Are Aging Curves Changing?

For years it’s been assumed hitters will get to the major leagues and peak offensively around age 30. Teams and fans can hope the new, shiny, 20-home-run-hitting rookie will improve over time and someday will hit 30 to 40 home runs. Hitters were expected to improve until their late twenties and then begin to decline. But recent data show there’s no longer a hitting-peak age. Instead, hitters arrive at their peak and simply decline with age.

I pretty much stumbled on this finding a few days ago. I created an stolen base aging curve for Mike Podhorzer and then created one for home runs. I separated the data into pre- and post-PED ban eras, the latter of which happened between the 2005 and 2006 seasons. It didn’t surprise me to see a slow decline in the home run curve during the PED era. My biggest surprise was the post-PED data where home runs no longer peaked, they only declined. I examined just about every overall offensive stat (OPS and wOBA, to name a couple) and found the same thing: Hitters no longer peaked, they only declined. Here’s a look at the wOBA aging curve from pre- and post-PED ban eras, along with a note on how the curves were created.

Note: The aging curve was created by the delta method by weighting plate appearances using their harmonic means. With this method, there’s a small survivor bias summarized by Mitchel Lichtman at the Hardball Times:

… survivor bias, an inherent defect in the delta method, which is that the pool of players who see the light of day at the end of a season (and live to play another day the following year) tend to have gotten lucky in Year 1 and will see a “false” drop in Year 2 even if their true talent were to remain the same. This survivor bias will tend to push down the overall peak age and magnify the decrease in performance (or mitigate the increase) at all age intervals.

For 20 seasons, hitter production began to decline significantly around age 30. Over the past seven seasons, the decline has occurred immediately.

A problem exist when using wOBA in the recent lower scoring environment. The league wOBA in 2006 was .337, and in 2013 it was at .318. That’s a drop of 19 points in seven seasons, or 2.7 points  per season. Players will have the appearance of aging from season to season.

Hitting (wOBA) has been on the decline for several reasons. Teams have been better at evaluating players’ defense abilities and deploying better defensive alignments in the field. Also, the quality and quantity of hard-throwing relief pitchers has increased across the league. Finally, 2006 was the first full season with the harsher PED punishments (from 50-game suspensions to 100-games suspensions t0 lifetime bans). This overall decline leads to a large year-to-year aging factor. The recent decline in offense led me to create aging curves with wRC+, which is weighted to the season’s, the league’s and the park’s run-scoring environment. I ran the aging curve to look at four, seven-year time frames.

With wRC+, the most recent aging curve doesn’t immediately begin declining like the wOBA curve. Instead, it remains constant until it begins to decline. The decline starts at the same point when previous players began declining (between age 25 to 26 season). The curve shape is the same for pitcher aging curves: no up and down, just constant and then down. Additionally, the most recent rate of decline is almost the same as the pre-PED aging rate (82-89).

This information is important in predicting young players’ performance. Once a hitter makes it to the majors, he doesn’t really improve. In the past, people used to hope for improvement and growth as the player aged. These days, people should expect to see the player performing at his career best immediately.

A couple possible reasons may be behind the lack of improvement. First, players are more prepared for majors, physically and mentally. In the past, a player may not have had the best conditioning, coaching and training while he was in the minors. Teams are putting more resources into their minor league affiliates, and there isn’t room for improvement with the major league team. Second, teams may be better at knowing if or when a player will be MLB ready, meaning the player doesn’t have to mature and grow at a lower level. They are ready to contribute immediately

This trend of contributing right away may have been occurring before 2006. The uncontrolled use of PEDs may have masked the lack of an up and down curve. Players were improving chemically past their previous peak and were able to maintain their performance over time.

For years, pitcher performance declined as those players aged, but hitters seemed to have an up and down performance curve. In the past few seasons, hitters no longer improve once they arrive in the majors. Instead, their performance is constant until they begin to decline, which, on average, is at 26 years old. Improved training and development is probably behind the shift. If fans are hoping for a young position player’s performance to peak, they might be sorely disappointed. Chances are the player is likely producing at his career-best already.




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Jeff writes for FanGraphs, The Hardball Times and Royals Review, as well as his own website, Baseball Heat Maps with his brother Darrell. In tandem with Bill Petti, he won the 2013 SABR Analytics Research Award for Contemporary Analysis. Follow him on Twitter @jeffwzimmerman.


134 Responses to “Are Aging Curves Changing?”

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  1. thrylos98 says:

    Can you list the size of the samples for each group? I suspect that what you are seeing with the wRC+ curves is artefactual on both edges because of the sample sizes and all 4 curves are within the standard deviation in the middle… wOBA too, potentially…

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  2. nada says:

    damn. I was really looking forward to witnessing Mike Trout’s 15 WAR seasons.

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    • Brian says:

      haha Mike Trout can do ANYTHING!!!!!!

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      • Julian says:

        What’s really crazy is that even though this curve looks way more aggressive than what we’ve come to expect, it’s still saying Trout will be worth 7 WAR when he’s 32. And that’s in 10 years. With 5% inflation and $6 million/win that’s worth $56.28 million in 2023.

        Even if he’s more of an 8 WAR player right now that’s still 5.6 WAR. In 10 years.

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    • Andy says:

      I wondered why Steamer has him performing at a slightly lower level next year than this past year or his rookie season.

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      • Jason B says:

        I would imagine projection systems generally will not project 10 WAR seasons from anyone. Even those that have them in the past.

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        • Catoblepas says:

          Oliver has his five year projections at 9.4, 10.0, 10.2, 10.2, 10.3, soooo… but yeah he just breaks the scale completely.

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        • Brad Johnson says:

          I can’t speak for Steamer, but I know Oliver doesn’t use the same aging curves as Jeff just shared. With Steamer (and again, I’m not sure here), I think it’s a little more like Tango’s Marcel where there’s year-to-year regression built into everyone.

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        • Catoblepas says:

          that seems odd to me, given that aging curves are probably more important in five-year projections than they are in one-year. thanks for the info.

