Blind Men Only See Black Skies

by Justin Freeze

In his most recent article, Owen tried to convince you of two things: (a) that steroids have a substantial positive impact on a baseball player’s performance, and (b) that this impact clearly shows up in the statistics of the period. If you did as little honest digging as Owen and those who think similarly seem to have done, you were probably convinced. However, I am confident that by the end of my piece, you will realize that these arguments collapse once their severely exaggerated credibility is exposed.

My goal with this post is not the masturbatory self-congratulation that Owen appears to seek. Rather, it is to provide a dispassionate examination of the facts surrounding steroids and their potential impact on the game of baseball. I shall start, as all good science should, with the null hypothesis: steroids do not significantly impact the game or its players’ performances in any perceptible way. We shall see if the available information is able to refute that hypothesis.

I present my article in three parts. Part 1 – Medical Science and Steroids will examine the medical research on the impact steroids have on the body, and whether this translates to better performance in the batter’s box. Part 2 – The Discontinuity Dilemma will look at the curious cases of abnormal performances during the so-called “Steroid Era”, and whether or not this allows us to reasonably conclude that certain players were juicing during this period. Finally, Part 3 – Should We Care? wraps up my piece by questioning whether or not this whole debate ought to affect our assessment of baseball and its history.

Those who are neither friends of math nor logic, nor those who are so obsessed with proving their own dubious correctness that they refuse to engage in fair discussion need not read on. To pun on Owen’s title, the correlation between blindness and thinking you’re always right is also one.

Part 1 – Medical Science and Steroids

For readability’s sake, I will divide this part into four sections that deal with Owen’s criticisms, as well as broad misperceptions about the potential impact of steroids on the human body.

§ 1.1 – Mr. Walker’s Sources

Eric Walker is the author of the original website that sparked this whole debate between Owen and I. In addition to several ad hominem attacks against the man, Owen devotes a large portion of his post to critiquing the sources Mr. Walker cites to support his argument that steroids predominantly affect muscles of the upper body (neck, shoulders, arms) rather than those of the lower body (legs, torso). This is important because batters derive their power almost entirely from their lower body. Since this is such a crucial point, it bears repeating: batting power is a function of lower body musculature; for steroids to impact a batter’s power, they must affect his lower body muscles. Thus, Owen tries to discredit Mr. Walker’s sources that seemingly provide evidence of steroids having a relatively minimal impact on lower body musculature. As it turns out, this is some of Owen’s best research, though, as will become thematic, his conclusions are overstated. Let’s reproduce the sources Mr. Walker cites and Owen critiques:

  • “The principal advantages ascribed to anabolic steroids are those associated with androgenicity, or masculine traits. Upper-body strength and muscularity are two such key traits. . . . anabolic steroids increase muscle mass and upper-body strength.” Anabolic Steroids in Sport and Exercise, Charles E. Yesalis, ed.
  • “Testosterone increases upper-body mass differentially, so performance in [upper-body] tasks like weight-lifting should improve more than lower-body tasks or tasks in which aerobic aerobic capacity rather than strength are assessed. As expected, the task in which increases have been reported most reliably are in the bench press.” Recent Progress in Hormone Research 57: 411-434 (2002), Cynthia M. Kuhn
  • “[S]teroids increase muscle mass and upper-body strength . . . . The effects of supraphysiologic doses of testosterone on muscle size and strength in normal men.” N Engl J Med 1996; 335: 1-7, Bhasin S, Storer TW, Berman N, et al.
  • “[M]uscle deposition promoted by testosterone tends to be greater in the upper body; this provides the greatest effects (and therefore the greatest likelihood of abuse) for sports like swimming, which rely on upper-body strength.” Buzzed: The Straight Facts about the Most Used and Abused Drugs, Cynthia Kuhn, Scott Swartzwelder, Wilkie Wilson (Duke University Medical Center)
  • “Testosterone also produces characteristic body changes, Dr. Pope said, with the most marked muscle growth in the upper body and the biceps.” Psychology: Concepts and Connections, Spencer A. Rathus

