Archive for aging curve

“Stuff” and Father Time

The question of how pitchers age is paramount to players and front offices. “Stuff,” the colloquial term for raw talent throwing the baseball, can really be boiled down to velocity and movement (if we really wanted to oversimplify things). PITCHf/x gives us an opportunity to use big data to estimate “stuff” by looking at measurements of velocity and movement. We can use the copious data collected to estimate what “stuff” we can expect from pitchers as they pass the dreaded 30-years-old mark and beyond.

PITCHf/x reports movement in horizontal and vertical vectors. Horizontal movement (Hmov) is the right or left movement of the pitch compared to the expected trajectory without air resistance. A positive value is away from a right-handed batter. Vertical movement (Vmov) is the amount the ball moves up or down relative to the expected drop in a vacuum. A positive value means the ball dropped less than would be expected without effective spin.

It has been established that fastball velocity tends to decrease with age, but movement trends haven’t been looked at before. Might aging pitchers compensate their decrease in velocity with an increase in movement? Or does time steal away effective spin as well?

Let’s find out.

Methods:

I collected all PITCHf/x data from every pitcher with at least 300 innings pitched from 2007 to 2018 (n=537). Data was aged based on the age of the player on April 1st of the corresponding season. Velocity, horizontal movement, and vertical movement were averaged for each age and graphed. The horizontal axis of left-handed pitchers was flipped so right and left-handed data could be analyzed together.

I then took out the top starters by WAR (n=63), according to FanGraphs, from 2007 to 2018 and graphed their data separately.

Results/Discussion: Graphs are available by clicking on the links below, and raw data available in tables at the end of this post. Read the rest of this entry »


On the Use of Aging Curves for Fantasy Baseball

A question that tends to pop up around this time of year: “When does fantasy baseball season start?” Of course, we all know that fantasy-baseball season never ends, especially for those of us in keeper and dynasty leagues. To wit, Brad Johnson’s “Keeper Questions” thread posted just the other day is now sitting at 350 comments and growing. As we all collectively count the days ‘til spring training and opening day, one of the most oft-discussed and most subjectively-answered topics is “Who do I keep?” Fantasy baseball players intuitively understand the idea of aging, at least qualitatively. Older players are less valuable, given that their performance is more likely to decrease due to both injury and ineffectiveness. But how much is age worth, really?

Read the rest of this entry »


What A Drag It Is Getting Old: Old Guys, Getting Older Faster

As I noted a few weeks ago, batters who were at least semi-regulars in both 2014 and 2015 were less effective in 2015 than in 2014, as measured by wRC+. That seemed directionally unsurprising — after all, players are subject to aging and regression every year — though the magnitude (an average decline of over five wRC+ points, or over four weighted by plate appearances) was a little higher than I’d expected. Was that decline, I wondered, unusual?

To answer, I calculated the change in wRC+ from one season to the next for players with at least 350 plate appearances in each season. I looked at every year from 1969 (four-team expansion, beginning of divisional play) to the present. (Fine print: I didn’t prorate my results for strike-shortened seasons, and I combined both leagues, with their different DH rules for most of the seasons, in the study. We’re looking at over 10,000 player-seasons, so small variations like the 1994 season and the four years in which the AL didn’t have a DH don’t amount to a lot.) Here are the results, with the second year of the pair of the x axis:

This graph should elicit two responses: (1) it looks as if year-on-year performance is declining, and (2) that is one noisy graph.

So I did another graph, taking the rolling three-year average change instead of the single-year change. Again, the second year of the pair is on the x axis, so 1972 refers to the average change for 1969-70, 1970-71, and 1971-72:

That’s less noisy, but it doesn’t change the conclusion: the year-over-year decline in offensive performance is the steepest it’s been in the nearly 50 years since divisional play began. I’ll use rolling average graphs for the remainder of this article.

The obvious question is: Why? What has changed that’s caused players to be nearly four points worse in terms of wRC+ in recent years when the long-term average decline is less than two, and hovered in a range of 0-2 in most years?

The first possibility that came to mind: Is it an age thing? Are players exhibiting different characteristics based on their year of birth? I divided the batters in my sample into four categories: Young (younger than 25 in the first season of the pair), Prime (25-29), Late Prime (30-34), and Old (35 or older). Here’s the decline in wRC+ for Young players. I used five-year moving averages, since limited sample sizes made the three-year moving averages pretty noisy.

Young players have been getting better, not worse, in consecutive years. That makes intuitive sense: we’d expect batters to improve a bit every year up to their peak in their late 20s. So youngsters aren’t the reason batters appear to be falling off more, year over year.

