Not Prince Hamlet is not a physicist or a statistician, but we did play a bit of baseball in high school and college, so I want to say something about how steroids actually work. The prevailing assumption is that a hitter aided by steroids will turn a routine fly ball to left field into a home run to left field and a home run to left field into a towering tape-measure job. That's not how it works.
If steroids chiefly build muscle mass and strength, then the advantage they grant to a hitter is increased bat speed. That doesn't mean that a hitter can hit the ball to the same part of the field, only harder and further. It means that a hitter can hit a ball that he otherwise would miss, or, more to the point, can hit a ball squarely that he otherwise would foul off or fight off his hands. Steroids don't turn routine fly balls into home runs; steroids turn weak ground balls into home runs.
So a hitter on 'roids has the bat speed to get the fat part of the bat around on a 96 mile-per-hour fastball on the inside corner. Other hitters will either be jammed by that pitch, or they will have to lay off it. So steroids expands a hitter's strike zone, allowing him to swing confidently at pitches he normally would take for a called strike.
Mind, he won't get the bat around on that pitch every time. But, whereas without steroids he'll get to it maybe once for every ten times he tries, with steroids that will go up to two or three times. That's statistically significant. It forces pitchers to find other ways to get him out.
This is a layman's analysis only. But the prevailing assumption about how steroids work doesn't go far enough. The drugs provide much more advantage to a hitter than popularly thought.
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