On the first source, Owen says it “is a book that I was unable to gain access to, and am therefore unable to parse for legitimacy (but, based on it’s [sic] title, we can conclude that it’s not legitimate science)”. Of course, judging a book purely based on its cover or title is the basest form of intellectual parochialism, but nevertheless the point that we cannot read the book itself is a fair one. However, we can do the next best thing: learn about its editor. A simple Google search will reveal that Dr. Charles E. Yesalis received his doctorate from Johns Hopkins University, has studied steroids for the past 25 years, is a well-published author, and has consulted for numerous government bodies. It is unequivocally unfair and patently dishonest to claim that a medical reference text edited by this man is “not legitimate science”. Moreover, the author of the chapter from which that quotation comes, Col. Karl E. Friedl, Ph.D., is the director of the U.S. Army’s Telemedicine & Advanced Technology Research Center, and has conducted research for the military for the past thirty years. I think we can skip Owen’s “parse for legitimacy” in this case. I’m comfortable saying Mr. Walker has gone 1-for-1 so far.

The second source, authored by Cynthia M. Kuhn (a primary faculty member at Duke University’s Department of Pharmacology and Cancer Biology, and impressive in her own right), is indeed, in Owen’s words, “a review, which is legitimate, but only insofar as it cites original research.” However, Owen’s claim that the first sentence of Kuhn’s quote is uncited and therefore illegitimate is disingenuous, especially since he himself notes that the very next sentence is followed by a citation of our good Col. Friedl, Ph.D. Owen and I have both written many academic papers, and I’m sure he knows as well as I that it is common practice to place a citation at the end of multiple sentences if they logically flow and are attributable to the same source. The point that this is essentially a duplicate citation is fair, but unfortunately it appears as if Owen forgot to read the rest of the source. If you read the entire paper, you’ll find that it focuses on supporting the Friedl assertion by pulling in many disparate scientific sources. Specifically, the review makes the argument that steroids affect the body by binding to androgen receptors, which are primarily found in the neck and shoulders. But don’t just take Dr.Kuhn’s word for it – this claim is supported by many other sources (see Hartgens & Kuipers, 2004; pp. 527-528, 545). Congratulations, Mr. Walker: you’re 2-for-2.

The third source is where Owen’s criticism begins to pick up steam. He is 100% correct that the first part of the quote is nowhere to be found in the cited article. Even though, as we will see, that article does not support Owen’s position nearly as much as he might think, it’s impossible to give Mr. Walker any credit here. 2-for-3.

I also accept Owen’s criticisms of the final two sources. While Kuhn is just one of three authors of source #4, she is still given lead billing and the source itself doesn’t quite belong among the top scientific journals. As for the final source, I agree that a Psychology textbook has no role as a noteworthy source in this debate. Thus, we’re left with Mr. Walker going 2-for-5. Incidentally, a .400 batting average is higher than Barry Bonds ever managed in a single season.

Don’t get too comfortable, Owen. We’re far from finished.

§ 1.2 – Science on Science’s Terms

It’s worth noting first of all that Mr. Walker never claims that steroids do not have any effect on lower body musculature; his argument relies instead on the assertion that their effect on the upper body happens to be significantly greater than their effect on the lower body. In his rush to prove Mr. Walker wrong, Owen conveniently glosses over this fact. Nevertheless, Mr. Walker’s claim of a disproportionate effect on the upper body (supported, as we have seen, by at least two reputable sources) is worthy of further investigation. Let’s begin with the very sources that Owen himself cites as evidence supporting his contrary claim.

The first source Owen cites is an article descriptively entitled “Testosterone Dose-Dependently Increases Maximal Voluntary Strength and Leg Power, but Does Not Affect Fatigability or Specific Tension” (Storer et al., 2003). As Owen correctly notes, the article concludes “that testosterone caused a dose-dependent increase in maximal voluntary strength of the leg (i.e., amount of weight lifted in a leg press), as well as in leg power (i.e., the rate of force generation)”. In plain English, taking steroids enabled the test subjects to lift more weight more frequently with their legs over a given time period compared to what they were able to do prior to taking steroids. Putting aside some fairly obvious methodological issues with this study (administration of steroids was not double-blind; no control group), there are two main problems with Owen parroting this study as vindication of his position. First, the study only studied steroidal effects on the lower body. Without concurrent study of how steroids might affect the upper body, it is impossible to use these results to disprove Mr. Walker’s assertion that the upper body effect is substantially greater than that of the lower body. Second, this study does nothing to disprove my original null hypothesis that steroids affect performance in a baseball game; it only suggests that steroids increase power and strength in the lower body. Hold that thought.