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    • Kas Gardiner says:

      A year ago wouldn’t Chris Davis have been among the group of players performing within a certain range? Despite the curve i’m having some difficulty accepting that rookies arrive at their peak and then simply decline. Perhaps peak means skills/talent but isn’t there a mental aspect to consider? Shouldn’t young players get better knowledge of the strike zone, better knowledge of pitchers, and thus improve their performance, if not their talent level?

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  3. Leo says:

    Interesting analysis.

    Is a factor in this curve selection bias because the only players who are called up at age 21 are exceptional talents? Has the practice changed in regard to who gets called up when?

    A related question, what proportion of that 06-13 sample for players under 22 is Mike Trout?

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    • Charlie says:

      I’d expect it doesn’t change the conclusion. If a player were to be called up as a 23 year old, the same still holds true from 23 years of age to 24 years of age.

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    • Jeff Zimmerman says:

      I agree this could be true: “Has the practice changed in regard to who gets called up when?” as I stated in the article. True reasoning behind the data is a little murky.

      There are no matched pair with Trout to compare. He is not even part of the data in the graphs since his only matched seasons are 19to20 and 20to21

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      • Peter says:

        The problem with this analysis (as mentioned by others previously) is that the level of talent of call-ups tend to drop with increasing age (since the best go through the minors faster) and the level of ‘native talent’ of older hitters tends increase. So aggregating gives a false picture of the statistics–it tends to increase the stats at the right and left sides of the graph at the expense of the ‘peak’.
        The difference between time periods is more interesting but is that merely a matter of certain clubs being more aggressive at bringing ‘super-talents’ up faster. I would like to see some stats on whether patterns of callups have changed at the same time.

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  4. Shao says:

    Does that suggest PED helps hitters more than pitchers?

    So the HOF should let Roger Clemens in and Barry Bonds out?

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  5. Brendan J. says:

    Jeff Sullivan, I’m feeling intimate things for you right now. I’m not even ashamed. Not at all.

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  6. sixto lezcano says:

    How is the curve altered if the best 5 or 10 or 25 percent of players under 25 are removed from the group? Is this trend true for every type of player or just overall, including the very best players?

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    • Bay Area Bucco says:

      I’m interested in this as well. Like Leo said above, only exceptional talents get called up when they’re 21, so that may skew the results in the lower age ranges a bit. This is an interesting overall trend, but doesn’t really mean much in terms of the development of a single player.

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      • tdi1985 says:

        Also, in looking just at the current group, I’m interested in how the drop-off varies by performance group. Sooner, steeper, etc.?

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  7. Gabriel says:

    A thing that’s been striking me recently is that as the players unions in different sports have been sacrificing the salaries of young players during labor negotiations, they’ve made those young players much more cost-efficient for teams, leading to greater usage of younger players rather than older players (and long-term forcing down salaries of older players).

    Now this comment is not totally related to the original post. That said, perhaps younger guys are getting more opportunities to show themselves while older guys have a shorter margin of error before being abandoned?

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    • Dan says:

      Actually, I think it is the opposite for guys who are impact players. Teams keep them in the minors longer to “make sure they’re ready.” See Will Myers last year, Mike Trout before him, and so on.

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      • John DiFool says:

        Yep (what Dan said). Rarely will teams have the patience to let a top prospect develop at the major-league level anymore. Gone is the day when the Milwaukee Brewers put a Robin Yount in the lineup at a young age (18!) and let him learn at the major-league level. Part of that is likely also due to wanting to control players at low costs during their prime seasons. But for whatever reasons teams seem to want to be pretty sure players can handle the majors before they are brought up for good.

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        • cass says:

          Bryce Harper.

          I do believe there have rarely been many teenagers in the majors. I’m not sure there’s a trend there. In fact, I’ve heard players talking how kids are rushed these days. Chipper said that about Bryce. Not sure about the numbers, but for teenagers, I am pretty sure there have always been very, very few.

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        • Mr Punch says:

          I think this latter point is very important – teams are now reluctant to accelerate loss of control of the most promising players.

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        • shoewizard says:

          Seasons by decade age 19 or younger, minimum 50 PA. (Not including Pitchers

          1950-59:24
          1960-69:19
          1970-79:5
          1980-89:5
          1990-99:6
          2000-09:2
          2010-13:3

          2004-2013:5

          2006-2007:4

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  8. Anon21 says:

    So you’re saying we should just expect Harper to get worse from here? Sounds good to me!

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  9. jdbolick says:

    Eno from January 2012: http://www.fangraphs.com/blogs/hitters-age-like-wine-power-like-cheese/

    Men physically peak in their early 20s, so it stands to reason that power and speed would decline from there. Some make up for that with improved skills and/or elimination of bad outcomes, such as the increasing walk rate and declining strikeout rate that Sarris noted. I do think it’s a mistake to say “Once a hitter makes it to the majors, he doesn’t really improve,” as even in the aggregate we see changes in behavior such as the results noted above. Those skill improvements don’t happen for everyone while they may exceed, equal, or be overwhelmed by physical decline even when they do.

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  10. Cybo says:

    So if what you’re saying is true the Josmil Pinto should be a stud next season. I was already targeting him as a late round flier now I think he just got bumped into the high teens for me.

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    • someone says:

      I’m not sure how serious you are here, but this article should have roughly zero impact on fantasy drafting strategy. These curves show general trends, and are somewhat meaningless for one player (especially for a player who posted a .440 BABIP in 83 PA).

      This comment does bring up an important point though, these plots give a general trend but provide absolutely no detail on how much variance there is in the aging curves (or what possible other factors might drive this variance)

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      • bjoak says:

        I don’t know if I’d say none. It would be an interesting study to see if high end prospects have been beating their projections when they’ve finally made it (since 2005). Projections are usually pretty low on minor leaguers even if they have an impressive pedigree.

        Also, I think whenever people draft a Bryce Harperthey have it in the back of their mind that he is primed for a breakout. The study shows he is not much more likely to break out than anyone else (or at least that he’s as likely to break out as collapse). So it changes how much you draft based on potential.

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  11. TKay says:

    This is hard information to swallow. We have so many hitters that defy the recent trend. Miggy came in at 20 and is peaking at 30. Chris Davis, Cutch, Cano, and others all seem to fit perfectly into the ’95-’05 aging curve.

