Biogenesis Arbitrage: What’s Braun Without the Juice?

We can now say, with confidence and the backing of legal proceedings and pronouncements, that Ryan Braun did steroids. Those in yearly leagues have all said their curses dropped him — a good percentage of them won’t dip back into that well again, choosing to hold a grudge, or to just avoid the insecurity. But in keeper and dynasty leagues, the opportunity for arbitrage is here. Ryan Braun is available, and in a particularly desperate way in some of those leagues. But what will he look like without the juice?

Assuming he does quit the juice — not a safe assumption, as the arms race will continue, and the doctors on shady payrolls make good money searching for the next undetectable miracle drug — there have to be consequences. Some studies — like our friend Dan Wade’s piece at Sports Illustrated in 2011 — have had a hard time finding the steroid effect in the numbers. But any analysis like this that focuses on named players in the Mitchell Report, or players that have failed tests, this type of analysis has sample issues.

There’s the nigh-indisputable fact that many players have put up great numbers using steroids and have gotten away with it. So there are players on steroids on both sides. Also, using results allows luck to skew the results, especially with a sample of that size. Some of those steroid users just had bad years, and some of the non-steroid users had fluky great years. Third, there’s an issue of aging curves and selection bias in comparing year-to-year results ‘before’ and ‘after’ a player has been caught for steroids. Not only do we not know when they stopped or started, but we also have the normal aging process to account for, and then the fact that many players just didn’t have much of an ‘after’ sample once they were outed. Plus, steroids, at the very least, have to do some damage to the playing time component of aging curves — even if they do nothing for your production, they must allow you to recover faster and get back on the field.

I remain skeptical that steroids have no influence at all. Those sample issues — and Wade was well aware of them and did a great job trying to correct for some of them — just make me think that trying to find the users and use them as the data points in a study might be folly. I think I prefer a bio-mechanical approach, one that focuses more on the physics of the swing and what additional muscle mass might do.

Baseball Physicist Alan Nathan (okay, he might not put that first word on the title, but he loves baseball and applies his knowledge to the sport frequently, so I think it holds) has done some work on this. Let me spot-light some findings from this piece for the Baseball Research Journal in 2009:

With the additional assumption that half of the batter’s pre-steroid weight is muscle, [Physicist Robert] Tobin and I both agree that a 10% increase in muscle mass can lead to about a 3.8% increase in bat speed.

…

[Tobin] then repeats the calculation with the mean batted ball speed increased by 3%, as expected for a 10% increase in muscle mass, resulting in the distribution shown by the dashed curve in the figure. He finds HRBiP increase to 0.149, an increase of nearly 50%.

…

By inspecting the distance of the landing point from the nearest fence, one can estimate that each additional foot of fly ball distance increases the home run probability by 4%. Combining that with the aerodynamics “rule of thumb” that each additional mph of batted ball speed increases the fly ball distance by 5.5 ft, along with the previously estimated mean increase of 3 mph in batted ball speed, and one arrives at a 66% increase in home run probability, a number even larger than Tobin’s estimate. Adair has carried out a similar analysis. Based on his detailed study of home run statistics, he estimates that each addition percent of fly ball distance increases home run probability by about 7%. Using 380 ft as the baseline home run distance, a 3 mph increase in batted ball speed leads to a 4.3% increase in batted ball distance and therefore a 30% increase in home run probability. Putting together all these independent analyses, I find that an increase in HRBiP in the range 30-70% is completely plausible

Let’s try this with the numbers at the extreme. Here are Ryan Braun’s home runs per ball in play numbers over his career:

Ryan Braun has hit seven percent of his balls in play over the fence for his career. He can expect that to decline anywhere from 30-70%. Yes, that’s a big range, but let’s describe the two extremes:

I put the 600 PA condition in because steroids might have helped him stay on the field longer, too. I’ll have to say that the 70% condition doesn’t pass my sniff test. That seems extreme. But the 30% decline? That fits my preconceived notions — I’ve been pencil-projecting him for a .280/25/10 season myself. Maybe that’s a little optimistic considering the 70% decline numbers, plus the fact that we haven’t added in aging and used his current-year stats to create a ‘real’ post-steroid projection.

Doesn’t matter what we think, though: the numbers suggest the downside for Braun without the juice is fairly immense. Even if we don’t think it could really be that bad.