Owen’s second (and final) source is the same as one of Mr. Walker’s: “The Effects of Supraphysiological Doses of Testosterone on Muscle Size and Strength in Normal Men” (Bhasin et al., 1996). Owen presents some impressive-sounding statistics along with an authoritative-looking graph: “[I]n the testosterone-plus-exercise group, the increase in muscle strength in the squatting exercise (38 percent) was greater than that in any other group, as was the increase in bench-press strength (22 percent)”. Those numbers seem substantial indeed. Unfortunately, whether Owen deliberately picked them in an effort to obfuscate what they actually tell us or simply forgot to critically think, they don’t tell the whole story. That quote reflects the effects of steroids on upper body (represented by bench presses) and lower body (represented by squats) strength for a group of men who were newly engaging in both strength training and steroid consumption. I think it’s safe to assume that baseball players underwent significant strength training prior to taking any steroids. Therefore, to get apples to apples, we must compare a group of men already participating in strength training to a group of men participating in strength training and taking steroids. Luckily, unlike Storer et al., Bhasin et al. were thorough in utilizing control groups and testing all possible combinations of strength training and steroid consumption. For the group of men that only participated in strength training, bench-press strength increased by 11% and squat strength increased by 21%. A quick bit of simple math reveals that the proportional benefit gained by steroid users was roughly a 10% increase in bench-press (upper body) strength and a 14% increase in squat (lower body) strength. Still a gain, to be sure, but much less overall and much more evenly distributed between the upper and lower body than Owen implies in his original post.

What then are we left with? Two sources from Mr. Walker indicating that steroids affect the upper body much more than the lower body, one source from Owen indicating only that leg strength is increased by steroids, and another source from Owen indicating that both upper and lower body strength are affected roughly the same. Hardly seems like any definitive evidence either way to me. Additionally, both of Owen’s sources seek to measure the additional strength gained by using steroids. Indeed, Owen accuses Mr. Walker of “conflat[ing] muscle size with strength”. In reality, this is not a conflation at all. As it turns out, we shouldn’t care about muscle strength as it relates to baseball performance; what really  matters is muscle mass.

§ 1.3 – It’s All About the Physics

It is widely accepted among physicists that there are five main factors contributing to the distance a batted ball travels (not accounting for wind): the masses of the bat and ball, the velocities of the bat and ball, and the angle at which the ball leaves the bat. The ideal angle is generally thought to be around 35 degrees; the relationship between the other factors can be simplified as follows:


where v is the ball’s outbound velocity, M is the mass of the bat, m is the mass of the ball, CR is the coefficient of restitution (i.e. the ball’s elasticity, generally found to be 0.55 for baseballs), vbat is the velocity of the bat, and vpitch is the velocity of the incoming pitch (A.M. Nathan, “Dynamics of the Baseball-Bat Collision, 2000 in R.G. Tobin, “Possible Effects of Steroids on Home Run Production in Baseball”, 2007). It should be obvious that the only factor here over which a batter has direct control is vbat, known colloquially as bat speed. (What about greater strength allowing a batter to use a bat of greater mass, you ask? Data have shown that increasing one’s bat weight beyond roughly 34 ounces provides diminishing returns and can even have a negative effect. See A.T. Bahill and W.J. Karnavas, “Determining Ideal Baseball Bat Weights Using Muscle Force-Velocity Relationships”, 1989.)

Luckily, physics also provides with a handy equation to figure out precisely what contributes to bat speed. In his paper “Swing Speed vs. Bat and Batter Mass” (2009), Alan M. Nathan derives the equation:


where v is bat speed, M is the batter’s mass, f is the proportion of the batter’s mass that is muscle (about 0.5 for athletes), m is the mass of the bat, and k and ε are constants. The conclusion is clear: as I hinted at earlier, the distance a batter can hit a ball is entirely driven by the batter’s muscle mass, not some experiential measure of “strength”. In fact, Nathan’s paper suggests that there may even be some diminishing returns with increasing batter mass, as batters with greater mass are able to transfer less kinetic energy to the bat. Owen’s assertion that Mr. Walker conflates muscle size with strength is not only wrong, it misses the point altogether.

