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As a dad of three (and soon to be two more!) I’ve seen my share of developmental milestones. I’ve watched my daughters take their first steps, say their first words, and attend their first baseball games. I even took my oldest daughter to her first no-hitter, which also happened to be my first time seeing a no-hitter. In the ninth inning, I turned to her and, speaking more to my own sense of reverie than anything else, told her that I wished she were older so that she could really appreciate what she was seeing.

But as someone with a degree in child psychology, I usually interact with the developmental milestone chart in a different way. Mostly, it’s nervous parents wondering if their kids are on target, whether that’s the 13-month old who hasn’t quite gotten around to walking or the 6-year-old who hasn’t quite figured out how to pronounce the letter “R.” The thing about charts is that they often show the “average” timeframe for when kids accomplish those milestones, when they should be showing the normal range on them. Yes, there’s a point where you need to start worrying if a child is not developing, but for example with walking, normal range is between eight and 18 months. Please calm down and stop judging your kids based on what you see on Facebook.

MLB teams have their own kids they are raising. Indeed, the go-to slogan for a team that’s rebuilding is some variation on “come watch the kids grow up!” But most of the kids aren’t actually minors, they’re just in the minors, studying for the day when they will be called on to be productive major leaguers. Or at least serviceably passable ones. A minor leaguer’s status is often evaluated (in part) by whether he is “old” or “young” for his level. And that makes sense. A hitter who is handling Triple-A pitching at 21 and another hitter who is handling it at 27 may have the same present value, but the 21-year-old is probably going to turn into something special at the big-league level. Or at least someone will eventually ask for his autograph.

How do we know if a minor leaguer is “on target” developmentally? (At least, those of us who don’t have a whole lot of time to drive around and watch a bunch of minor-league games.)

Warning! Gory Mathematical Details Ahead!

For today, I’m going to look at one variable and one variable only: player age. (Yes, I know there’s so much more to it, but right now we’re just going to look at age. Just go with it.)

I downloaded minor-league stats from 2006-2011, because those players have at least had a chance to age through their team’s farm system in the interim. Of course, some players made the bigs and some did not. I coded for that, with a minimum of 100 plate appearances (sorry cup-of-coffee guys). I also coded for whether the player eventually put up a total of 1.0 win above replacement (cumulative over his career to this point), and whether he had gotten to 5.0 WARP.

First, the hitters. We know that a player generally goes through the levels of the minors in a specified order. He must first master low Single-A before being promoted to high Single-A and then to Double-A. Of course, if a player doesn’t get promoted he eventually just gets kicked out. Some guys top out at Double-A or Triple-A. (Or in my case, seventh grade rec league softball.)

This graph shows us something interesting. Here are the chances that a player who has “made it” to a level will eventually do what his team is hoping, which is become a major leaguer and put up some sort of value. The graph starts in rookie-ball, where fewer than 10 percent of the hitters in the sample make it to the majors, and goes through Low-A, High-A, Double-A, and Triple-A. Not even a majority of hitters who make their way to Triple-A appear in the show for anything more than a cameo, but that’s still not bad odds.

Let’s look at 18-year-olds the minors. There were 764 hitters who had an age-18 season in the data base and 700 of them played that year in rookie-ball. (This hopefully surprises no one.) Of those 700, 9.4 percent eventually made the majors, 4.4 percent eventually tallied 1.0 WARP, and 1.9 percent got to 5.0 WARP. Not bad. Of the 64 who were more advanced than rookie-ball, it will come as no shock that 62.5 percent of them made some sort of mark in MLB (compared to the 9.4 percent of their rookie-ball brothers.)

We move on to 21-year-olds, of whom I had 1,559 players, and the spread was a little more even: 587 of them were in rookie-ball, 500 of them in Low-A, 324 of them in High-A, 113 in Double-A, and 35 in Triple-A. The “made it to the majors” numbers tell the story. In order, 6.3, 13.2, 34.6, 64.6, and 82.9 percent. Again, this is no surprise. A player who had made it to Double-A by 21 has been judged by his organization to be pretty good, and assuming that these guys have some clue of what’s going on we shouldn’t be surprised when more of them make the big leagues.

But let’s check in on the 25-year-olds. By 25, a player is starting to lose his shine as a prospect. Shouldn’t he have grown up by now? In our sample, there were a smattering of hitters who were in rookie-ball (?) and Low-A, but none made it to the majors. But, six of the 260 guys (2.3 percent) who were still in High-A at 25 made it to the majors (and four put up a win’s worth of value.) That’s not a great percentage, but at least it’s not zero. At 25, 10 percent of those who were in Double-A made the majors and 43.4 percent who were at Triple-A did so.

Let’s turn these analyses around. This graph shows the success percentage for all players, based on the year that they first made it to Triple-A.

