Steroids Probably Aren’t Causing Baseball’s Power Surge | FiveThirtyEight
Kind of nerdy, but the tl;dr version is the increase in home runs is too even and too widespread for it to likely be related to steroids. Steroid use takes a while to pervade the league, so some players start to show improvements before others. What we're seeing instead is that pretty much ALL batters are seeing increases in home runs and slugging percentage in lock step with the league average, which is more analogous to other times the composition of the ball has changed.
I've always been pretty skeptical of how much steroids really help as far as home run power. I think at best it lets guys train harder/more frequently, which probably has some marginal impact on bat speed.
I don't think is actually feasible, but if you could somehow design a proper study that controlled for stuff like natural hitting talent, placebo effects, whether the opposing pitcher is also using PEDs, or whether guys who juice are psychologically inclined to work out more/harder or just feel more confident in the batters box, I think ultimately the difference between roiding and not would be pretty small.