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    • Ruki Motomiya says:

      There’s pretty much exceptions to almost every rule.

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      • cass says:

        I noticed this when I looked at infielders of the Ryan Zimmerman generation. They all generally peaked at 24 or 25. Then they had one down year and after that came back a bit but almost never were significantly better. Doesn’t surprise me it applies to everyone.

        Ian Desmond is has improved tremendously, but he’s an exception.

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    • The Foils says:

      He’s probably lying, then. Or those are anecdotes.

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    • Occam's Razor says:

      Maybe those guys are on PEDs….

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  12. Daniel says:

    Now I’d like to see an aging curve for Adrian Beltre…

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  13. nada says:

    A suggestion: could you make confidence intervals on each age by bootstrapping? I am not sure I believe that there is a curve at all–maybe what we are seeing is totally random variation.

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    • Jeff Zimmerman says:

      It could be a variation, but there has not been a similar one ever I could find.

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      • someone says:

        I tend to agree with you Jeff, but it certainly would help your argument to calculate the variance. Plus, finding a bootstrap estimate for the standard error of the mean would be relatively easy, so why not?

        Along those lines, I’d be interested in the amount of variance at each age level. I imagine there’s a lot more variance at younger ages (and perhaps older ages as well), which could be very interesting.

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      • nada says:

        “but there has not been a similar one ever I could find”

        could you explain what you mean by this? I’m not trying to be snarky, I genuinely don’t understand.

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        • Jeff Zimmerman says:

          I looked for other seven year intervals.

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        • nada says:

          OK, gotcha.
          But I have to say, I still think the most parsimonious explanation is that for some luck-based reasons, 2-3x more HoF-class hitters were born in a 5 year span than expected (e.g. Bryce Harper, Mike Trout). If it continues for a while, I will be convinced. And it’s very interesting, regardless of the reason.

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        • someone says:

          You didn’t get a similar pattern for 2005-2012? That would worry me that this is just an aberration.

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  14. RMD says:

    Too bad Seattle didn’t see this last week…

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    • chuckb says:

      I think it’s pretty clear that no one in a decision-making capacity in Seattle wouldn’t know what to do with a graph that didn’t plot batting average on one axis and RBI on the other.

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  15. garrioch13 says:

    There are hurdles to clear for me to fully accept this.

    In general, wOBA has regressed in a similar arc over the time period that you are representing here. Ignoring age, the arc is still similar to that so it doesn’t have strong meaning to me. Maybe I am not interpreting it properly, as wOBA isn’t a stat I have studied thoroughly, but the table above looks similar to the regression shown here. http://www.fangraphs.com/library/offense/woba/

    I’d like to see the numbers of each player compared to league average. Would using wRAA be better? Again, I haven’t studied these numbers, so I’m not sure.

    Looking at the wRC+ aging curve also has issues to me. For one thing, young players have always been good but it was very hard to justify moving the productive 35 year old to the bench to give the 21 year old offensive player a shot. This was especially true for positions with typically higher offensive production like LF, RF, 1B.

    Whereas aging middle infielders were easier to unseat with younger more athletic players who also produced less offensively. That could be one explanation for the younger players to have less production in the past but I’m less certain this applies. This could be ascertained by looking at percentage of each age for each position played.

    You are also saying that players are decling immediately, where I would say they are improving less and aging more rapidly past age 26. The line from age 21 to 26 is pretty level on the second graph.

    I do think that players are getting better, younger, thanks to more improved competition in the amateur ranks for the highest level players. Players now get their first exposure to 90+ MPH velo at a young age, not in rookie ball.

    Fascinating research but this makes me ask so many questions. This is exactly why I haven’t posted much of my research. If I can’t answer my own questions, I don’t feel it is complete. This makes me ask a lot of questions and I don’t feel that any of the findings are definitive.

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    • bjoak says:

      You do research and then others add to it. Darwin didn’t have every answer and neither did Voros McCracken. You put your work out and others verify and add to it. That is what will porobably happen here.

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  16. Ruki Motomiya says:

    Theory from someone not very smart: Could it be because of increased focus on patience and other such things?

    Presumably, players peak physically younger rather than older. Your body would be more fit at 20 than 30, assuming all your major growth is done. Therefor, most improvement presumably would come from non-physical areas, such as pitch recognition, which in older times would come “with age”, so a player would “peak” when their mental skills and physical skills are both at their highest. But with much more focus, in general, on taking pitches and so on and such forth, players are learning that at a much sooner level and reaching their expected BB%, K% and so on faster, so these improve less with time. Thus, both of their skills are at or near their highest at a younger age. The biggest thing that would dismiss this is the 82-89 numbers are similiar.

    One other thing I was interested in: Judging from that wRC+ graph not only is this a constant rate of decline, but it is the most decline from 27 on of any of the years looked at. Are players not only declining sooner, but declining harder?

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  17. jkd says:

    How new is this phenomenon, really? Fred Lynn had his second-best season as a rookie – Cal Ripken, his 2nd- and 3rd-best seasons in Years 1 and 2 – A-Rod, his 2nd-best in Year 2 – Doc Gooden’s best two years were his first two – Don Mattingly’s first three full years were his best – and that’s just some of the best from the late-70s and early-80s off the top of my head. I’d love to see the age curves for different eras – it might be that the steroid era was the outlier but that this phenomenon was present all along (which would make a kind of sense).

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    • Steve says:

      This is splitting hairs with A-Rod, he’s had six different 8.8+ WAR seasons at various points during his career.

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    • Brad Johnson says:

      I’m seeing a lot of people pull anecdotes for various reasons. That’s kind of missing the point. Jeff isn’t saying that all or even most players follow this exact path, just that the aggregate of all players does. In other words, in the given period for every Ian Desmond there is a Starlin Castro.*

      *not to say that I think Castro is done, he’s just the first guy that came to mind who suddenly went from pretty good to terrible in his early 20′s.

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      • Jason B says:

        I thought the same thing. “This doesn’t work because of X player” is not a way to discredit a particular analysis, assuming the data sets are large enough.