How about Prime years:

That’s the same scale as the last graph. This is a classic “You can go about your business, move along” graph. There’s been no notable change here. Batters entering their prime years have improved by about 1.5 wRC+ points in consecutive years, year-in, year-out.

Late Prime players:

Now we’re seeing declines, along with more noise. Players under 30, on average, improved their wRC+ from one year to the next. On the other side of 30, we see decline start to set in, to the tune of about a 3.8-point wRC+ average. And it’s gotten worse over the last ten years, rising from an average of about 3.1 in 1986-2005 to 4.1 in 2006-2015.

But we haven’t explained the problem yet. There’s nothing in the prior three graphs that would explain why the decline in wRC+ from one season to the next for semi-regular players has risen by over two points, because none of the prior three age groups has fallen off sharply. One more group left; let’s look at the Old players, 35 and up:

Whoa. That’s pretty dramatic. Year-over year, old players who are semi-regulars are declining a lot more now than they have been at any time since the mid-1970s, when trotting out the fossilized remains of Henry Aaron, Deron Johnson, and Billy Williams to play DH seemed like a good idea. This is the noisiest graph I’ve showed you so far, due to the limited number of older players in the game each year, but the marked climb since the 1990s is unmistakable.

Why is that? What’s happening to guys 35 and older? Nothing exactly leaps out, so here are some possible explanations:

Steroids. Admit it — that’s the first thing you thought. Same here. Fifteen or so years ago, you had all these guys in their late 30s putting up .300/.400/.500 lines with a couple dozen (or more, a lot more) bombs. Or at least it seemed that way. And sure enough, the five-year moving average decline in wRC+ for players aged 35 years or older was below the long-term average decline of about five wRC+ points for all but two years between 1989 and 2004. I think this points to a possibility of chemically-delayed aging patterns that have returned to normal, or perhaps even gotten worse.

More old guys. It’s not a secret that baseball players are better when they’re young than when they’re older. But, as noted above, the Steroid Era featured a lot of old guys hitting the crap out of the ball. Maybe that changed the thinking regarding roster construction, and teams are still carrying a lot of older hitters, even though they’re no longer as effective. Well, here’s a graph showing the percentage of players with 350+ plate appearances per season who were 35 or older.

No, GMs aren’t nostalgic for baseball in the late 1990s and early 2000s. There are fewer older players with regular or semi-regular roles today now than at any time over the past 20 years.

Worse old guys. Maybe the problem is just one of quality. Maybe older players today just aren’t as good as they were in years past. Maybe there was something about babies born in the 1970s. (Disco? The clothes? Watergate?) Here’s a chart showing players who were at least semi-regulars in consecutive seasons, aged 35 or older in their first season, and their wRC+ in their first and second seasons.


Nope, the older guys who’re good enough to get at least 350 plate appearances are still good players. They’re just getting worse faster, as evidenced by the widening gap between the red and yellow lines above.

Amphetamines. In baseball, the term performance-enhancing drugs is synonymous with steroids (and, to a lesser degree, HGH) in the public mind. But the list of banned substances is long, including all manner of illegal recreational drugs and, of relevance here, stimulants. Amphetamines — greenies, in baseball vernacular — have been associated with the game dating back to at least the 1960s. Baseball, of course, has a long season, with many more games than any other North American sport. Amphetamines help players improve reaction time, focus, and ward off fatigue. Those benefits accrue to everyone, of course, but they seem particularly relevant to older athletes, who face the inevitability of the aging process, mentally and physically. The amphetamine ban, which began in 2006, has likely had a larger impact on older players than younger ones. Of course, we’re talking about ten years of amphetamine testing, while the decline in older hitter year-on-year performance has lasted longer, so this can be only a partial explanation.

Sunk costs. Regular readers of FanGraphs are well acquainted with the concept of sunk costs; Dave Cameron has written about it repeatedly. Basically, a team should look at its total payroll as a cost of doing business, then allocate playing time in a manner that optimizes its chances of winning ballgames. That’s theoretical, of course. What actually happens is that teams are often reluctant to put high-salaried players into supporting roles. Take the 2016 Yankees, for example. They have a projected 2016 payroll of $230 million. They’ll spend about three quarters of that amount on nine players, all but one older than 30. Ideally, they should be willing to put CC Sabathia ($25 million in 2016, his age-35 season) in the bullpen, or make a DH platoon out of Mark Teixeira ($22.5 million, 36) and Alex Rodriguez ($20 million in each of 2016 and 2017, 40), or release Carlos Beltran ($15 million, 39) if any of them start particularly slowly. That’s what they might do with a 25-year-old making the major-league minimum. But the payroll obligation makes that move harder, even though that obligation’s a sunk cost — the team has to pay it regardless of how much the player plays. Here are the eight players aged 35 or older who, over the past two years, have suffered a wRC+ decline of 25 or more while retaining at least a semi-regular role, along with their contract status beyond the decline season:

