversation” here to a large extent: even 15 of the 83 players 30 and older made it to MLB, whether for the first time or a return trip.

Let’s see how a linear regression weights age vs. FIP now.

Probability of making MLB = -.076(Age) - .154(FIP) + 2.872. (R-squared = .188)

MLB IP = -35.87(Age) - 48.03(FIP) + 1115.5. (R-squared = .127)

There’s notably a way stronger weight on FIP relative to age here, as the first equation weights age slightly under half as much as a run of FIP, whereas it was closer to an even split at the earlier levels. What we’re seeing here is probably, as it was with batters, the increased meaning of performance.

Professional experience wasn’t much of an additional factor at the A levels with pitchers, but I’ll still throw it in here to see if it’s anything.

Probability of making MLB = -.081(Age) - .164(FIP) - .017(Years Pro) + 3.07. (R-squared = .192)

MLB IP = -33.89(Age) - 48.19(FIP) - 12.11(Years Pro) + 1124.22. (R-squared = .141)

It’s statistically significant in both equations, but doesn’t really change the picture significantly. Overall, it doesn’t add nearly as much statistical utility for pitchers as it does for position players.

Finally, let’s proceed to our last table: slopes and intercepts for each year.

We see the trend of particularly young players having a lower slope than more normally-aged players persist here too. Otherwise this is fairly normal-looking I suppose: there’s maybe something interesting with the slopes of age 25-27 players clustering together before a stark dropoff at age 28-29 (counteracted perhaps a bit with the high age-30 slope, which I’m writing off as a small-sample anomaly). There’s maybe something interesting in the fact that these equations predict that a 28-year-old with a 4.50 FIP would be 4% more likely to make the majors than a 27-year-old with a 4.50 FIP, but a 27-year-old with a 3.50 FIP would be 2% more likely than a 28-year-old with that number…but neither age group has a robust enough sample to really treat that as much more than an interesting curiosity.

Trying to fit an equation to these slopes initially looks like a mess…

..but that’s just thrown off by ages 20, 21, and 30. Remove them and you get something that looks linear:

We don’t quite get the nearly perfectly-fitting quadratic equation to predict these intercepts, but it’s only so far off:

Under these equations, a 22-year-old with a 5.00 Double-A FIP would have a 41.8% chance of making it to the big leagues, about exactly the average chance of a Double-A pitcher. That would also be the case for a 23-year-old with a 4.50 FIP, a 24-year-old with a 3.96 FIP, a 25-year-old at 3.37, a 26-year-old at 2.71, and a 27-year-old at 1.93. That is…well under a run per year, just a bit over half a run actually, as the earlier equations indicated.

Overall Thoughts on Pitchers

Pitchers seem a little more volatile to predict than position players, but the multilevel approach still makes pretty decent sense of them. The position player analyses had a few intricacies that were level-specific, but followed a pretty similar trend across the board. Here, we had some strange patterns in High-A and a much lower value of age relative to performance in Double-A.

It seems that “a year is a run of FIP in A-ball and half a run or so in Double-A” isn’t a terrible heuristic to go by, although the strangeness of the High-A data might point toward a more specific approach at that level, for whatever reason.

It seems that my idea of Double-A being the level where ARL starts to matter less, though it wasn’t particularly borne out on the position player side, does show up here. And that squares with what we know about pitching: sometimes, even anonymous guys suddenly show legitimate MLB stuff, and if they do, they have a chance to rocket right to MLB and be effective.

Concluding Thoughts

This may well be the longest thing I’ve ever written about baseball, which is saying something–I’ve long lost track of the hundreds of things I wrote in my Bleacher Report and FanSided days that are now over a decade past, but it’s up there, anyway. Yet I feel like I’ve barely scratched the surface of statistically investigating this issue. Originally, I planned on including a third dependent variable–the actual wRC+s and FIPs the players posted in MLB, but I scrapped that because a) it gets pretty distorted by the guys who were only up for a short period of time, and b) this article is long enough already. Perhaps at some point I’ll do a followup and run those analyses and others. There are certainly some interesting trends that show up here that merit following up on, and I’d certainly be interested to read the work of anyone else tackling ARL-related valuation.

At the same time, as much more as there is that could be done, I think the analyses presented here generally taught me what I wanted to learn from doing them. The goal isn’t to reduce the valuation of prospects to quantitative science: first off, that’s not feasible, for many reasons. In some ways, I actually feel more comfortable as an analyst with ideas like “it’s around 25 points of wRC+” than ideas like “it’s 26.81 points of wRC+ to move from age 21 to 22 in High-A.” I just wanted to advance the conversation, and my own thinking, from “this guy’s old for his level, so we have to somewhat discount his performance” to “this guy’s old for his level, so our starting point for thinking about his performance would involve discounting it by somewhere in the vicinity of x.” I feel like these analyses accomplish that goal for me, and hopefully they do for interested readers as well.

If you’ve made it through my maze of math and miniscule observations, thanks for reading. If I didn’t explain a particular analysis well, or you have questions, thoughts about the analysis, or recommendations for additional analyses or further readings, let me know.