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  18. Johnhavok says:

    I love the work but I would be interested to know about different types of players. How the power hitters declining curves differ from contact/speed guys for example.

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  19. Monkeyepoxy says:

    Yo, Jeff, can you hook us up with a 2006- chart that has Trout, Harper, and Stanton stricken from it?

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    • garrioch13 says:

      That will make the wRC+ graph start lower but if we are to be fair the top three players from the previous group should be eliminated. Most likely Cabrera, Pujols, A-Rod. I’m not trying to make it say what I want it to, it’s just that the result says players don’t improve and that’s wrong.

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      • garrioch13 says:

        We have a group of great young players in the majors and it is weighting youth aggresively right now. It may continue but you can’t say it will. I can’t say that it won’t continue for a few more years and with teams more focused on saving money with youth and the influx of talent right now, it very well could.

        Next year the 21 year olds could include Xander, Moran, Sano, Baez, Gary Sanchez. COULD be good, may not be.

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    • Catoblepas says:

      I wonder if there’s a way to do this using medians as opposed to means, or something analogous (my high school stat knowledge is not sufficient to really know what’s going on here). But some measure of “average” that decreases the influence of the biggest outliers somehow.

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    • Brad Johnson says:

      Jeff said above in the comments that Trout isn’t part of the data set. I assume Harper isn’t either.

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  20. Shankbone says:

    Very interesting article. Thanks.

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  21. Nivra says:

    I’m not sure if these results pass a face validity test.

    If we assume the new post-PED era aging curves apply to all major league ballplayers, then the logical conclusion would be that teams should start calling up all their hot prospects around age 21 to get peak production out of them.

    That clearly isn’t happening, and I’m sure almost all would agree, that most of the hot hitting prospects in the minors would be unable to hack it if called up before they were ready for the majors which happens typically between the ages 22 and 26.

    Thus, either the aging curve isn’t representing the subset of players who get called up between ages 22 and 26 accurately, or major league teams are just f*cked up in their evaluation of their prospects, and should be calling them all up around age 21.

    Obviously, I think the easier conclusion to reach is the curve isn’t representative. The next question is “Why? What’s wrong with the methodology? and how do we fix it?”

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    • nsacip says:

      I think you have it backwards. The curves indicate that the team’s are not calling up players until they are fully ready. Until they have little room for improvement. The financial incentives for letting the players fully develop their skills while in the minors have increased.

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  22. nsacip says:

    As the gap in the salaries of the post-free agency years and pre-free agency years grow, teams have an increased incentive to make sure the young players they call up are fully ready so they get a maximum return during those first six years they have the player under contractual control. That could be contributing to the flatter curves during the early years of a player’s career.

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  23. glib says:

    It is a bias effect no doubt. Congratulations to Leo for finding out. If one were to plot wOBA versus year, year 0 defined any reasonable way (first year with more than 200 PA for example), the peak would reappear.

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  24. Nate G says:

    survivor bias

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  25. pft says:

    Not sure I buy this.

    Whats going on may be whatever is behind the historic strike out rates. Some evidence suggests MLB is allowing umpires to call a much larger strike out zone since pitch f/x came into play, with declining offense the result.

    This trend makes hitters age prematurely and perhaps is giving the illusion that the test program is effective, when really much of the decline in HR and wOBA is due to the higher K rates.

    Interesting enough, BABIP has not declined much. When you look at the advent of the steroid era and the jump in HR and runs, BABIP jumped lock step with HR. If steroids were behind the jump, the testing program should also have resulted in a much larger drop in BABIP, especially in conjunction with a larger strike zone which forces hitters to swing at more bad pitches and make poorer contact.

    When batters put the ball between the foul lines today, they have almost the same chance at a HR (actually about 5% less) or hit (about 1% less) as in the steroid era. Problem is they do so much less often, and this trend must be giving the illusion that players start their decline sooner.

    All of which makes David Ortiz defiance of the age related decline curves the past 4 years all that more interesting and impressive.

    OTOH, testosterone levels in the male population have declined significantly since the 1960′s. An average 25 yo has levels that were seen in a 35 yo 50 years ago, so perhaps players are declining earlier.

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    • GilaMonster says:

      As for your testosterone level claim, I think it could be true…BUT not in athletes. The general male population is overweight,eats terribly, and doesn’t exercise compared to the 60′s. Athletes are in better shape, eat a lot better, and train harder compared to those of the 60′s.

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      • pft says:

        Granted athletes will be the upper end of the testosterone spectrum relative to the average population. Not sure higher body fat is the sole reason for the declining testosterone levels seen in the general population since the effect of increased BMI has been taken into account.

        http://jcem.endojournals.org/content/92/12/4696.long

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        • GilaMonster says:

          But BMI is a poor indicator anyways. You’d need to control things like exercise levels,nutrition,body fat,stress levels…etc.

          I would done this in the original study because you can relatively safely assume athletes are at the pinnacle of health with the knowledge known at the time. The only problem is the small sample size.

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        • Brad Johnson says:

          Case in point for GilaMonster, at my most physically fit in late HS early college, I was considered borderline obese by BMI. Despite having a body fat ranging from 4-6%.

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        • pft says:

          Yeah, Prince Fielder, Pablo and CC are at the pinnacle of health

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        • RC says:

          Mike Trout’s BMI is 30.3, which is obese.

          Jacoby Ellsbury’s is 27. Which is overweight.

          BMI is silly.

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    • pft says:

      The 06-13 RC+ curve does show a dramatic drop off in performance of players over age 36, even relative to the pre-steroid era of 82-89, suggesting the earlier aging due to declining testosterone hypothesis may be true. Only solution seems to be therapeutic testosterone replacement therapy.

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  26. GilaMonster says:

    I think they are a few effects.

    1. Players are starting younger and going hard. If you are any good, you are going to be training everyday and practicing everyday since little league, because we take children’s sports seriously now. Males physically peak by age 23 or so. This means if they train/practice hard enough, they should peak around then.

    2. PEDs did have an effect. PEDs allowed players to keep growing despite natural growth stopping. You could grow further into your 20′s with aid of PEDs. Once growth stopped, you could keep your peak for much longer and delay decline.