All but Beltre and Byrd were below-average hitters in the second year, arguably not deserving of the plate appearances they received. But all but Suzuki, Utley, and Byrd were due at least eight figures after the year of their large decline. By contrast, a decade earlier, in 2004-2005, there were eleven semi-regular batters who, aged 35 or older, who had a wRC+ decline of 25 or more. Of them, only three — Luis Gonzalez and Jim Edmonds in 2005 and Bret Boone in 2004 — were in the midst of unexpired long-term multi-million-dollar contracts. Small sample size warnings and all, but there was a lot more future money committed to declining old batters in 2014-15 than 2004-05. Maybe those players wouldn’t be getting the plate appearances to meet the 350 threshold if it weren’t for the money that’s owed them.

Fastballs. One of the notable changes in baseball in recent years has been that pitchers throw harder. From 2007 to 2015, per PITCHf/x, the average fastball velocity increased from 91.1 mph to 92.4 mph. The increase was 1.3 mph, to 91.9 mph, for starters and 1.5 mph, to 93.2 mph, for relievers. Older batters can take advantage of their knowledge of the strike zone and pitch sequencing, but maybe they just can’t catch up to some pitches.

Granted, I’m guessing here. I’m leaning towards PEDs, both strength-enhancing and amphetamines, faster fastballs, and a tendency to put high-paid players in the lineup regardless of performance as the key drivers. But I’m not sure. This is an interesting trend, and sufficiently well-established that I don’t think we can write it off as a recent fluke. Something’s going on with players in the second half of their fourth decade that hasn’t happened in a long time.


Different Aging Curves For Different Strikeout Profiles

What follows will look at aging curves as they relate to players with specific strikeout profiles. Specifically, we will look at how wOBA ages for players that strikeout more than the league-average strikeout rate and less than the league-average strikeout rate.

Through the research that is presented in this post, two points will be proven:

  1. Players of different strikeout profiles age—their wOBAs change—at different rates.
  2. The aging curve for players of different strikeout profiles has changed over time.

Before I present the methodology, the research that was conducted, and their conclusions, I want to give a big thank you to Jeff Zimmerman, who has not only done a lot of research around aging curves, but has also helped me throughout this process and pushed me in the right direction several times when I was stuck. Thank you.

Population

In order to give a non insignificant amount of time for a player’s wOBA to stabilize, but not place the playing time threshold for plate appearances so high that we artificially limit the population even more than it naturally is at the ends of the age spectrum, I looked at all player season from 1950 to 2014 where a player had a minimum of 600 plate appearances for the first aging curve in this post. The second aging curve in this post looks at all player seasons from 1990 to 2014 with a minimum of 600 plate appearances.

Now that we have our population, we need to split our population into two groups: players that strikeout more than league average and players that strikeout less than league average.

Because the league average strikeout rate of today is very different than it was 65 years ago, we can’t look at a player’s strikeout rate from 1950 and compare it to the league average strikeout rate of today.

In order to divide the population into two groups, I created a stat that weighs a player’s strikeout rate against the league average strikeout rate for the years that they played. For example, if a player played from 1970 to 1975, their adjusted strikeout rate would reflect how their strikeout rate compares to the league average strikeout rate from 1970 to 1975.

Players were then placed into two buckets based on their adjusted strikeout rate: players that struck out more than league average and players that struck out less than league average.

Methodology

There has been a lot of discussion over the years about the correct methodology to use for aging curves. This conversation has had altruistic intentions in the sense that it’s aim has been to minimize the survivorship bias that is inherent in the process, and, through the progress that has been made over the years, this study uses what the author has found to his knowledge to be the best technique to date. This article by Mitchell Lichtman summarizes a lot of the opinions.

While there is a survivorship bias inherent in any aging curve, the purpose of the different techniques used to create aging curves is to minimize the survivorship bias wherever possible.

What We Don’t Want In an Aging Curve 

An aging curve is not the average of all performances by players of specific ages. For example, say you have a group of 30-year-old players that have an average of a .320 wOBA and group of 29-year-old players that have an average of a .300 wOBA.

