The 33% Solution

July 15, 2018

I have ideas from time to time that help me think about baseball (as if I needed help in that area of my life. What I really need is ideas that will help free me from thinking obsessively about baseball, but that’s another essay altogether….)  I like to think that some of these ideas preceded my interest in sabermetrics, or at least made me receptive to sabermetric thinking, but the truth is that I’ve been using them to structure my thoughts about baseball for so long, I can’t remember NOT having these ideas.


The one I’ll share with you now derives from (or leads into, I’m not sure) Bill’s early articulation of players’ peak years, around the age of 27. It’s a semi-mathematical formula for the percentage of physical and mental abilities that major league ballplayers have, and need to have, to function at various high levels of play. It’s an attempt to re-calibrate the formula of a certain wise and gnomic yogi, much-quoted in my youth, who once calculated that fully half of " baseball" is 90% mental.


This re-calculation places two-thirds of "baseball" as physical, and one-third as mental. "Mental" is not strictly intellectual or cognitive—it’s more like "non-physical," and may include categories like "instinct," "training," "observation," "experience," and the like. For convenience’s sake, let’s say the ideal baseball player would win every game he plays, and further say that this 1.000 winning percentage is .667 physical and .333 mental.


What this proportion (of admittedly arbitrary percentages) means, first off, is that a baseball genius with marginal MLB physical abilities could have a successful, if not spectacular, big-league career: someone whose mental grasp on the game is exceptional (above .250) could play MLB even if his physical abilities are below average (for symmetry’s sake, say also about .250).  And secondly that you or I could never play major league baseball (which the more mature among us have long since accepted—I fully intend to embrace this idea sometime in my late 60s or early 70s) because most of our contributions will come from the .333% portion, which is never going to be sufficient in itself to fool anyone to think that we belong on a major league roster. Maybe I’d get a few percentage points on the physical scale from my ability to walk or stand up straight, but it would be very few points, elevating me above only the physically handicapped or people in a coma. If I’m relying on my mental abilities to play MLB, well, there aren’t enough of those to get me to Step One.  Depending on the .333% part without significant contributions from the .667 part just doesn’t cut it, doesn’t even come close.


And I don’t have anything like .333% to begin with.  A smart, aware, thoughtful amateur outside of MLB, like all of us here, stands at maybe a few mental points. I will boast, for me and for all of you, that we’ve probably got twice or three times the mental abilities of our wives or girlfriends or kids or co-workers, assuming none of them follow baseball, but that just gets us up to .030 or .060 in the mental categories. (Not in the Ed Grimley sense—in Grimley’s connotation of "mental," I’m sure I rate very high.) Your average white, suburbanite slob is never going to rate any higher than .080 in his baseball smarts, and that’s cutting him a lot of slack. That’s about where I peg your typical high school baseball player; a good college player, with decent coaching, maybe gets up to .100. The best of the best college players enter the minor leagues at .120, and the smartest AAA player in the game today is maybe at .150 mentally, with most minor-leaguers being in .100-.150 range, mentally.


Physically, of course, that’s a whole nother story. Young players, in college or shortly thereafter, are close to their physical peaks. If .667 is the maximum conceivable physical measure, then some players are at .300 or .350 before they ever play an MLB inning. A kid who’s extremely smart who’s also close to his physical peak at 18 or 19 (each of which is extremely rare, and the combination practically unheard of), then he’s ready to play in the .500 range right out of high school. Much more typically, a minor league star is around .400-.450, and represents some marginal ability to play immediately in the big leagues.


Fortunately, though, playing in the big leagues at a very young age is the perfect learning environment for such players and they sometimes improve rapidly in it, both physically and mentally. Still growing in both senses, a .400-.450 kid, placed on a MLB roster, can shoot right past .500 in a few months.


(Side note here: I was a lunatic Mets fan in the early 1980s, and I remember the barely 21-year-old Darryl Strawberry being called up in mid-May of 1983 and excelling from the very start. And you know what? I remember wrong. The Mets were still terrible, Straw was hyped, we were all excited to hear about his fast progress through the minor league system, and were thrilled to see him break through to Rookie-of-the-Year status despite the late callup, but I totally forgot that he sucked eggs for his first month: in his first 34 big league games, Strawberry batted .179 with no power and very little OBP,  47 strikeouts in 123 ABs. People rave about Al Kaline coming up straight out of high school at age 18, but in his first 25 games, do you know how he did? .154 BA, .368 OPS.  Mays, you all know about for his first month at age 20. 18-year-old Robin Yount?  First 21 games .176 BA, .444 OPS.  This is all anecdotal, but the youngest stars often struggle adjusting to big-league pitching. They adjust fast, and they learn a lot of things in very brief periods of time, but even world-class talent can’t outweigh the disadvantages of extreme youth and inexperience, no matter how favorably we might remember Strawberry’s or Kaline’s or Mays’ or Yount’s first big-league games in retrospect.)


