Great, great thread and great avatar (she's one of my personal heroes as well: but you probably know that we don't have a picture of Hypatia herself: I believe that's picture of an unidentified woman from Roman Egypt that in modern times has been appropriated to Hypatia.).
But I am still trying to understand Gould. For one thing, a batter doesn't hit in isolation. Pitcher, defense, relief pitching, night baseball, travel, rising the mound (IIRC), etc--things everyone's discussed above--must condition the singular act of reading a pitch and swinging the bat at it. These are exogenous factors, separate from whether the time for the mile or the number of perfect bowling games or the lowest PGA score nears a limit--where opponents don't't prevent excellence of that individual but actually help it by creating parallel, rather than oppositional, competition.
And let's not forget that Williams barely hit 400--getting over 395.5 on the last day of the season, while George Brett seemed sure to beat it in 1980 and just faded at the end of the (now longer) season. So, it can well be a statistical anomaly that punctuated Gould's own equilibrium! (And seriously, is Gould over-determining baseball to make it conform to his theory of evolution? I dunno; just asking.)
But a great, great thread: thanks!
Thanks for the support and encouragement (which you may regret).
I never paused to think that the pic is not a representation of the historical Hypatia. But what you say certainly makes sense.
You are correct about the fact that unlike a runner whose performance is measured against an absolute (stopwatch) and relatively unaffected by the performance of another, a hitter's performance is affected by the performance of others. I think Gould's point is this. In a sport where the athlete's performance is not affected by others (running, long-jump, etc.), we can accurately chart improvement and narrowing standard deviation among the best. This suggests that the athletes are "getting better", both individually and as a whole. The assumption is that if this is demonstrably true in the 400 meter hurdles, 1500 meter butterfly, the deadlift, the long-jump, the javelin, etc., then it is probably true in sports where athletes compete against each other.
That said, there are any number of things that could explain the decline of the .400 hitter. Consider the permutations (and for this let's call "pitching" everything that operates in opposition to batter success--pitching, fielding, strategy, etc.):
1. hitting worse; pitching has remained the same
2. hitting worse; pitching better
3. hitting worse; pitching worse but less so than hitting
4. hitting better; pitching better but more so than hitting
None of these fully explain the disappearance of the .400 hitter. The reason is because .400 is a meaningful average only when measured against the league average. And even then, the .400 figure is meaningful as between different seasons only if we can determine whether overall performance has improved from one year to the next, decade to decade, and so on. Putsimply, 0.400 is not some disembodied metaphysical entity. It is a measure of
relative performance. Little leaguers hit.750. But they'd go 0 for 500 in the majors.
So . . . how do we know that overall performance has gotten better. Well, our
assumption is that pitching has probably gotten better. This follows from the premise that increased performance generally across many sports implies the same in baseball. More narrowly, it is probable that pitching has gotten "better", if by better we mean (1) faster, (2) greater variety in kinds of pitches thrown, (3) more accurate (think of the shrinking strike zone and lowering of the pitching mound in 1969). Those all seem viable measures of pitching success.
It is even more probable--and in fact demonstrable--that
fielding has gotten better. The primary measure of good fielding is absolute--fielder against the ball. "Fielding average should therefore provide an absolute measure of changing excellence in play. If baseball has improved, there should be a declerating rise in fielding averages through time." And there is!
All this goes to support--not "prove"--the thesis: the decline of the .400 hitter reflects a general improvement in performance. As the statistical mean (the league average for all hitters) moves closer and closer toward the "wall" of human limits, there is a shrinkage of the percentage of those best hitters at the leading edge of the statistical distribution:
Gould shows that, remarkably, the mean batting average has remained pretty steady around .260
throughout the entire history of baseball. (This is partially the result of the baseball overlords periodically tweaking the rules to even out any developments that gave the advantage to the offense or defense--hence, eliminating the spitter in 1920, lowering the mound in 1969, etc.) As all players improve, the mean stays the same. But the mean moves closer and closer to the right wall of human limitation, with the "average" player improving relative to their fore-bearers.
Finally, Gould candidly acknowledges that those of extraordinary talent may push their skills to the very limit of human accomplishment and reside "nearer to the right wall". As he explains, in the early days of baseball, those men stood so far above the mean that their performance was measured as 0.400 batting. Today, the very best may hit .360+.
Now . . . back to basketball?