    3. More players are staying the game older due to long contracts and the incentive of tons of money. For some reason, I don’t thin Colon or Pettite would bother to try to come back if they money wasn’t there. If the Yankees weren’t dumb, Jeter would be benched and Ichiro out of the game. In increased competitiveness and even media attention have kept players on the field longer.

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    • Ruki Motomiya says:

      Ichiro was worth 1.1 WAR last year. While he shouldn’t be starting, Ichiro in the game as a bench player would make great sense.

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  27. Buck Turgidson says:

    My wife’s aging curves sure are changing.

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  28. MGL says:

    Fascinating stuff, Jeff! Nice work!

    Many people do not understand how the delta method works. If there are lots of very good (talent-wise), or very few, young players, that has no effect on the aging curves. Now, if there happen to be lots of good AND LUCKY young players (not counterbalanced by good and unlucky ones), then that would very much affect the curve.

    Which brings up my 2 major concerns. One is sample size. I am concerned that the sample size (6 or 7 tears) is small enough that the unusual curve has some non-deminimus chance of occurring by chance. I have no idea though, of the standard errors associated with these types of curves. That is beyond my pay grade.

    The other thing, which Jeff mentions, is that I am concerned with the survivor bias. Remember that always works in the direction of the curve going down at any point. I wonder if maybe there is a lot of survivor bias going on in this small sample, especially at the younger ages. I would like to have seen Jeff correct for this (I do it by using projections to provide “phantom performance” for those players who get less playing time in year X+1).

    In any case, really fascinating observation.

    BTW, the reason you see players like Trout with lower projections than what they put up in the previous year has nothing to do with aging. I assume that Steamer (and all the other projection systems) assumes that players still get better until age 26-28 or so. The reason you see worse projections that prior performance even at a young age, for players who performed above average, is regression. If Trout puts up 10 WAR in his age 21 season and we assume that he is going to get 1 WAR better in his age 22 season, his projection would still be less than 10 WAR. How can that be? Because we assume he is not really a 10 WAR player at age 21 in true talent. That is what regression is all about. It is much more likely that he was a true 8 7 WAR player who got lucky than he was a true 10 WAR player who neither got lucky nor unlucky. That is because there are MANY more 7 WAR players than 10 WAR players (who are practically non-existent). So first you estimate his true talent at age 21 to be around 7 WAR. Then you add another 1 WAR for improvement and you get an 8 WAR projection! So a 10 WAR player is projected to get better, yet he is projected to be an 8 WAR player! It is the same thing as projecting a player who bats .390 in 130 AB as a 21 year old. You project he will get better as he ages, but you are not going to project him hitting above .390. First you do the appropriate regression, and then you add in the aging component. That is a very important concept. Well-above average players are never projected to “improve” and well-below average players are never projected to decline, no matter what part of the aging curve they are in, unless their expected change in talent from one year to the next (up or down) due to aging is greater than the amount of regression. In most cases it is not, unless the player is only a little above or below average.

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  29. Nik says:

    The impact of knowledge.

    From the beginning until 2005, most teams and players in most years didn’t really know what made a good hitter. Sure, they thought they knew, but in reality they were more in a fog than they realized. Players were thrown into the big leagues and natural selection took its course. Those that happened to develop the traits of a better hitter at the big league level survived, and the sample in general showed improvement based on natural learning until the late 20′s (age).

    2006 to the present, modern knowledge of developmental factors and hitting skill factors have wiped out this big league natural selection process. Most teams pretty much know what makes a good hitter. Young player development is streamlined and the natural selection process has shifted more to the minor leagues. Players now reach the big leagues as finished products, in general. We don’t see nearly as many players throughout their 20′s “learning” how to be better hitters. There’s nothing for them to figure out on the field. Lots of players still do, of course, but the sample in general shows no improvement from learning.

    The physical peak of natural athleticism has and always will be something around 20 years old. This should be obvious.

    Increased knowledge has removed the foggy learning period. Modern baseball now explicitly knows from the get-go what old school baseball used to inexplicitly figure out via a slower, natural process.

    (this very probably is not true)

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  30. MrKnowNothing says:

    But, so many people keep telling me PEDs didn’t impact player performance!

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  31. Joel says:

    Variance or it didn’t happen.

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    • K says:

      I’m persistently amazed at a blog that claims to be statistically savvy at how statistically sloppy a lot of stuff at fangraphs is. You never see variance, you never see statistical significance. This is kind of interesting, but sadly now requires someone else to go back and actually do the work right to see if there’s anything there. Furthermore, if the aging curve is truly a more or less linear downhill trend as the author claims, a simple OLS regression would do the trick. On the other hand, at fangraphs with little acknowledgement of variance, they’d probably run that regression without even bothering to tell readers what the p-values are. I think this is fake and being driven by a couple of players who have been elite at age 21 in the last couple of years, they thus hold a lot more sway in the data because hardly anyone is in the majors at age 21. So to your point on variance, my suspicion is that the error bars on those first couple of years are huge and account for the entire loss of the previous aging curve.

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      • flapjack says:

        If you are so statistically savvy go ahead and query the data, choose a bias-less method, and reparametrize your OLS in order to fit the data better than what Zimmerman and what other economists have tried. If you are really concerned with the methodology feel free to take the time out to look at the articles written by world renowned economist linked above in this very article and follow through on your end. I feel like half the point of this article is to display that aging curves are not static but very dynamic and constantly evolving by showing what has become of the curve while not claiming that these will in any way be predictive, simply descriptive. In this token it is merely a guide as what has happened to aging curves through each decade not how curves will progress in the future so I don’t see how much added value a moderate p-value (one that won’t be “statistically significant”) due to small samples sizes or a large variance will tell you that much more about the dataset. If this really bothers you so much don’t bother to read the article or start your own website since the barriers to entry are so low and the quality by your standards is subpar. Don’t be so harsh concerning the analysis while sitting back in an armchair and criticizing with very vague criticisms when a lot of the information you are looking for has already been discussed and is linked (directly or indirectly through other links on that linked page) to this very article. Don’t hate on it just because the data did not enable any specific conclusions to be made in this dynamic environment, appreciate the time and effort that went into this probably full knowing that the result would be inconclusive but it would be something interesting to note and keep in the back of our head.

