The article by Dinardo and Winfree argues rather pessimistically that steroids effects on homeruns are almost impossible to measure. They argue that there are too many variables that can go into hitting homeruns, including quality of pitching, weather, distribution of talent across teams and the number of games played. They argued that to prove this hypothesis would take considerably more shoe leather than a simple statistical analysis.
The authors investigate bold claims by a researcher named DeVany, who claims that the law of homerun hitting is the same as the laws of human accomplishment. He assumes infinite variance of homeruns with a probability one. He claims that steroids have no effect on homerun output. The authors claim that the infinite variance is flawed and that the size distribution of homeruns cannot follow a power law distribution and a posited class distribution would misrepresent the data. While much of the analytics went over my head, the basic theory was that they could not prove the effects that steroids had in baseball. They did not refute the claim that there may be an effect on homeruns; however, they did make the point clear that it would be difficult to prove.
The author notes that “Inferring the existence of fundamental causal laws—that is, the law of genius—from the statistical distribution of some outcome is difficult, at best. The authors focused on looking at the distributions of these different causal laws, and they found that their distributions came out weird. For the power law, the distribution predicted that 11% of players hit negative homeruns. While I respect the overall message that finding the results from this data will be difficult, I felt as if the authors did not disprove that steroids could have an effect on performance. While I did not see any immediate issues with the assumptions of the classical linear regression model, I feel as if further analysis into the paper’s message is needed to grasp the full value of the article in its relation to my paper.
hoppmi03 
Hi, I’m one of the co-authors on this paper, but I’m not sure all of your comments are exactly correct. We in no way tried to “disprove that steroids could have an effect on performance”. In fact, I strongly suspect that it does and an earlier, longer version of our paper tried to make that point. However, our paper is largely a critique of the methodology used in previous studies. Our point is that it is largely impossible to prove that steroids had no effect by simply looking at the distribution of home runs. A more classical statistical analysis (regression with many independent variables) may give strong evidence of this relationship, although there would be many caveats to this analysis as well. DeVany’s point was that this would be invalid (infinite variance, central limit theorem, and so on…), our point was that there is not infinite variance and the methodology he was using is incorrect.
Jason,
Thank you for the clarification. I misinterpreted the basis of the paper and I appreciate you taking the time to leave a comment. After running my regression using different independent variables I too came to the conclusion that it would be extremely difficult to prove this relationship between steroids and homerun production. There are far too many variables that are difficult/impossible to gather into a data set. I am sure a researcher with more time/resources may be better suited to prove this relationship, but it still would be difficult to analyze like you said. I want to thank you again and I appreciate your post.
-Drew Hoppes