Henry Aaron and the Lucas Critique

No, not the Henry Aaron at the Brookings Institution.  I mean what the ten year old Tyler Cowen would have called “the real Henry Aaron.”  Nate Silver writes:

What if Aaron had never hit a home run? What if those 755 round-trippers had fallen for base hits instead? (If we’re trying to isolate the effect of his power, that seems like the fairer way to do it, instead of turning them into popups or something.) Would he still be a Hall of Famer?

If all of his homers had been singles, Aaron would still have his 3,771 hits. Instead of being the second-best home-run hitter of all time, he’d be the third-best singles hitter of all time, after Ty Cobb and Pete Rose. His RBI total would have gone way down; based on the number of runs that Aaron knocked in on home runs and singles throughout his career, I estimate that he’d have 1,232 of them rather than 2,297. But 1,232 isn’t a shabby total; it would rank Aaron 141st all time, in the general vicinity of Derek Jeter, Edgar Martinez and George Sisler. He’d still be a lifetime .305 hitter and have a .374 on-base average.

OK, here is where Lucas comes in.  If Hank Aaron did not carry significant home run potential to the plate, he would have seen a lot more blazing fastballs, pitchers’ “best stuff,” and so on.  Why not challenge the hitter and try to blow it by him if all you are risking is a single up the middle?  As it was, pitchers often threw Aaron a variety of slower curves and off-speed junk, stuff he might grab a piece of with the bat but would have a harder time drilling straight over the fence.

And thus a homer-less version of Aaron probably would have had a harder time making contact at all.  And he certainly would have had many fewer walks.  But yet, with the amazing wrists he had…pitchers were afraid of him.

It is funny how the Lucas critique went from one of the most underrated ideas in economics (pre-Lucas), to one of the most overrated ideas (1980s-early 1990s), and now it is back as one of the most underrated ideas again.  If we vary one policy or one element of a calculation or algorithm, other individuals will respond strategically.

Addendum: Scott Sumner adds comment.


Just as important, a singles hitting right fielder would have had a tougher time reaching the majors. Corner outfielders were expected to be power hitters. He most likely would have been moved to second base where he would have had a shorter career. Aaron played some center, but it was not his best position. Additionally, a single hitter is not batting behind high on-base guys.

If things were different, they wouldn't be the same.

Why exactly is there a correlation between fielding in the outfield and batting style ? Wasn't Tony Gwynn a corner outfielder?

He was also an exception. When Aaron was coming along slap hitters were pushed to the middle of the field, either as outfielders, second basemen or shortstops. Maybe he would have been an exception. We can't know. Rod Carew was an exception. It's just underscoring the defect of what-if history. Also keep in mind that when Aaron was coming along, baseball was scouring the Negro Leagues for speed and power, not slap hitting second basemen.

Center field is much harder to play than left or right. There is more ground to cover and it is harder to see ball when it is coming straight at you, as opposed to slicing one way or the other. As such, if you can play it well, you don't need to be a power hitter.

LF and RF are relatively easy positions to play. (Only 1B is easier.) Whoever plays them better be able to hit for power to justify value to the team.

There is a correlation because there are only so many places on the field where one can "hide" power hitters, who tend to be slower than other players. That's why a lot of first basemen are power hitters, for example. They tend to be slower both because they tend to be bigger (common cause) and also due to selection. (A slow player is less likely to be selected unless he is a power hitter, and a hitter with less power is less likely to be selected unless he has speed.)

That said, corner outfielders and third basemen see more of a mix between power hitters and speedier players. Hence, Tony Gwynn (and Wade Boggs at 3B). I think that a hitter that was destined to have a lifetime 0.305 batting average and 3771 hits would find a place somewhere on the field, even without power. Also, to answer Silver's question, I think Aaron would undoubtedly still be a Hall of Famer, although he might be "just" as normal Hall of Famer, not the (steroid-less) home run king.

From Tyler's earlier post:

"Here is Silver’s introductory essay as to what they are about. It is too sprawling and evinces a greater affiliation to rigor with data analysis than to rigor with philosophy of science or for that matter rigor with rhetoric."

I'm starting to see what Tyler meant by this.

This is maybe Tyler's best post ever.

You sure this wasn't Tyrone?

If we vary one policy or one element of a calculation or algorithm, other individuals will respond strategically.

E.g, changing + and - :
22 + 66 = 88
22 - 66 = -44

x and /:
22 x 66 = 1452
22 / 66 = 0.33333


At the same time, Aaron would arguably have found it easier to make contact if he weren't swinging for the fences. Who's to say which effect would dominate?