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        • K says:

          I suspect the p-values on a lot of stuff you see at fangraphs are really bad, the poor p-value would tell us that all we’re seeing is random noise. If that’s not the case then suddenly we’re looking at something interesting. Your suspicion appears to be the same as mine, that the change from the normal understanding of an aging curve is totally nonsignificant, therefore this isn’t really a finding, just an illustration that changes in a small cohort can appear to create effects that aren’t there. The point is that its easy to report the variance on this stuff and make some assessment of the statistical significance of the finding and it routinely does not happen here, leaving the reader to wonder whether its real or not. Just report the damn statistical significance is all I ask.

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        • flapjack says:

          After rereading this, this rambling response came off a LOT harsher than I really intended… Sorry about that, honest and open criticism is the point of blog like forum on fangraphs and I did not mean to be harsh, a simple understanding of the distribution of the data would be nice too.

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  32. Jason says:

    To me these numbers are very telling about why this article may not tell the whole picture:

    21 and 22 year olds from 2006-2013: yearly wRC+ ranging from 92 to 106(Median of 98.5)
    21 and 22 year olds from 1998-2005: yearly wRC+ ranging from 78 to 101(Median of 94.5)
    21 and 22 year olds from 1990-1997: yearly wRC+ ranging from 73 to 99(Median of 94.5)
    21 and 22 year olds from 1982-1989: yearly wRC+ ranging from 77 to 100(Median of 86)

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  33. Green Mountain Boy says:

    Sorry, not ready to buy in on this article yet.

    What I’d like to see is the same study done for a period of time where we KNOW PEDs were not part of the game, because frankly, we really don’t know the exact state of PED usage in MLB right now. I remember reading an interview with an anonymous MLB player in the early 2000s, after Canseco’s book came out. The question put to him was something to the effect of “Aren’t you worried about steroid testing being implemented now that Canseco’s book has blown the lid off the story?”. His response was “We’re so far beyond that stuff right now they can test for it all they want. We don’t care. HGH is what everyone’s into now”. And that was at least 8 years ago! What could they potentially be into by now?

    So, let’s run this study for say, 1950 – 1975 and see what the results are. Just to pick a few examples of players of that era who DID peak in their later 20s after breaking in years earlier, I’d point to Carl Yastrzemski, Roberto Clemente, and Sandy Koufax. I’m sure a little research would yield dozens more.

    I’d also point out that the idea that MLB batters peaked at age 27 had to come from *somewhere*, and the earliest recollection I can recall of that being documented was in an 80s-ers Bill James Baseball Abstract. So I would assume the reason the idea became accepted was because James was the source, documented his research so well, and others found the same thing, verifying James.

    Another logical potential reason for this study’s findings is that we’re entering another “Age of the Pitcher”. Was the study normalized for the new yearly “league average”? Sorry if someone may have already asked that. I didn’t have the stamina to read through ALL the previous responses.

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  34. chel says:

    This is a really interesting article and the discussion has been great.
    Other effect that no one has mention may be the stats teams were and are using to evaluate their players.
    If teams were more fooled by AVG before, then they were more likely to graduate players whose WRC+ would be lower than the players teams are graduating now, eventually learning a thing or two about patience at their late 20s.

    Basically I’m saying there was a perception curve before and it’s being skewed by our new metrics

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  35. Chris Hannum says:

    To the extent that any of this reflects things that are actually happening in baseball, rather than chance or statistical methodology, I would suspect that the causes would be the same ones credited above with driving the lower overall run-scoring environment. Imagine that the average young and succussful hitter is a little like Smaug. Teams lately have a superabundance of data – and actually put it to use – in setting up defensive shifts and figuring out what to throw a guy. 20 years ago this was all scouts with binoculars in the stands. In short, the longer he’s in the big leagues, the more information about a guy’s weaknesses the other teams have and the better their strategies against him get. If there is a chink in his armor, it will be found. I understand that making adjustments has always been a part of the game, but I think the nature and balance of that part of the game may have changed. As a corollary, maybe all this information limits some of what used to be considered to be the benefits of experience – a rookie doesn’t have to learn, on his own, how to pitch to Adam Dunn anymore. It’s somebody else’s job to figure that out for him and for the 36-year old too.

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    • fromthemachine says:

      It goes beyond that.

      Scouting now can conduct percentages based on intended result. For instance, if a team wants a batter to ground out to the right side of the infield, they know the pitch sequence with the highest probability of making this happen.

      The reason batting stats are declining post-rookie season is because the data sets become more complete the more ABs a player earns.

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  36. pft says:

    There seems to be a perception there are more younger players in the game, or older players.

    For the heck of it, looking at PA for under 25 and over 35 in 1993, 2003, 2013

    1993 46,252 (25 & under), 7941 (over 35) +4 OPS adv to older hitters
    2003 36,428 (25&under), 14,540 (over 35)+54 OPS adv to older hitters
    2013, 41,820 (25& under), 11,183 (over 35) 0 OPS difference

    So from 1993, it seems there were more younger and fewer older hitters, and younger hitters were more or less replaced with older hitters. The trend seems to be reversing although I did not look at each year in between.

    In 2003, older hitters were much better than younger hitters, but this was essentially nill in 1993 and 2003. That’s a pretty clear suggestion of a PED effect in 2003 that did not seem to be present in 1993 and 2013, but it may be a SSS artifact skewed by players like Trout and Bonds in their respective classes

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  37. MGL says:

    Again, how good players are at any age has NOT effect on the aging curves. let’s say that during one time period, only great players under the age of 25 are playing in the majors, say an average OPS+ of 110.

    And say in another era, only terrible players under age 25 are playing, say with a mean OPS+ of 85.

    No effect on the aging curves, at least with regard to the talent level of the players.

    He is using the “DELTA METHOD” which treats every player as his own universe and the talent level of each player regardless of his age is irrelevant.

    In the first example, where all 22 year olds are great players, he looks at the average difference between age 22 and age 23. If at age 22 a player is a true talent 100 OPS+ player, then if 22 year olds gain talent from age 22 to age 23, then his OPS+ at age 23 will be higher than 100, on the average.