This tells us mostly what we already knew. Age and relative age to level is a pretty good proxy for how good a prospect is. What we might not know is how important a predictor it really is.

With variables that are dichotomous (i.e., yes or no) it can be hard to figure out the strength of the relationship between that variable and another one. We can’t do a regular Pearson correlation, but we can use something known as Nagelkerke’s R-squared that does pretty much the same thing. The Nagelkerke’s R-squared between age at first Triple-A appearance and whether he would make the majors was .192 (roughly a correlation of .438). That’s pretty good, but it looks even better when you pit it against what the hitter actually did in Triple-A.

I looked at the hitter’s on-base percentage as a predictor of whether he would make the majors (Nagelkerke = .132) and slugging percentage (.157), and they were close, but not quite as good as just knowing his age. But then again, minor-league SLG and OBP are going to have a lot of noise in them due to the fact that park effects can be a little more extreme in the minors (hello, PCL!). So I looked at walk and strikeout rates, which are a little more resistant to park effects (though are not particularly comprehensive looks at a player’s skill), and neither showed much predictive ability (.03 and .01).

So, if you want to know about a prospect and whether great things lie ahead for him and you can only know one piece of information about him, ask for his age. By extension, it’s better to know what his organization thinks of him and how quick they are willing to advance him than it is to know what he actually does in the games he plays. But I don’t even think that’s new information to people who really pay attention, and you come to BP to learn new things. Instead, I have another piece of information that might seem to come out of left field, but it’s important given the data we’ve already seen: the median age for first marriage in the United States for men is around 29 years old.

Wait … what?

A few notes on that. That’s a median age. Some are older, some are younger. Also, the formal marriage is the last step in the process after meeting someone, and then deciding that they are in fact the one person in the world who will drive you crazy the slowest. Not all couples formally marry either, or perhaps they delay the ceremony but are functionally married otherwise. The point is that around their mid-20s, many (though not all) men are developmentally at a stage where they are thinking about a committed relationship. It’s reasonable to think that some baseball players in their mid-20s—who also happen to be human beings in their mid-20s—are thinking in that direction, around the age when the prospect shine starts to wear off.

Why that little detour into demographic data? For a moment, imagine yourself in the position of a 26-year-old hitter who is just now getting to Triple-A and who is considering his options. His team is willing to keep him around for another year, but he’s also thinking about the rest of his life. He’s in a relationship that he believes is a long-term one and he wants to think about building a life together. Perhaps he’s starting to think about financial stability.

Last week, there was an article in USA Today written by Ted Berg which focused on the wages that minor leaguers are paid. In it, Berg profiled Kyle Johnson, who is part of a lawsuit which contends that minor-league wages—minor leaguers are commonly paid in the range of $10,750 (the minimum) to $15,000 per season—violate Federal laws. I will allow the courts to settle the issue of legality. But Johnson pointed out that it’s tough having a family (he is married and has a child) while pursuing the dream. I have to wonder how many players simply give up because they can’t afford to chase the dream or because the pull of a wanting to make money to support a family is simply stronger.

It’s easy to dismiss those guys because that time in their lives coincides with a time when their prospect status is starting to fade. But the chances that they will eventually become useful major leaguers are not zero. So, that brings up an interesting math problem. In his article, Berg brought up the example of the American Hockey League, which is a minor league for the NHL and has a minimum salary of $45,000. He calculated that for MLB organizations to raise their salaries by $30,000 per player, it would take something in the neighborhood of $7.5 million. Presumably a salary around $40,000 would make things a little easier for a minor leaguer to live on.

The information that we don’t have is how many minor leaguers walk away from the game in a given year, even though their teams would welcome them back, specifically because they can’t afford to make $12,000 for another year? With that information, we could construct some measure of how many lottery tickets those teams are throwing away and what the odds on those lottery tickets are. They aren’t great, but as they data shows us, they aren’t nil either.

He'll Need Money to Rent a Tux

In the past, I’ve suggested that teams might increase player wages as a way to make sure that they are well-fed and able to concentrate on learning, rather than worrying about money. Now, we have another piece to add to the case. It’s possible that teams are pushing away guys who might be late bloomers and could provide value to the team. It’s an intersection of human development and player development that could be unintentionally working against a team.

Even aside from the potential lessons for minor-league wages, there’s another lesson to be had. There are later bloomers in baseball and not everyone develops on the same linear track. Player development actually turns out to be messy and a bit unpredictable, just like actual human development. If your favorite prospect has gotten to the point where he should have grown up by now but just hasn’t, there’s still some hope. Just like kids, there are late bloomers, and once in a while they turn out better than the blue chippers. It’s not the way to bet, but it’s nice to know that once in a while life keeps you honest.