The study estimates a 5% increase in bat speed (estimated bat speed generated from additional muscle mass of steroid use) can increase the speed of the ball off the bat by about 4mph, and is projected to result in 50% or more increase in home run production. Here's the story.
I got curious to see how far from historical norms we are now, and while there was a clear surge in the 1990s, we're actually seeing home run leader totals moving back to more historical norms in recent years. Probably a better measure is the average or median level of home run total in the league, but I don't have the data to get there, but this gives an idea. Thanks to infoplease as the data source.

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