    In the second example, if 22 year olds are terrible players, and aging is the same as with the first example, then an 80 OPS+ player will simply be better than 80 at age 23.

    Again, if the performance levels at any age are unbiased (which they should be since Jeff is using no prior information to include them in his sample, other than they were allowed to play in MLB (which is contemporaneous and not prior information), then the quality of the players at any age will NOT affect the aging curves!

    The only ways in which aging curves could be misleading is this: One, they are reflecting noise due to sample error, which is more likely of course for small samples. Two, if the survivor bias is greater in one sample than another. Which is why it would have been good for Jeff to correct for this.

    For example, let’s say that in one era, and for some reason, teams decide that if a young player has a bad season, he is not going to get much playing time in the next season. That would create a lot of survivor bias and thus create the illusion of a flat or downward (or not so steep, upward) curve. If, in another era, teams, for whatever reasons, allow young players who had a bad season to continue playing, then that would reduce the survivor bias and the aging curve in that segment would be close to “true” even without correction for this bias.

    Here is survivor bias in a nutshell:

    Let’s say that 22 year old players gain 5 points in OPS+ from age 22 to age 23. Let’s say that there are 10 players age 22 and their true OPS+ is 90. Around half will over-perform at age 22 and half will under-perform. This is a simplification but that is pretty much what occurs in any group of players (or for one player, he has a 50% chance of under and a 50% chance of over-performing).

    So let’s say that 5 have an OPS+ of 85 and 5, 95. Again, that is pretty much what happens among 10 players all with a true OPS+ of 90 (obviously those numbers are all spread out each one subject to random deviations).

    If they all had 300 PA at age 22 and 300 PA at age 23, we would see that the average OPS+ at age 23 for these players was 95 (remember I said that they improve by 5 points in that 22-23 year interval). If we use the delta method, which takes the change in OPS+ for each player and then averages all the players, weighted by the harmonic mean of the two PA (at age 22 and at age 23), we would still get an average increase of 5 points (on the average – in a sample of 10 players, it could end up being anything).

    Now what if teams decided that the 5 players who under-performed did not play at all at age 23 and the ones who over-performed did get to play? Well, the average OPS+ at age 23 of those 5 players who got lucky at age 22 would still be 95 (they gained 5 points), so it seems like our curve would still be correct. But, using the delta method, it will not be. What would happen?

    Well, the only players in our sample are the ones who got lucky at age 22. Unfortunately since the ones who got unlucky at age 22 did not play at age 23, they are not included in our sample. So now when we do the delta method (or any other method) we get a 95 OPS+ at age 22 (they were true 90 players who got lucky) and a 95 OPS+ at age 23 (now they are true 95 players, and because we have an unbiased sample at age 23 they perform at their true talent levels). So we get NO improvement from age 22 to age 23, even though we already made the rule that there WAS a 5 point improvement (and there actually was).

    The survivor bias is not a huge deal across the board, but if you happen to have a lot of lucky players at any one age or small group of contiguous ages OR, for some reason, teams create this effect (as I said, they don’t let the unlucky players play much the next year), then the aging curve can get really screwed up.

    So, if there were a lot of good young players in Jeff’s sample, that will have NO effect on the aging curve, but if there were a lot of lucky (and good or bad – it doesn’t matter) young players (or teams benched the unlucky ones more than usual) in their rookie years, then that would create a flatter curve at the young ages than what we would expect given “true” aging patterns.

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    • nada says:

      thank you for your explanation–that eliminates a lot of the concerns raised above.

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    • Ted Nelson says:

      Right or wrong (and I’m not even sure Trout and Harper are in this sample because they are so young), I think the talent argument has more to do with the perception that some really talented guys mature early.

      Basically, you are assuming that the same aging curve applies to all players. I would be willing to bet, though, that some clear patterns or segments of players emerge when you break the data down.

      If in your relatively small sample of very young players (only 13 qualifying position player seasons at 23 or younger last season) you happen to have a few more guys who can be classified as early maturers, say, that might be a shear coincidence that throws off the whole curve for a given period.

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    • JY says:

      This is a really good point, about the effect being measured for each individual player. However, for this point to be correct, we are assuming that every player ages the same way. This can’t be true, if it were we wouldn’t be seeing players called up at 24/25. Presumably the reason that the 24/25 year old is not called up before is because he improved his skills between 21 to 25.

      The players called up at 21 are MLB ready, while the player called up at 25 was improving from his age 21 to 25 season, and that improvement was missed in the estimate.

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  38. Ted Nelson says:

    I would be really careful using a league average as indicatve of what to expect from an individual player. Like others have said, I would want to see a lot more detail about variation and some segmented results before applying this to an individual player.

    What I mean is that you say we should expect a player to just get worse. At best what this curve shows, though, is that the average of all players will get worse. It could be that we should expect one segment of players to get significantly better and another to get worse.

    This is especially important when you’re talking about young guys who only recently came up, giving us a small sample to work with.

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  39. JY says:

    Regarding the survivor bias, couldn’t you just use fixed effects for each age? This would allow you to get estimates for each age without the prerequisite that you observe a second year of data for the player.

    You could then control for the age of the player’s rookie season to try and remove any bias due to better prospects being called up earlier (although the organization, Cardinals, would also seem to have an impact). This method would likely be imperfect, but if the estimates with and without the control were similar we could worry less about this bias.

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  40. David says:

    Though Barry Bonds and his jillion percent slugging average is the face of PED era, Andy Pettite using them to salvage his career in 2004 after surgery might be more representative.

    The effect of PED’s on average numbers should lift the entire aging curve, rather than just the 30 something part of it. But its effect on major and minor injury recovery might explain the worsening aging curves entirely.

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  41. pft says:

    Perhaps something systematic is going on that is working against young hitters. One possibility might be the new bat rule that has younger hitters using higher density maple bats than older hitters. I believe this started for young hitters in 2010 who had never had a MLB AB before 2010. While it may not affect an individuals decline calculation, or delta, perhaps the transition skewed the numbers somehow. Maybe enforcement was laxer in the earlier years of the new rule but enforcement stepped up in more recent years causing the apparent earlier peak

    I could almost understand it being true for pitchers due to velocity loss and injuries, but not for hitters.