Yes, I think we could safely assume that a highly motivated athlete (and athletes at the very top tend to be very skilled, but also work very hard) would attempt to maximize their skills, even before free agency made such athletes multi-millionaires.

Here's a list of pitchers who became position players. Note how often this was after they hurt their arms. The arms was dead, the motivation and much of the athletic skill remained. http://baseballpastandpresent.com/2010/05/05/the-10-best-pitchers-turned-position-players-in-baseball/

"7. Stan Musial: Signed with the St. Louis Cardinals organization as a pitcher in 1938, went 33-13 over the next three years, including 18-5 with a 2.62 ERA for Daytona Beach in 1940. However, Musial hurt his arm and was converted into an outfielder before his major league debut the following year."

"2. Lefty O’Doul: If only O’Doul discovered he could hit sooner. First, he floundered as a pitcher in parts of four seasons. After a five year break, O’Doul resurfaced at 31 as an outfielder and compiled a .349 lifetime batting average, fourth highest all-time. With a full career, O’Doul would have been a Hall of Famer."

"6. Smoky Joe Wood: The Rick Ankiel of his time, Wood went 34-5 for Boston in 1912, then his arm died. He toiled for five subsequent years and then became an outfielder with Cleveland. Wood played five seasons in the field, never managing much power, though he bowed out hitting .297 with eight triples in 1922."

In view of the Lucas critique, where do you come down on the whole "hot hand" controversy?

We still don't know is my view.

As with the "clutch" debate, those who played sports believe one thing and the dorks with spreadsheets say something different. But, at a visceral level both want the jocks to be right.

Cowen hit a home run on this one: effective pitchers throw "junk" at home run hitters to keep them off balance, while home run hitters love a steady stream of fastballs they can launch like a rocket. No, I didn't play professional baseball, but I have coached boys baseball (up through high school). Whenever we faced a lineup filled with power, we always used pitchers with less velocity and more "junk". My nephew, a high school pitcher, never throws more than 70-75 miles per hour, yet the opponents' best hitters can't touch him. And the "dead" bats that replaced the "hot" bats in high school and college a few years ago give pitchers like my nephew star potential. I will say that Cowen misses the call when he suggests that all pitchers, including junk-ball throwers like my nephew, will change their technique against weak hitters and simply try to throw the fastball right past them. No, a junk-ball pitcher is a junk-ball pitcher, even when he faces his grandmother. I also have to comment on this irony in Cowen's post: he criticizes Silver for relying too much on statistics rather than intuition (i.e., that Aaron would have faced a different set of pitches if he hadn't been the hitter that he was). Marginal revolution, indeed!

At the major-league level, pitchers absolutely do change their approach based on the profile of the hitter. Obviously each pitcher can only throw a few types of pitches and won't suddenly become a different pitcher based on the situation. But he will decide which pitch from his repertoire to throw, as well as where to throw it, based on his opponent. Singles hitters are more likely to see pitches in the middle of the plate, because pitchers are not worried about the home run and want to avoid walking them.

This isn't a statistics vs. intuition point, either. Both Tyler and Nate are speculating about what might happen in an alternative universe, which obviously isn't measurable with stats! I think, however that you could make a strong statistical case for Tyler's claims above that different hitters see different types of pitches.

He would not have been pitched around so often. You would have to assume he would have been thrown more strikes which means his walk total would have declined . This could have also increased his total amount of hits, rbis etc. Managers would have also been more likely to send runners in motion with Aaron at bat rather than play for the 3 run homer. The point is when you change a key variable all other variables are affected. In terms of budget analysis this post is an example of static vs. dynamic scoring or general vs. partial equilibrium analysis. ( I think)

Nicely done. You could accurately call this the Lucas critique, as you do. But you could also call it, “People respond to incentives.” I can imagine Armen Alchian having this insight in the 1960s, well before the Lucas critique.

You could also call it common sense.

It would be more accurate to call it “People respond to incentives in unpredictable ways.” The Lucas critic would not be valid if general equilibrium analysis could correctly predict the effect of policy changes.

Tyler: what is the maximum number of home runs someone could hit in a season, given that if you hit too many they start walking you? E.g. Superman would get walked every at bat, but Clark Kent would hit more by sandbagging.

The best way for Clark Kent to hit the most home runs would be to be as all-or-nothing as possible. Either hit a home run or strike out in every at-bat. The key is to make your batting as worthless as possible while still hitting homers.

Logically speaking, the point of equilibrium should be the value of walking in every plate appearance. If your value as a hitter goes above that, then everyone starts walking you. Using a simplistic model where every base gained has the same value, the maximum homers you could hit would be one every four plate appearances. That would work out to about 175 homers in a typical season.

