I had e-mailed my questions about the Bradbury-Dinen paper to J.C. Bradbury, who responded in a very nice e-mail to me. Firstly, there’s an updated version of the paper on the effects of the DH on hit batsmen - I had been looking at an old one. (I blame the fact that the New York Times website doesn’t, for some reason, have hyperlinks to appropriate places.) As Bradbury points out:
In the new version we address some your concerns. For example, we discuss the role of umpires and the Japanese league experience. Also, in a second paper looking at interleague games, we find the DH affects NL and AL pitchers the same. So, it’s not just some difference between leagues. Check out this blog post that summarizes the issue.
Really great of him to respond since I was just thinking off the top of my head.