Can steroids increase HRs by 50%? (Update)

This is a follow-up to my previous post on the Tobin steroids paper. Thanks to Joe P. and John Matthew for letting me know that R. G. Tobin's steroids paper is now available online, at Alan Nathan's site, here.

Tobin starts by quoting a study that found that weightlifters given steroids showed a 9.3% increase in muscle mass (compared to 2.7% for non-users following the same training regimen). He therefore assumes a steroid-induced 10% increase in muscle mass. This corresponds to a 10% increase in *cross-sectional* muscle mass (I presume this is because muscles don't grow in length, just width). It is "well established" that a 10% increase in cross-sectional mass leads to a 10% increase in the force the muscles can exert. A 10% increase in force means a 10% increase in energy. And a 10% increase in energy leads to a 5% increase in bat speed (Tobin doesn't say, but I assume this is because energy is proportional to the square of velocity).

Then, after making some assumptions about the physics of the collision and the ball's travel, Tobin calculates that after a 5% increase in bat speed, the percentage of home runs per ball in play would increase from 10% to 16.6%, a 66% increase.

All this seems perfectly plausible to me, except that I'm not sure it matches the empirical home run data. Tobin shows a historical chart of home runs (as a percentage of balls in play) by top sluggers over the years. There is a significant increase starting in 1995. But Tobin argues that there is a significant *decrease* starting in 2003, the year MLB steroid testing was introduced. And, yes, there is a drop between 2002 and 2003, but an increase in the following years, so that 2005 is the fifth highest ever (and one of the top four is 1961!). So it would seem there's something happening other than steroids – and if steroids have indeed increased users' HR rates by 50%, we should have expected to see a much larger drop.

My feeling is that there must be other reasons than steroids -- or at least *additional* reasons -- for the recent power increase. Tobin argues against that:

"Such dramatic changes in performance over a short period of time are rare in well-established sports."

I'm not so sure that's true. NHL offense was at its highest level ever in the early 1980s, but close to its lowest ever only 15 years later. Fifty-goal scorers were rare until about the mid-1960s, when suddenly they became commonplace. I don't know enough about other sports, but I'd bet that there were similar changes in football and basketball, too.

Tobin notes, correctly, that a small change in the distance a ball travels can lead to a large change in the number of home runs hit. But even if the change resulted from something other than steroids, players would notice the change, and hit more fly balls in order to take advantage. (Power-hitting players would also become more valuable, and therefore there would be more of them signed to contracts – but since Tobin concentrates mostly on the leagues' top sluggers, this doesn't affect his conclusions.) So if physics suggested a 50% increase in home runs, you'd expect empirical results to be even higher: maybe, say 75% higher, 50% from physics, multiplied by another 17% increase from players trying to hit more fly balls than usual.

I guess my bottom line is that I'm willing to accept that 10% more muscle mass means 50% more home runs. But I'm skeptical that we're actually seeing the effects of a 50% increase. If we're not, that means that players on steroids are gaining less than 10% muscle mass.

An alternative is that *some* players are gaining 50% more home runs, but not *all* of the top sluggers. But, in that case, where are those other top sluggers getting their power? It must be from something other than steroids.

Finally, Tobin gives a little bit of attention to pitching. Just as a 10% increase in muscle leads to 5% more bat speed, it would also lead to 5% more velocity on the pitch. That correlates to an ERA improvement of 0.5 runs per game. As Tobin points out, that's not much compared to the effect on home runs. But it's still huge from a baseball standpoint. You'd expect extra velocity to lead to an increase in strikeouts (given that the range of ability in terms of DIPS is small). And that's what we've seen in recent years. But, again, couldn't the change have also been caused by other factors?

So this study points out that steroids can increase performance substantially. And, recently, we have indeed seen substantial performance increases. But does that mean that steroids caused them? The empirical record fails to convince me.