The principle I’ve been working under, for as far back as I can remember, explains Bill’s thesis of most players’ peaks coming in their late 20s. In its simplest form, this principle says that players arrive in the big league at, or close to, their physical peaks. They might improve their physical abilities, especially if they debut at a very tender age, and that peak might plateau for a few years, but by a player’s mid-20s, his physical decline has already begun. In catastrophic circumstances, it will decline precipitiously, but typically, the physical decline is gradual: a player who debuts at a .400 physical measure (out of .667) may get it up as high as .450 before the decline begins, and then he will drop (irregularly, mostly dependent on injuries) increasingly for the rest of his life.


Meanwhile, the mental-processes line is rising, and steeply. He may add to his knowledge, probably he does, for as long as he plays in the big leagues, but most of his mental progress will come in his first few years, and most of that will come in his first year, and most of that will come in the first half of his first year.  The mental processes will eventually look like a plateau, though it will have a slight upward grade to it as it approaches the maximum of .333.


So the overall peak, mental and physical combined, will come early on. Here’s what a typical star career might look like, broken down into mental and physical components:



Young star’s age




19 (college)




20 (low minors)




21 (high minors)




22 (rookie MLB)




23 (MLB)








































33 (loses starting role?)








35 (released?)






Of course, no one’s career would actually proceed so uniformly or predictably—injuries, luck, usage, etc. would introduce randomizing elements, but what I’m trying to illustrate is how I’ve broken down into imaginary percentage figures the factors that go into a player peaking around age 27.


I think I came up with this breakdown years before I even read Bill James’ theory, though I probably placed the peak years incorrectly, in the players’ early thirties, before reading his (at the time, radical and iconoclastic) evidence of a much earlier peak than anyone had thought. It’s just an arithmetical way of expressing the concept of "Your mind continues to grow as your body deteriorates" but very specifically related to baseball players’s careers, about which I need to think much less than I do.


I’ve been thinking about this stuff my whole life, and I assume everyone else shares my assumptions , though I realize that maybe some BJOL readers may find this assumption unreasonable or even crazy. Let me know if any part of this breakdown seems strange to you, or objectionable, or just flat-out wrong, and thanks as ever for reading.



COMMENTS (19 Comments, most recent shown first)

Steven Goldleaf
Bryce Harper, age 19, first 20 MLB games: .230, .737. Rest of rookie season:.277, .830
5:02 PM Jul 18th
Steven Goldleaf
Bryce Harper, age 19, first 20 MLB games: .230, .737. Rest of rookie season:.277, .830
5:02 PM Jul 18th
(I don't see any prickness there.)
1:25 PM Jul 17th
well, to alleviate me sounding like too big of a prick. Many here on this site make very good points. Observations well founded are illuminating. Math and stats bound the theory but may not preclude the statement. Math is a tool, not the answer ....... and yes, I had a few Barley Pops
12:27 AM Jul 17th
MarisFan61: I have background in Physics, Stats, Geophysics, Systems, and got through it to now be retired. I was gonna say a sine wave, but too hard to say how a phase shift leads to constructive interference. To me, the hardest thing is to explain to very smart people the way things are perceived by those who have studied the problem with words that convey our meaning that they understand. I know, us guys will sound like a prick but unless we agree on the terminology we're screwed. So back in the day: I was told if you can't derive/explain from first principles you don't know .....
12:08 AM Jul 17th
Frank: Gaussian peaks, eh? (lower case, no less) :-)
BTW, are you a physicist? If not, you must have some serious physics background.
(I have pretty serious physics background but I must have forgotten it all.)

