Q: I'd like to pick apart this article. Where should I start?
A: Pretty much anywhere. Everything in the article -- especially the number 616 -- is rooted in educated guesswork.
Q: Such as?
A: The player mass to bat speed formula. Physically modeling a big-league swing -- what physicist Robert Adair calls "a rather complex energy transfer system" -- isn't easy. Adair's formula is a logical approximation rooted in the assumption that the total energy a batter can generate is linearly proportional to his muscle mass. The root assumption is pretty sound; the bat speeds it produces are estimates.
Q: Speaking of bat speed, what part of the bat are we talking about?
A: Adair's formula calculates the speed of the sweet spot, which we assume is where Bonds is making contact. On any given swing, the tip of the bat actually moves faster -- around 85 mph on a 70-mph sweet spot swing, according to Adair.
Q: Why did you focus on bat speed when other factors -- like undercut on the ball -- can greatly impact the distance a flyball travels?
A: Simple. Steroids build muscle. Muscle enhances bat speed. We are trying to isolate the effects of steroids. As such, we assume that all other factors during each home run -- such as the speed and spin of the pitch, or the angle of contact with the bat -- would have been the same whether Bonds weighed 180 pounds or 230 pounds at the time.
Q: Let's talk distance. Are Bonds' home run lengths totally accurate?
A: No. Home run distances are historically -- and notoriously -- inaccurate, calculated via mathematical formulas, specialized cameras, inexact eyeballing and old fashioned walking out the distance by foot. Some teams, like Boston, don't even bother. Check out this excellent Wall Street Journal article for more information.
Q: OK, so the home run distances are approximations. How about your estimates of where they cleared the park?
A: Also guesses. And fairly crude ones at that. Along with date, opponent and distance, each Bonds home run came tagged with a letter code marking the general area it left the stadium. Stats, Inc. provided Page 2 with a radial chart (click to see popup) matching each letter to a portion of the field. Page 2 then matched groups of letters to the outfield distances available for each stadium: center, right, left, down both foul lines, and sometimes a few additional (often quirky) markers. In general, we broke things up as follows: C-E, left-field line; F-K, left; L-O, center: P-U, right; T-X, right-field line.
Could these estimates be more accurate? Definitely. Watching videotape of each Bonds home run, for instance, would be a good place to start. Unfortunately, Page 2 has neither the time nor the access. (If anyone out there wants to take up the gauntlet, drop us a line. We'd love to know what you find out).
Q: So you're not exactly sure how far Bonds' home runs traveled, and not exactly sure where they left the park, and not exactly sure about the distance between the fence and where they landed. Is that right?
Q: What exactly are you sure of?
A: The bat speed to fly ball distance equation. Alan Nathan is confident that it is accurate to within five percent. And since he's a nuclear physicist, we're not going to quibble with his calculations.
Q: OK, so why did you decide to subtract another nine feet of flyball distance to account for late-season fatigue? Why not two feet? Why not 20?
A: Two reasons: 1) scouts and players often say that fatigue is the difference between the warning track and out of the park, which is in the neighborhood of nine feet; 2) it made for a nice symmetry with the amount of distance Bonds gained from his increased bulk.
Q: If Bonds' home run rate had dropped off at ages 34-39 like the average of the top 10 other all-time longball hitters, he would have hit 131 less home runs than he actually did. Why didn't you factor that into your calculations and take away even more home runs? Are you being nice to Barry?
A: Steroids or no steroids, Bonds is a freak, a once-in-a-generation player reaping the benefits of modern nutrition and training. As such, we thought it was reasonable to assume that a non-steroidal Bonds would have enjoyed the same sort of late-career production as Hank Aaron.
Since the home run projections from those numbers were close to the ones we had already taken away from Bonds, we figured it was a wash.
Q: Hey, baseball instituted a steroid testing plan last year. And Bonds has never failed a test, at least that we know about. So even if he used steroids at some point, why are you taking away one of his 2005 home runs? He wouldn't have still been using last year, would he?
A: Why not? Even relatively stringent Olympic drug testing can be beaten, and baseball's program is far less extensive. Besides, "Game of Shadows" reports that Bonds used performance-enhancing drugs to bulk up to his current weight. Oh, and one of the drugs he reportedly used to get big and stay big -- Human Growth Hormone -- can't be tested for reliably.
Q: How about all those extra walks the supposedly juiced-up Bonds started receiving? Even if a non-juiced Bonds hit home runs less often, he would have seen more pitches. Shouldn't Barry get a few home runs back?
A: We struggled with this, but ultimately decided to leave it out, mostly because walks are highly dependent on: a) game situation; b) the pitcher on the mound; c) manager discretion.
Still, for the sake of argument, suppose that a non-juiced Bonds walks in 1999-2005 at the same rate he did in 1996-98, once every 4.84 plate appearances. He gets 223 extra at-bats, and at his 1996-98 home run rate (one per 13.45 at-bats), hits another 17 home runs.
We're not giving Bonds those 17 dingers. But you can.
Q: If everything is so inexact, why even bother?
A: Because it's better than nothing, and a starting point for better research. Look, no one will ever be able to measure the exact effects of alleged steroid use on each and every Bonds home run. As Adiar puts it, we can only paint with a very broad brush.
That said, a muddled picture beats a blank canvas.