How then might we measure the impact of steroids on bat speed, and by extension batted ball speed and distance traveled? Mr. Walker offers us a handy chart culled from the seminal book by Professor Robert K. Adair, The Physics of Baseball (2002):


From the this table, we can see that every 1 mph increase in batted ball speed results in about 5 extra feet of batted ball distance, a figure echoed elsewhere. Unfortunately, precious little precise data exists tracking the increase in muscle mass attributable to steroids. Therefore, we’ll have to get a little creative. For our guinea pig, let’s use Exhibit A trotted out by those who believe in the “Steroid Era”: Barry Bonds.

Data on player weight is spotty at best and often altogether unavailable. None of the publicly available statistics databases track player weight over time. However, I was able to dig up this Time magazine slideshow that offers up stats for Bonds’s games played, batting average, home runs, at bats per home run, and playing weight for each year of his MLB career. The Time piece clearly has an agenda and does not cite any sources, but the stats at least seem reasonable, so we’ll go with them. To track changes in Bonds’s mass, let’s take his playing weight from his last two years with Pittsburgh (190 lbs) and compare it to his playing weight during his 73 HR season (228 lbs). This works out nicely to a 20% increase in Bonds’s weight (our substitute for mass). Now, to tease out some concrete numbers, we need to make some assumptions. In the interest of fairness to steroid believers, I’ll try to make these assumptions as conservative and reasonable as possible. We’re not just interested in absolute weight gain, just the mass of muscle that was added, but let’s assume that all 38 pounds was additional muscle attributable to steroids. We must also determine how that muscle was distributed, for as we established earlier, virtually all of a batter’s power comes from his lower body. Despite many sources (acknowledged by Owen, I might add) suggesting that muscle size increases at greater rate in the upper body, I’ll make the simplifying assumption that it’s an even 50-50 split for Bonds. That leaves us with 19 extra lbs of lower body muscle and a 10% increase in mass that matters for additional batting power. Consequently, if you had proof that he juiced, you could conclude that Bonds gained an extra 10 feet of batted ball distance just by taking steroids. Does this get him from 33 HR in 1990 to 73 HR in 2001? I doubt it.

Let’s revise those assumptions a bit. First, let’s assume that Bonds is acutely aware of how power is generated and focuses all of his training while on steroids to improve his lower body; in other words, we’ll say that the steroidal gain affects the lower body only. However, I don’t think it’s reasonable to assume that all of Bonds’s weight gain from 1990/91 to 2001 was pure muscle. We’ll go back to the data to get a more accurate assessment of how much of that weight gain can reasonably be considered muscle only. As mentioned earlier from Alan M. Nathan’s article, roughly half of an athlete’s mass tends to be muscle mass. Starting with our baseline of 190 lbs, let’s say that Bonds was 95 lbs of muscle in 1990/91. We’ll also bring back in the results of the Bhasin et. al. article cited by Owen in support of his case. The authors of that study included measurements of changes in muscle size in addition to changes in muscle strength. While size is an admittedly imperfect substitute for mass, it’ll do in a pinch. Doing some quick math from that article’s Table 4: Body Weight, Fat-Free Mass, and Muscle Size and Strength Before and After the 10 Weeks of Treatment reveals that steroid consumption resulted in a roughly 14% increase in muscle size in the quadriceps. Returning to Mr. Bonds, we’ll extrapolate and say that he could reasonably expect a 13 lb gain (95 lbs x 0.14) in lower body muscle from using steroids. Re-running our original equations, we find that Bonds now has a 7% gain in effective muscle mass, granting him the magical steroid-fueled power of hitting balls a whopping 7 feet further.

Perhaps you’re saying to yourself right now, “But Justin, even seven feet seems like a huge number. Think of all the fly balls that die on the warning track – they’d immediately become home runs!” You’d be absolutely correct, if those fly balls weren’t already home runs. Let’s conservatively assume that a regular hitter swings a 34-ounce bat with 67 mph of bat speed (see Welch et al., “Hitting a Baseball: A Biomechanical Description”, 1995). Returning to our original equation for outbound ball velocity and assuming an exit angle of 35 degrees, we discover that our lucky batter crushes the ball 440 feet. See for yourself. That’s easily already a home run in any major league ballpark; to argue that a batter hitting the ball 450 feet instead of 440 feet has a demonstrable impact on the game is an exercise in absurdity.

