Parity is, and always has been, increasing. This graph shows the standard deviation of team winning %ages for each year, counting all "major" leagues. Do remember, though, that pre-1901, seasons were significantly shorter, and talent was spread around more leagues, leading to higher SDs.
SD(Lg OPS) to SD(Lg ERA) is practically uncorrelated. There is a slight negative correlation, which if it means anything, means that sometimes pitchers dominate--squishing the range of offensive results--and sometimes it is reversed.
Looking at the data without being zoomed in emphasizes how flat it really is within the range of possibilities. There is something fundamental keeping SD of OPS around 15% and SD of ERA around 20%.
I actually only glanced through his work a few months ago, and so am not qualified to argue its veracity. But as near as I can tell, he concentrated on the disappearance of the .400 hitter. If you look at the ML average batting average, and the max and min average of any regular in that year, then those differences are indeed shrinking over time.
But the better explanation for this may simply be the decreased emphasis on mere base hits as hitters try for extra bases and pitchers try for strikeouts (leading to more walks). Look at my chart on offense.
People today speak of having an "empty" batting average the way you might speak of cola having empty calories. A .400 hitter with few walks or HRs would be interesting, but would definitely not be paid as well as a .270 hitter with lots of walks and HRs. Why do you suppose nobody holds their hands apart on the bat and tries to "hit 'em where they ain't" anymore? That's why I will focus on OPS when discussing offense, as it better represents what hitters are trying to do. (create runs and win ballgames)
Also, I went ahead and did this calculation myself:
This looks at max/min candidates with at least 400 AB, but the league average is the batting average of the (major) league, not the average of these candidates. Not sure what Gould did. I really ought to read that again. I think he did look not at the extreme values, but at the average of the 5 most extreme values each for top and bottom.
So let's do that for OPS.
Kind of a killing blow. Clearly, there is no shrinkage of (avg(top5)-lg) or (avg(bot5)-lg) over time in OPS. Batting average just worked because of the changing nature of great hitting away from safe hits, and toward more productive run-creation.
I do not know why the series for the two leagues appear to move together. The performance of 5 good/bad hitters in one league should not be related to their counterparts in the other league, for any reason I can see. Again, if you have a theory, let me know.
... Also, he did not have the luxury of Mr. Lahman's database, and this was probably an asset as he could make a more reasoned judgment of who was a "regular" than simply saying 400 ABs, which is inideal since the season has been growing longer over time. (and this shrinks SDs of older and shorter seasons since a slightly better class of player would get 400 AB in 154 games than in 162. Ignoring pre-1901 data makes my life much easier, since the seasons varied widely from 60-130 games.)
True that extreme events used to be more extreme, and it seems reasonable that it's explainable from increased uniformity of excellent competition. Especially as the color barrier fell and worldwide scouting grew more widespread. Also, if you read histories of early baseball, the path to the major leagues had huge chunks of luck in it. Now, it seems unlikely that there are too many people capable of playing major league baseball well that are not doing just that. Furthermore, pay is much, much higher than it used to be. Talented people very literally gave up promising baseball careers because they couldn't make a living at it. Obviously, that doesn't happen much now. Even competition from other major league sports is not drawing off too many athletes right now. I present these facts not in some kind of orchestrated attack on Gould's position, but simply as a discussion.
I've started analyzing super batting seasons, and there are way too many of them! The assumption of normal distribution breaks down a teeny bit above the level of OPS = 1.000. Again, we are starting at 1901 and looking at seasons of American and National League batters with more than 400 AB.
The tail end of the histogram bin chart looks like:
