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To this we could add the Colorado light air, and probably the likliehood that as pay went up for hitters better atheletes gravitated away from pitching to hitting where the money was. Lastly, I mentioned homeruns, but suppose home uns are more exciting on TV bringing ratings up; but that to appreciate a double play you are in a better position if you are at the stadium where most viewers are not. as baseball became a televised sport it lost some charm.

On other factors influencing hit batters (including Biggio). As I mentioned in my previous comment, I’m not saying that expansion explains all of the rise in hit batters. Even if there was there is no way to prove this. However, it does fit with the facts, and therefore it’s sufficient to infer that expansion and hit batters are related. Again, I have an entire chapter devoted to hit batters in the book that has nothing to do with expansion.

As for other factors influencing home runs, I agree with all of these factors contributing. That lends further support to the notion that home runs rose for a reason other than steroids.

Why hasn’t the batting record been broken? I don’t know, but I can think of a few possible explanations. 1) Hitting .400 is more difficult than breaking home run records. 2) Defense has improved as players have grown bigger and faster. 3) Grounds keeping is better.

There are lots of potential records that have not fallen, and I cannot say why. Gould’s theory doesn’t say all records will fall, just that they are more likely to fall. What I have done is point out a few examples.

Why didn’t past expansions influence the game in the same way? Good question, and this puzzled me for a while, and I continue to think on it. But the thing that I do know, is that talent is much more dispersed now than is was (using a direct measure that I discuss in the book) and that we have good reason to expect records to fall in this environment. Maybe expansion has nothing to do with that, but suspect that it does.

Also Andrew is correct about the appearance of armor (when did Bonds start with that elbow equipment?). I’d like to see the progression of HBP over time. McCarver is constantly going on about how the use of aluminium bats in college makes batters stand closer to the plate.

And nothing about the ball itself? Are you assuming its elasticity has been constant over this period?

At the same time, please bear in mind: Human Growth Hormone cannot be detected by the MLB drug testing. The list of players who have and have not gotten caught under the MLB’s system is pretty much irrelevant in the debate of what has caused the HR increase and the bulkier players in the last 15 years. I believe fans have issue with performance enhancing drugs, not just steroids. Currently, ballplayers have only one single incentive not to use HGH – their conscience. They all know they can’t get caught, they all know the advantages to using that, and they know that thus far, the side effects are really quite minor.

If you want to argue that home runs have increased more due to expansion than due to performance enhancing drugs, I think there’s a future in that investigation – though it would be hard to prove. But I fail to understand how the documented effects of these drugs, combined with the somewhat-documented, obvious use of them, can simply be assumed to have no effect at all.

In addition… what does the expansion hypothesis have to say about the lack of .400 batting average seasons? Surely if expansion and pitcher dilution is giving an advantage to home run hitters on a level that’s never been reached before in the history of baseball, there should be a similar advantage obtained by hitters in terms of batting average as well. And yet, no one has really come close to hitting .400 since the expansion; Gwynn in 94 was the only one within .020 points, and that was a smaller sample size due to the short season.

The NFL is probably the worst candidate for the dilution by expansion theory. There is today more talent on a single NFL team than there used to be in an entire league. More talent = less records. In the case of the NFL, the increase in record breaking is due to rule changes that favor the offenses, and also, the enormous drug problem they face. Heck, even the punters are on steriods.

Also, expansion has occurred in each of the three other major North American sports leagues without a parallel increase in record breaking. No one is scoring 100 points in a basketball game. No one is approaching Gretzky’s records. Only the NFL has seen many records recently broken–it seems to be a better candidate for the dilution-by-expansion argument, because it has had a strict drug-testing policy in effect for several years.

First, let me say that I’m amazed that I was able to say as much as I did in 610 words. I’ll have to thank my editor for his excellent help. However, there is still a lot that I had to cut out for space. I spend 15 pages in the book laying out the dilution argument, so there is a lot more to this. These questions are understandable and I address them in the book.

I’ll tackle a few issues.

Correlation between HBP rates and some proxies of pitching quality since 1993 (min 30 innings pitched): ERA = 0.17, Walks = 0.15, Strikeouts = -0.05, HR = 0.02. Not super-strong correlations, but all except home runs are statistically significant. The correlation between HBPs and walks is the most telling to me.

There is no doubt that expansion does not explain all of the rise in hit batters, in fact, I wrote the chapter on expansion before the HBP numbers jumped out it me. The first chapter of the book develops a model for predicting hit batters based on numerous factors. It’s just one piece of evidence that fits.

As for using the population-to-player ratio to proxy dispersion, this is something I do in the book. However, I’m not sure how informative it is. First, population is rising also because of longer life spans. A lot more people are alive today, but all are not able to play baseball. Second, there are many more opportunities (athletic and non-athletic) for athletes today than there were in the past that shrinks the talent pool. So, this is not much of a guide. This is why I directly proxy the dispersion of player quality for both hitters and pitchers using the coefficient of variation in ERA for pitchers and OPS for batters (I only had time to hint at this in the op-ed). The disparity between pitchers is at an all time high. Batters have grown more dispersed as well, but not to the extent that pitchers have.