In addition, keep in mind that these perfect conditions (ball hit on the sweet spot, ideal exit angle) are the exact same conditions under which the distance added from steroids has been calculated. Any variation from this (which, it hardly bears mentioning, is extremely likely), and the marginal gain a batter experiences from steroids could easily be reduced to almost nothing. You know this already – no matter how jacked a hitter is, he’s going to weakly ground out if the ball gets in on his hands. To state it as clearly as possible, the balls a juiced batter hits that are significantly affected by steroids would have been home runs anyway.

After a thorough examination of the available scientific evidence, it becomes painfully obvious: the notion that steroids can and do have a substantial effect on batting performance is simply not borne out by statistics, logic, and the laws of physics.

§ 1.4 – The Recovery Fallacy

Owen purports to “explain” the benefits of steroids by suggesting that they aid muscles in their recovery. Ironically, he deviates here from his beloved legitimate scientific sources in an effort to find evidence to back up his claim. Oddly, the earlier scientific sources he cites to prove himself “right” make no mention of steroids aiding recovery. Why is that, you ask? Simple: there is no conclusive scientific evidence suggesting that steroids help muscles repair and recover. Owen’s recovery claims and the sources that supposedly support them are, to borrow his colorful phrasing, “a bunch of unsubstantiated bullshit that doesn’t qualify as science or that no one actually ever said at all.”

But don’t just take my word for it—let’s look to the literature. First, again to an article that Owen cites then appears to forget. In their own words, Storer et al. (2003) conclude that “failure to observe a significant testosterone dose relationship with fatigability suggests that testosterone does not affect this component of muscle performance”. In fact, despite Owen’s fondness for judging titles, he appears not to have read the one for this article, for this finding appears there plainly: “Testosterone Dose-Dependently Increases Maximal Voluntary Strength and Leg Power, but Does Not Affect Fatigability or Specific Tension [emphasis added]”. In case you’re wondering, fatigability is “the quality of being susceptible to fatigue”. Contrary to Owen’s claims on our last podcast and the non-scientific sources he cites, steroids do not help you train longer. There is no scientific evidence to support the assertion that steroids help prevent muscle breakdown during a workout. Indeed, the overwhelming majority of studies have demonstrated that steroids were not able to increase athletes’ endurance (see Hartgens and Kuipers, pp. 534).

What about after a workout – do steroids help in the recovery of muscles after an exercise regimen? Again, the scientific answer is no. Our very thorough friends Hartgens and Kuipers state in no uncertain terms that “research on [steroids’ effect on] the recovery rate in humans is too limited to draw definite conclusions yet” (pp. 534). Owen seems to suggest that knowledge of how steroids affect the body has advanced rapidly in recent years, so let’s take a look at a more recent review of the scientific literature. Alas, a 2009 review of research on how steroids affect humans reaches the exact same conclusion: there is zero conclusive proof that steroids enhance muscle recovery in humans (Husak and Irshick, “Steroid Use and Human Performance: Lessons for Integrative Biologists”). If Owen is to hold himself to his own admirably lofty standard for supporting claims with scientific evidence, he must abandon his perception that steroids help athletes by healing them more quickly.

A quick note on Human Growth Hormone. Owen states (without citation) that hGH works similarly to steroids, presumably via the same mechanism of aiding muscle recovery (as its name would seem to imply). While a full overview of the scientific evidence regarding hGH is out of the scope of this already lengthy article, allow me two quotes from medical professionals that shroud the efficacy of hGH in serious doubt. First, from Dr. Mary Lee Vance (author of this scientific review debunking the notion of hGH as an anti-aging agent) in the Baltimore Sun: “There’s no evidence at all that [hGH] helps anyone recover from injuries.” Second, from two doctors and professors of medicine at the University of Chicago: “Not a single clinical trial has effectively demonstrated that the metabolic effects of growth hormone, even including a temporary increase in lean body mass, have resulted in improved performance. The view of some athletes that a few injections of the hormone might have beneficial effects on sore arms has never been rigorously tested, but is very unlikely to be effective….Taking any form of growth hormone in the hope of improved athletic performance is misinformed at best” (Richard Landau and Louis H. Philipson, “Baseball and Growth Hormones: Big Muscles, Big Bodies, Big Trouble,” The Wall Street Journal, 20 December 2007, pp. A15).