The point of an aging curve is to see how a player aged, not how they played. The group of 30-year-old players has a high wOBA because they are a talented group of players; they lasted long enough to play until they are 30. As they aged from the previous year, when they were 29 to their current age 30 season, they lost the bottom portion of players from their player pool. These are the players that couldn’t hang on any longer, whether it be because of a decline in defense, offense, or a combination of both. This bottom portion of players lower the wOBA of the current 29-year-old population through their presence and raise the wOBA of the 30-year-old population through their absence.

At the same time, the current 30-year-olds aged from their age-29 season to their age-30 season. Sure, there may be players who had a better age-30 season than age-29 season, but the current group of 30-year-olds, as a whole, still played worse at 30 than they did at 29.

When you look at the average of a particular age group, in this case 30-year-olds, you only see the players that survived, and, because they no longer play, you leave behind the players that are hidden from you sample. The method that follows resolves this issue to an extent.

What We Do Want In an Aging Curve

This study uses the delta method which looks at the differences of player seasons (i.e. a players age 29 wOBA minus their age 28 wOBA) and weighs those differences by the harmonic mean of the plate appearances for each pair seasons in question.

I would explain this further, but Jeff Zimmerman does an excellent job of this in a post on hitter aging curves that he did several years ago. While Jeff Zimmerman looked at RAA, which is a counting state, the methodology is basically the same for our purposes and wOBA, which is a rate stat:

In a nutshell, to do accurate work on this, I needed to go through all the hitters who ever played two consecutive seasons. If a player played back-to-back seasons, the RAA values were compared. The RAA values were adjusted to the harmonic mean of that player’s plate appearances.

Consider this fictional player:

Year1: RAA = 40 in 600 PA age 25
Year2: RAA = 30 in 300 PA age 26

Adjusting to harmonic mean: 2/((1/PA_y1)+(1/PA_y2)) = PA_hm
/((1/600)+(1/300)) = 400

Adjust RAA to PA_hm: (PA_hm/PA_y1)*RAA_y1 = RAA_y1_hm
(400/600)*40 = 26.7 RAA for Year1
(400/300)*30 = 40 RAA for Year2

This player would have gained 13.3 RAR (40 RAA – 26.7 RAA) in 400 PA from ages 25 to 26. From then, I then would add all the changes in RAA and PA together and adjust the values to 600 PA to see how much a player improved as he aged.

Findings

Below is an aging curve by strikeout profile for all player seasons with over 600 plate appearances in a season from 1950 until 2015.

Screen Shot 2015-04-18 at 1.23.52 PM

We can see several findings immediately:

  1. Players do age differently based on their strikeout profile.
  2. Players that strikeout more than league average peak at 23.
  3. Players that strikeout less than league average take longer to hit their peak—their age 26 season.
  4. Players that strikeout more than league average age better than players that strikeout less than league average.

From a historical perspective, this graph is fun to look at, but the way the game was played over half a century ago is eclipsed by societal evolutions that today’s players benefit from.

To give us a more realistic idea of how today’s players age relative to their strikeout rate, I made another graph the at looks at player seasons from 1990 to 2014.

Screen Shot 2015-04-18 at 1.40.36 PM

What we find in this graph, which is more current with today’s style of play, is that players still age differently dependent on their strikeout profile, but not in the same way that they did in the previous sample.

Players that strikeout more than league average still peak earlier than players that strike out less than league average, but in this more current population of players, players that strikeout more than league average peak very early—their age 21 season. This information would reciprocate the sentiment that has been conveyed through recent work that suggests that the aging curve has changed to the point that players peak almost as soon as when they enter the league.

The peak age for players that strikeout at below league average rates is still 26, but whereas this group aged more poorly than the strikeout heavy group in our previous population, players that strikeout at below league average rates now age better than their counterparts.

Conclusions

This information can make material differences for our overall expectations and outlooks on players.

Previous knowledge would suggest that players like George Springer and Kris Bryant—players who have exorbitant strikeout rates—are still on the climb as far as their talent goes, but this information shows that these players may already be at/close to their peaks or on the decline as far a their wOBA is concerned.

This information also shows that we should be patient with prospects that have a penchant to put balls is play; while they peak more quickly than they did in the previous population, they take longer to develop than players with more swing and miss in their game, and when they do start to decline, there isn’t much need to worry, because their climb from their peaks will be gradual.

Like many other studies that have looked at new aging curves, this study confirms that players/prospects peak earlier now than at any other point throughout history, but it also shows that a player’s trajectory upward and downward is dependent on characteristics specific to their approaches at the plate.

Devon Jordan is obsessed with statistical analysis, non-fiction literature, and electronic music. If you enjoyed reading him, follow him on Twitter @devonjjordan.