In reality, it would be lower than that, though, because a homer is worth more than four walks. Baseball Think Factory uses a statistical model that suggests a home run is worth 1.44 runs, while a walk is worth .165. This would mean you could only get about 80 home runs in a season. However, their model implies that the best hitters are routinely generating more value than would be generated by walking someone every time, so I am a bit skeptical.

But if this were true, shouldn't most/all players with little power also have low walk rates? On the whole, I am not sure if this is true, but I can think of many counter-examples, namely the lead-off hitter of any team that has at least slightly sabremetrically inclined front office.

Pitchers will be more disinclined to walk a singles hitter, especially a lead-off hitter with speed. Working against this, however, is that lead-off hitters with speed may be more selective because drawing a walk will be more valuable to them than to a slower hitter.

I somewhat agree on a normative level, but in practice I think that the "plate discipline" of the batter is more important to receiving a walk than the choice of a pitcher to pitch around a batter, which made be made on the basis of the potential damage that batter may do. To your point about speed, while the logic certainly makes sense, take a look at Ricky Henderson's 1982 season in which he stole 130 bases: .267/.398/.382. Mediocre AVG, mediocre ISO (10 HR, 4 3B, 24 2B), lots of SBs with a high walk rate. This is just one cherry-picked case, but I'd hypothesize that it is not uncommon.

Getting on base that often while not hitting for power is quite rare, while many power hitters have OBPs of .400 or higher.

Baseball is vulnerable to rampant numerology. The "3000 hits" pedestal. Is Omar Visquel a lesser light because he had only 2877 lifetime hits (4 more than Babe Ruth).?It's doubtful that Visquel will ever make the Hall of Fame, even though he was a remarkably consistent and productive player during a 24 year major league career. There other lines in the statistical sand as well, 300 career victories for a pitcher is a big one that leaves out hurlers like Bob Gibson, Jim Kaat, Bob Feller and Robin Roberts.

Visquel may well make the HOF on the strength of his defense and b/c he won't face steroid accusations. We'll see.

Many more statistically-minded baseball fans are annoyed with the focus on milestones like 300 wins.

However, Omar Vizquel and Jim Kaat do not have very strong Hall of Fame cases when you look at there career value in a more rounded way.

This is not the Lucas critique. Not at all. The Lucas critique (which has much to do with rationalisation and the cognitive dissonance caused by the macro paradoxes and fallacies) would be that the representative pitcher would exactly know - just know - how this would affect the results of the representative hitter and change his behaviour correspondingly (inducing a possible change in the behavior of the respresentative hitter etc. etc.). The point is that so called micro-founded theory does not delve into real micro-relations at all. While the relation between the pitcher and the hitter is a real micro-relation. And therewith impervious to the Lucas critique (like real macro-relations, with their paradoxes and fallacies).

Arguing that a homer-less Aaron would have been pitched differently is a valid Lucas critique. However, it seems just as plausible to argue that a low-power Aaron would have seen more hittable pitches (and fewer balls), and could have had more bat control, and hence might have made more contact.

What this illustrates is that any "micro" model of policy variance needs to be rooted in detailed statistics, not intuition--perhaps ultimately a multi-level model of individual situational batting performance. Silver's "wins above replacement" analysis is, arguably, a start on a more detailed analysis, since WAR does involve some useful situational factors.

I'd give Silver some credit for looking at a couple of different approaches (hopefully he didn't toss out any that he tried). What I would like to see on his site is some discussion of the possible confounders and associated uncertainties (also, IMO, the largest deficiency in Pielke's controversial column).

The trouble with these sort of Rational Man type Lucas game theory analysis is that it ignores: (1) economics is non-linear, (2) even a rational relationship a non-linear system can produce bubbles and crashes (amplification, the proverbial butterfly-into-cyclone phenomena), (3) does not explain policies that have never been tried or little tried. On this last theme, imagine a world of zero government, or patent rights that are strong (the opposite of zero government in some ways), or community commons in a society with common morals (Elenor Ostrom). What does Lucas say about all that? Not much, since it assumes a mythical "Rational Man" that always acts the same in all societies. Lucas is for explaining the 'steady state' not the 'transient' response.

PS--I recently saw a reference to GM Rogoff in a book by GM L. Christiansen "Storming the Barracades" it was funny as Christiansen was complaining Rogoff did not have any weaknesses in his playing style back in the 70s.

Love this and Tyler but .....

But I want to echo other commenters like Dan Riley.