If you think steroids or hGH will lead you to your modern-day Fountain of Youth, I’d advise you to look elsewhere.

§ 1.5 – Summary of Findings

We’ve had quite a long journey, but ultimately we’re back where we started. There is substantial evidence suggesting that steroids increase muscle strength and size in the upper and lower body, although several studies have indicated that muscle size in the upper body increases at a greater rate than that of the lower body. Size is indeed the effect about which we should be concerned, for the main factor a batter controls in determining the distance a batted ball is hit is his bat speed, which is driven by his muscle mass. Examining the physics behind batted ball interactions reveals several interesting findings. First, there seem to be some diminishing returns with added muscle mass in terms of the ratio of kinetic energy a batter can generate in his bat. More importantly, while added muscle mass from steroids can noticeably increase the distance a ball is hit, this is only under conditions that would already produce a home run from a batter with normal bat speed; the advantage conferred by steroids quickly disappears when (very likely) non-ideal conditions are introduced into the batted ball interaction. Finally, despite a cornucopia of perceptions and non-scientific evidence to the contrary, steroids have never been conclusively proven to speed or otherwise aid muscle recovery. When all of the evidence is considered, it is impossible to conclude that steroids can or did have a perceptible effect on performance in the game of baseball. Our null hypothesis remains utterly unrefuted.

Part 2 – The Discontinuity Dilemma

We’ve seen what math and science can tell us, or rather can’t tell us, about the impact of steroids on baseball, but what about history and logic? On our last podcast Raphael made the following statement, which Owen seemed to agree with: “I do think that the number like 73 home runs or 70 home runs or 66 home runs coming from these guys – I mean Sammy Sosa hit 60 home runs in two consecutive seasons. I just think that is an inflated number. I do not think that Sammy Sosa is that kind of player without steroids.” I’d wager this is a fairly representative sentiment among those who believe in the “Steroid Era”. Thus, it warrants some investigation. Is there any evidence of an exogenous impact on the performances of players who played during this era? Can we logically conclude that steroids are responsible for the power production we saw during that time?

§ 2.1 – Under-rated

Towards the end of his article, Owen posts an authoritative-looking table of HR leaders allegedly using steroids along with an imposing graph supposedly proving the existence of an increase in power attributable to steroids. Unfortunately for him, critically thinking about this “data” quickly reveals its fundamental disingenuousness. It ought not be necessary to point out that concocting a list of players “who were almost certainly taking steroids at the time of achievement” without providing any evidence whatsoever that (a) those players actually ever took steroids or (b) that they were taking steroids at the time he claims is the utmost in intellectual dishonesty. I wouldn’t dare accuse Owen of conspiring to use red text to lend an air of legitimacy to a point that has none; perhaps he merely forgot that hearsay does not automatically count as evidence.

As for that graph, Owen posits that the heyday of steroids was the late 1990’s to the early 2000’s, and that the bump in power on the graph from 1999-2001 proves their impact. This conclusion is rather curious for a number of reasons. First, I’d argue that even the most ardent anti-steroid crusaders would say that the “Steroid Era” spanned a range of years more like 1997-2003. Unfortunately for them and the conclusion Owen wishes to draw, the power baseline established in 1997-98 persisted all the way through 2009. Furthermore, Owen would like you to believe both that Jose Canseco began using steroids in 1987, but that the entire league didn’t start using them until 1999. What are we to believe, then? That a very small group of players begin using steroids in the late 1980s to great effect, but the word didn’t get out until twelve years later? Did a case of steroids escape from Jose Canseco’s grasp, take a hard left away from Cecil Fielder, circle around Albert Belle, skip over Ken Griffey Jr., and land squarely in Barry Bonds’s lap? And then did the entire league begin using steroids, see a significant boost in their power, then inexplicably decide to stop using three years later (except for, apparently, A-Rod)? The fundamental absurdity in all of this should be obvious. Let me be clear: you do not get to cherry pick data to prove a point with evidence that does not exist.

With that said, let’s look at some complete data to analyze the entire careers of some of the most famous “Steroid Era” players. We’ll begin with Mark McGwire, the man the aforementioned Sammy Sosa always seemed to be chasing. For all players, I’ve excluded some data points at the beginning or end of their careers that do not represent full seasons or do not reflect performance that we care about. All data comes from the indispensable Baseball-Reference.