Mantle's first 15 games....nah, let's say 14:
Next 14: .397/.465/.619
Next 41 (y'know, palindrome) :-) (till he got sent down) .212/.307/.364
Rest of season, after recalled (27 games): .284/.370/.495
11:22 PM Jul 16th
Steven Goldleaf
David Wright, age 21, first 24 games: .261. 755 (rest of the year 45 games: .310, .911).
8:55 PM Jul 16th
wish I could do a graph here. Lets visualize two gaussian peaks: one centered on the maximum physical performance of a given person or group; another, displaced later in time, is the peak baseball mental acuity of same. We'll assume the peaks of these two curves are displaced in time (physical peak is 20, mental peak is?). Given above, the peaks of non-pitchers is such that the peaks are close enough that the aggregate 'skill' is higher than either peak. But with pitchers the peaks are so separated that the physical peak and the mental peak are resovable - we see two humps. This makes sense to me: the 27 year old peak for non-pitchers is really an additive phenomena, just like your numbers.
8:41 PM Jul 16th
yes .... pitchers are very hard to bin on learning/physical ladder - always seem to be one pitch away from Tommy John or end of career. I dunno if they do it in baseball but I think the NFL tests at least QBs for intelligence (ability to learn?) before the draft. The classic fast-ball pitcher is Dalkowski, who, to put it kindly, had a learning disability. Had they just let him throw hard with out confusing him, who knows? Rube Waddel, well great for a time. Has there been a non-pitcher like Rube? Where intelligence is just ignored. Maybe Babe Herman? Sometimes studying the outliers is illustrative. If you can throw +100 over the plate who cares? It seems to me, without studying it, that all though Ruth and others are characters they seem more stable and intelligent than the pitchers who are characters. and then there is a group of pitchers who seem way more intelligent than the avg player (Maddux et. al.). Perhaps pitching rating is like a two-humped camel: hard throwers dominate in the young ages, then the old skill pitchers dominate later. I think this has been discussed in the old Baseball Abstracts .....
8:12 PM Jul 16th
Steven Goldleaf
Bryce Harper's first 20 games, age 19: .230. 737.
5:17 PM Jul 16th
Steven Goldleaf
Mookie Betts' first 25 games, age 21: .247, .744.
5:15 PM Jul 16th
Steven Goldleaf
Mike Trout's first 40 games, age 19: .220 BA, .562 OPS.
5:12 PM Jul 16th
Steven Goldleaf
Mantle's rookie year, like Aaron's, gave little indication of his potential--or rather that's ALL it indicated, that he was talented but still raw. I looked up Jose Reyes whom I was familiar with as a rookie (he broke in at age 19) and he also had a very unimpressive first month (.209 BA. .540 OPS in his first 25 games) but then caught fire (.355, .881) the rest of the way. Some of this is just luck, of course, but I don't doubt it often takes a while for young stars to adjust to big-league pitching--from this small sample, it looks like a month or so.

Sometimes, as with Mantle the luck runs good for a while before it turns bad. I remember Ron Swoboda's rookie year--he was among the league leaders in HRs, right behind MVP-to-be Willie Mays for a short while, when pitchers simply stopped throwing him fastballs. I don't know if he ever really adjusted to curveballs.
4:53 PM Jul 16th
Ah, not an injury...he spent a month or so at KC, hitting .361/.445/.651. But his performance after being recalled was still just about the same as before he was demoted...
12:46 PM Jul 16th
Mantle missed the last half of July and the first 3 weeks of August. But I think that was an injury; there seems to be no particular discontinuity in his performance (although he did tail off a bit in June).
12:42 PM Jul 16th
Steven Goldleaf
Over his next 30 starts, Mantle batted .215, with a .687 OPS, that got him sent to the minors for nearly two months.
2:26 AM Jul 16th
Steven Goldleaf
Ah, yes, FrankD, I'd forgotten to note that this proportion (2/1) was good for position players, not pitchers. I've long thought that pitchers have a greater mental proportion than position players that could extend their careers further, though the probability of physical breakdowns are also larger, which could cut them down more quickly too.

doncoffin--I wonder about Mantle. DIdn't he get sent down to the minors (perhaps after 30 games?) for failing to hit?
2:16 AM Jul 16th
Interesting. Lucky you didn't try this thought experience during the steroid era: would have to have a physical level big jump when the player learns to take PEDs - one small shot for a man, one great leap for Bonds. Also, at first blush, I might have a different curve for learning for pitchers. How many times do you hear "old crafty left-hander" but hardly any similar statement for other ball players.​
8:53 PM Jul 15th
An additional case in point: Ryne Sandberg in 1982, after 37 games:
.198/.220/.281 and -0.154 Win Probability Added.

There are, of course, the other guys.
Mantle after 30 games:
Eddie Matthews after 30:
.248/.320/.496 7 HRs
8:35 PM Jul 15th
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