Engines of Our Ingenuity

No. 1196:
BATTING 400

by John H. Lienhard

Click here for audio of Episode 1196.

Today, what do batting averages, evolution, and the economy have in common? The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

Stephen Jay Gould is up to an odd business in his book, Full House. His theme is subtle. He says we don't look at the full range of cases when we talk about progress. For example, we talk about the evolution of species as though human beings were the highly organized end result of evolutionary progress.

To do that we have to close our eyes to the full range of biodiversity. In nature's "full house" of all living things, the most successful species aren't humans; they're bacteria. The mass of living bacteria is far greater than the mass of all other life. The diversity of bacterial species is far larger. And bacteria have survived far longer than any other living creatures.

Gould (who loves baseball) uses batting averages to make his point. He asks, why has no one batted over 400 since 1941? Does that mean today's batters aren't as good? No, Gould assures us, it's actually because the quality of baseball players has risen.

Does that sound crazy? Well, it makes perfect sense if you know some mathematical statistics. Gould looks at statistics through the eyes of an intelligent layman, and he leads us through his learning process. The gist of it goes like this:

In a world filled with possibility, everyone does well and there's less variability. Though Gould doesn't mention it, economists have known this for a long time. They track income inequality. In a healthy free economy, a small range of incomes indicates good times. When times are hard, the variation increases and you find many poor people balanced by a few very rich ones.

As quality of baseball play has improved, it has also become far less variable. In earlier days of baseball, a few great batters were far better than the average batter. And they were up against far more variable pitchers, basemen and fielders. Therefore batting averages were far more widely distributed.

Now the distribution of ability among all players has tightened up as they become more uniformly good. And we'll never see anyone bat like Ted Williams again in our lifetimes.

Gould goes on to describe what he calls the right wall. Distribution curves for performance approach absolute human limits on the right side. The closer we come, the less the variation can be. He doubts that Isaac Stern or Vladimir Horowitz play any better than Paganini or Liszt did. We've long since come close to that right wall of human performance in violin and piano playing.

Gould tells us we can't understand evolution without looking at the full house -- the whole variation -- of living things. Evolutionary adaptation has produced many living things, ourselves included. Without understanding the variation, we'll believe all the wrong things. We'll believe that baseball has deteriorated -- and we'll believe that we are the end product of the Creation.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)


Gould, S. J., Full House: The Spread of Excellence from Plato to Darwin. New York: Harmony Books, 1996.

Lienhard, J. H., and Davis, L. B., Jr., An Extension of Statistical Mechanics to the Description of a Broad Class of Macroscopic Systems. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), Vol. 22, No. 1, 1971. (This article lays out the statistical basis for the connection between equality of income and "good times" in a free economy.)


The Engines of Our Ingenuity is Copyright © 1988-1997 by John H. Lienhard.

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