This first graph shows Mark McGwire’s games played (GP, plotted on the left axis) and home runs (HR, plotted on the right axis). Two things jump out from this graph. The first is that McGwire displayed 50 HR power early in his career (49 HR in his age-23 season, to be exact). If that’s his baseline, is it particularly unreasonable that with the development of his body and batting skills he could add 10-15 HR to his yearly totals? Food for thought, at least. Secondly, the power surge late in McGwire’s career coincides with two things: he finally gets healthy for an extended period, and he moves out of Oakland (a notorious pitcher’s park) and into St. Louis (a neutral field, if not a slight hitter’s park).

However, the biggest takeaway here is that home run counts are strongly dependent on time spent on the field. This seems obvious, but it’s often forgotten: you can’t just consider raw numbers, you must also consider the context in which they’re produced. A player jumping from nine home runs one season to thirty-nine the next might seem initially suspicious until you realize he played nearly sixty more games in that second season. With that in mind, let’s take a look at McGwire’s power rate over his career:


This graph shows McGwire’s at-bats per home run over the same time period. Note that a lower figure is better for the hitter: this means he hits home runs more frequently. Other than two outlier seasons in 1991 and 1994 (the latter being the strike-shortened season), there’s a fairly obvious downward trend until the rate becomes steady in his later years. Can you pinpoint the time when McGwire began using steroids? I certainly can’t. To me, this seems like a fairly natural course for a player who improves rapidly during his formative years, then settles around his peak talent as a mature hitter.

What about Mr. McGwire’s counterpart in those late-90’s home run record chases, Sammy Sosa? Since we’ve established the importance of rate stats to contextualize counting stats, let’s include them together on the next graph:


Here we see Sosa’s HR (in green, plotted on the left axis) and AB/HR (in purple, plotted on the right axis; these values have been made negative for easier comparison with HR – in this graph a higher AB/HR is better) for all but the first and last years of his career. Again, I’m not sure where we’re supposed to see Sosa using steroids. Was it from 1992-1993? I’d argue that, like many young players thrust into the majors, he was still adjusting to the league and establishing himself as an everyday player, which he didn’t really do until that 1993 season. Was it from 1995-1996? Then why did his power rate drop precipitously in 1997? Was it from 1997 to 1998? Then why the dip in 2000? Personally, I see a player who puts it all together in 1993, then steadily improves (except for a bad season in 1997) until he hits his peak in 1998. His best years are from 1998-2001, save for a slight blip in 2000, and then he declines as he ages, dropping off a cliff (as many old power hitters do) in 2005. The only thing abnormal here seems to be the raw counts of home runs produced.

So what of those abnormally high counts? Owen dismisses it with a (non-scientific) wave of his hand, but there is significant evidence suggesting that the baseball itself underwent substantial changes during this period that resulted in it becoming springier. In other words, the baseballs, not the players, were “juiced”. Welters and Ordonez (2000) analyzed baseballs from 1963, 1970, 1989, 1995, and 2000, finding that the materials comprising  the 1989, 1995, and 2000 balls differed from the official Major League Baseball specifications. More significantly, the balls from 1995 and 2000 bounced over 30% higher than the earlier ones. This is crucial because the ball’s bounce is a measure of its coefficient of restitution (CR), a key term in our equation for outbound ball velocity in batted ball interactions. In addition, a study by researchers at Universal Medical Systems and Penn State (described here and here) performed CT scans on baseballs from 1915 to 2007. They found that the density of the balls had increased over time, particularly after Rawlings became the manufacturer in 1977, and they discovered the existence of a rubber ring around the cork center of the ball—again, a feature not included in MLB’s official baseball specifications. See an image of the greater density for yourself. Why is this noteworthy? Not only will a denser ball will travel farther when hit, the rubber band will add to the ball’s springiness.