It is true that we do not know exactly what would have happened.

But theory proposed by Tyler doesn't seem to make much sense.

The theory that pitchers pitch better, that they use their most effective stuff, against weaker hitter seems completely backwards.

The more likely outcome is what Dan suggests more pitches more hits and maybe less walks. (Aaron's approach would also have changed. For a singles hitter a walk is much more valuable. He would have valued walks more and attempted to get more of them.)

Nate's general point that Aaron would still have been very good seems correct.

It is not that they pitch "better", it is that different pitches are optimal against different batters.

Tyler is very clearly claiming that Aaron would have had a harder time hitting singles because pitchers would have went after him with their best/more effective stuff.

'OK, here is where Lucas comes in. If Hank Aaron did not carry significant home run potential to the plate, he would have seen a lot more blazing fastballs, pitchers’ “best stuff,” and so on.'

'And thus a homer-less version of Aaron probably would have had a harder time making contact at all. And he certainly would have had many fewer walks.'

Nothing is certain but this very likely incorrect. A higher percentage of hittable pitches, pitches inside the strike zone as pitchers went after Aaron 'with their best stuff', would lead to a higher average for Aaron. Not lower. On top of this depending on how Aaron changed his style he might end up with just as many walks. As a singles hitter he would value walks more and attempt to draw more. A home run hitter will value walks and contact less.

Tyler lacks any requisite subject knowledge and thus is incorrect.

As I tell my students, ceteris paribus is a fine tool for simplifying thought experiments, but it doesn't hold in the real world.

I wonder if baseball stats guys are making a similar mistake these days with the hyperbolic infield shifts now popular. They place the fielders where the majority of the hits by an individual hitter went without consideration, it seems, for a hitter's ability to adapt their hitting to infielders who are out of position.

It's more complicated than that. Infield and outfield positioning in a given at bat are also affected by the inning, score, men on base, number of outs, ball-strike count and pitch selection. Managers also position fielders according to past hitter patterns because doing so minimizes their responsibility in the event of a hit.

The invocation of the Lucas critique here strikes me as obtuse. Nate isn't modeling what the career stats would have been of a hypothetical Aaron who was physically incapable of jacking dongers. He's just conducting a thought experiment to show that the actual donger-jacking Aaron derived a small portion of his career value from donger jacking compared to other prodigious power hitters, despite being the all-time home run king.*

The first commenter on Sumner's post articulates perhaps better than I did my point: Tyler's criticism assumes Nate was asking what Aaron would have accomplished if he was incapable of hitting home runs. Nate is in fact asking how valuable was Aaron if we ignore HRs. Two totally different thought experiments, and the Lucas critique seems I'll suited for the second one.

Also, surprised Joey Votto's name hasn't come up yet. He pretty much announced he was adopting the first approach outlined by Sumner of exchanging slugging percentage for on-base percentage. An interesting case study.

Usually the more dangerous hitters get a worse selection of pitches to attempt to hit than less dangerous hitters, so I'd guess that being a singles might improve the pitch selection. Someone hitting in the 3rd or 4th slot in the lineup will see different pitches than someone in the 1st or 2nd slot due to game situation, and also the pitches a batter will see depend on the quality of batter who is after him in the lineup. (I'm assuming Aaron mostly was in the 4th slot in the lineup, but that is assumption).

A dangerous hitter in the 4th slot without a good hitter behind him in the 5th slot will get a bad selection of pitches. I don't know how to study it, but I'd think Aaron got a worse selection of pitches than a singles hitter.

Hasn't a lot of statistical analysis shown that "line-up protection" is largely a myth?

Sumner's comment is priceless, and includes this: "I completely agree with Tyler Cowen on the Lucas Critique going from being undervalued to overvalued to undervalued. I believe the overvaluation resulted from the excessive prestige associated with new classical macroeconomics in the 1980s. And the recent undervaluation is due to a lack or understanding of how important the Lucas Critique is in non-monetary areas, such as fiscal policy, health care, financial regulation, etc. And this reflects the fact that many of the most important behavioral changes that occur with policy changes happen in the ultra-long run. They tend not to show up in time series tests, but do show up cross-sectionally." See, it is possible that we can all be friends. In the long run.

I've been wondering a lot about what applying the lucas critique to sabrmetrics in general could mean. Since baseball is a "game" shouldn't there not be permanently exploitable relationships between something like say walks and "runs created"? Shouldn't teams be adjusting the way they play the game as a result of teams trying to draft and develop a specific type of batter? Is there a "microfounded" baseball analytics revolution coming somewhere?

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