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  42. pft says:

    Also wondering if the increasing strike zone in recent years has more of an impact on younger hitters. Older hitters might adjust better to and year by year increase in the strike zone than younger hitters. If this is it, the age decline curves for pitchers should be showing the opposite effect.

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  43. yep says:

    For the past seven years, pitchers have been getting better.

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  44. Pennsy says:

    As a matter of course I would imagine aging curves are always in some degree of development as the game of baseball changes, cumulative of human conditioning increases and medical technology improves. But in the short term I have to wonder if these results are impacted by trends in the baseball scoring environment itself.

    Let’s say next season the recent trend in improving pitching starts to reverse itself, for whatever reason these things do. Wouldn’t a player who began his playing career just last season, at the peak of pitching dominance, seem to appear to get better as he ages with the declining pitching quality?

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  45. Alan says:

    I think this has to be a factor of the league’s pitching and defense getting better for reasons from another one of your articles. Power hitters peaked early with a very clearly marked peak at age 24-25 which seems to say that players were still on average physically developing at least until then, not declining. The conclusion of the article was that tools like patience and contact quality aged like wine and power aged like cheese if I remember right, it makes a ton of sense intuitively and I still believe a hitters peak is a little past the age of 25 at some point where the gain in motor skills and experience is no longer worth the physical decline.

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  46. tz says:

    What would be the best way to extrapolate Rudolph’s aging curve?

    http://www.baseball-reference.com/friv/rudolph.html

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  47. Lanidrac says:

    Catchers appear to be the exception, as they are generally first called up for their defense and often develop their offense later. It’s hard to believe that Yadier Molina once had a healthy full season .595 OPS in 2006 (before the playoffs, anyway).

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  48. slash12 says:

    Could the results be skewed because players that are brought up incredibly early are exceptional players to begin with, and the pool of data gets polluted as the older less talented players are brought up later in their career? I wonder what this would look like if you only followed individuals that happened to come up at a young age, throughout their career.

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  49. Marc says:

    I wasn’t able to read through all the comments, but I wonder if the decline in offense over the last 7 years has been taken into account.

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  50. Dan says:

    I believe what may be flawed in your study is that overall offensive production has declined significantly over the same time as your study. I know for example that league average wOBA has declined along a similar arc over the period. As the great Jack White sang “You cant take the effect and make it the cause.”

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  51. Jonathan Judge says:

    Jeff, I assume you are basing this study on “baseball ages” rather than actual birthdays, correct?

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  52. Eric M. Van says:

    Just discovered this. I’m fairly certain that if you included accurate MLEs (assuming there were such a thing, of course) for every hitter who qualifies for the study, you’d restore the rise at the left side of the curve. The majority of the sample is guys who didn’t reach the majors until 23 or 24. And all those guys typically were putting up similar numbers, one year after another, from ages 21 to 23-4, as they moved up from A+ to the majors. If they hadn’t been improving as hitters from ages 21 to 23-4, you’d see a decline as they moved up through increasingly challenging competition, and their numbers in A+ would be amazing.

    Therefore, as several people hypothesized, if the aging curve of players once they reach the majors has indeed changed, it’s because players are now, as a rule, not given regular PT until they have essentially completed the maturation process as hitters. Since we haven’t seen a decline in the number of young players, that indicates an offsetting improvement in maturation speed, which is easily explained by improvements in technological tools for hitters, etc. And teams are able to hold off promoting the young talent because the player pool is sufficiently deep, and they do so because a) they have an economic incentive to get the best possible six years of control, and b) its possible that there is a developmental risk in promoting players too soon, which can be avoided by being cautious about it.

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  53. Jason Powers says:

    One thing I find problematic: wOBA measures, and I quote Fangraphs here, “Weighted On-Base Average combines all the different aspects of hitting into one metric, weighting each of them in proportion to their actual run value. While batting average, on-base percentage, and slugging percentage…”

    The different aspects of hitting each have a curve. I suspect if one was motivated, the separation of patience, power, and contact tools would be more telling analysis.

    That said, I did a much larger sample (utilizing Fangraphs nifty WAR values): http://deepcenterfieldmlb.wordpress.com/2014/02/18/father-time-in-baseball-age-curve-equals-parabolas-for-all-types-of-players/

    What can be pulled out of these graphs: TOP Batters (WAR>=5) do generate better results earlier (at 25) while TOP pitchers (WAR>=4) have more success after 33 years of age.

    Everyday players – can find more batters after supposed peak 26, in 27-28 years.

    This was a quick and dirty study based on finding a pattern and not sampling a small range with large errors. In essence, I took the population in total – from “modern” baseball forward. Again, if motivated, I’d break down to pre/post 1950, and do one modern.

    Then do it on various tools approach.

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  54. Why are so many folks claiming athletic abilities peak at 20 years old? What about “old man power” ?? I’m 34 and I could crush the 20 year old version of myself (neither version did any serious physical training).

    I am really twice as strong as I was at 20 just by nature. I disagree that 20 years old is the total peak … different types of peaks are reached between 20 and the 30s.

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  55. yoyoneil says:

    No offense to Jeff Zimmerman, but here is what’s wrong with this article:

    The league’s average wOBA has gone down pretty significantly every year between 2006 and 2013 (except ’08-’09). So when you use the “delta” method for players in such an era and just compare each player’s wOBA in year x+1 against his wOBA from year x, it will of course appear that players on average are not improving from year to year. In any period where the league’s average wOBA is going down each year (perhaps because of improved pitching or better defensive positioning), hitters are going to have a much harder time making their wOBAs go up.

    In reality, if a player can maintain the same wOBA that he had the previous year and the league’s average wOBA goes down that year, I would argue that he has demonstrated improvement: he has improved relative to his peers.

    This article doesn’t show that player curves are changing at all. It just reflects the fact that wOBA has been going down every year. And since wRC+ is directly correlated to wOBA (when corrected for ballpark factors), the wRC+ graph suffers from this same deficiency.

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