Of course, MLB has denied any change or variance from specifications in the construction of the baseballs. They even commissioned a study from the University of Massachusetts at Lowell to analyze a sample of official baseballs, though there were significant methodological problems with the study. First, the study only compared baseballs from 1999 and 2000, ignoring the fact that the most recent ball changes appear to have started around 1994. But most obviously, MLB funded the study and proudly paraded its finding that there was “no difference” between the two years’ balls and that they met “performance specifications” to any media outlet that would listen. (Oddly, the study itself admits that “some of the internal components of the dissected samples were slightly out of tolerance”, while MLB quietly computerized the strike zone and removed the words “cushioned cork center” from all baseballs in 2000). If you’re inclined to uncritically accept the results of a study funded by a party with an obvious interest in a specific outcome, I’ve got a carton of very healthy cigarettes I’d like to sell you.

At the very least, it’s quite plausible that the unprecedented home run totals of the late 1990s and early 2000s were due to changes in the baseball. Perhaps MLB was afraid about what the 1994 labor strike would do to fan interest in the game, and so they directed Rawlings to alter the baseball to increase offense and drum up fan excitement. Maybe the results of those changes didn’t show up in gaudy HR totals until the game’s best power hitters in McGwire and Sosa entered their primes a few years later. Or suppose the ball had nothing to do with it. We know the game goes through cycles; perhaps the “Steroid Era” was just a high-offense period that happened to feature two or three of the best power hitters the game has ever seen. Maybe there’s a bit of a chicken-and-egg issue. The spike of money and media attention in the game focused on those who hit lots of home runs, and McGwire/Sosa/Bonds were just better at it than everyone else. Everyone attempted to emulate them by trying to jack every pitch out of the park until the advanced stats revolution of the early 2000s realized that most hitters were best served just trying to get on base.

I’ll be the first to admit that this is all speculation with little evidence backing any of it. Yet, as our journey through the research and the numbers has shown, it is important to realize that steroids stand in the exact same place. They may very well have had an effect, but there’s no evidence that they did and nowhere to point to find that evidence. If you can’t separate the effect of steroids from the hundreds of other factors that also may or may not have had an effect, you have no proof of the existence of any effect at all.

§ 2.2 – Don’t Fear the Career Year

Despite all of my best efforts thus far, I imagine there’s still a little hint of nagging doubt in your mind. Even with data showing that, for all hitters in the Mitchell Report, their average number of home runs decreased by 0.246 and their slugging percentage only improved by an average of 0.019 after 1997 (for a 600 AB season in 1998, that’s three triples and a double, or a heavyset family of four’s regular order from Wendy’s), I bet there’s still one thing holding you back from ridding the thought of steroids affecting the game from your mind altogether: Barry Bonds’s 73 home runs. That number seems so ridiculous, so out of step with his career and what we were taught is possible in a single season of baseball that it’s almost impossible not to think that he must have had something other than skill pushing him to that achievement. The key word there, of course, is almost. Is 73 home runs really that implausible? To find out, let’s start with a graph, and a simple one at that:


This graph merely shows Bonds’s home run totals throughout his remarkably long career, excluding his first season. Two huge outliers immediately pop out: the 2001 season, his record-setting year; and 2005, when he got hurt and was never the same afterwards. Besides those, the graph appears to be a fairly steady upward trend until we hit the year 2000, when his power seems to kick up a notch. You might argue that’s when he began using steroids; I’d argue that a simpler and more obvious change was the fact that he moved out of Candlestick Park and into AT&T Park. While the latter isn’t exactly a hitter’s haven, it’s miles better than the notoriously windy Candlestick. With that exogenous factor in mind, I think it’s fair that our true baseline for analyzing Bonds’s 2001 should be his 2000 and 2002-2004 seasons. Still, that 2001 year is an increase of about 25 HR from what we’d normally expect. Ridiculous, right?

Maybe, but it’s certainly not unprecedented. Consider the following list:

  • Babe Ruth went from hitting 29 HR in 1919 to hitting 54 HR in 1920. Margin of increase: 15 HR
  • Jimmie Foxx went from hitting 30 HR in 1931 to hitting 58 HR in 1932. He did something similar later in his career, going from 36 HR in 1937 to 50 HR in 1938. Margin of increase: 18 HR; 14 HR
  • Ted Kluszewski went from hitting 16 HR in 1952 to hitting 40 HR in 1953. Margin of increase: 24 HR
  • Hank Aaron went from hitting 26 HR in 1956 to hitting 44 HR in 1957. He hit 30 HR the following year. Margin of increase: 18 HR
  • Roger Maris went from hitting 39 HR in 1960 to hitting 61 HR in 1961. He hit 33 HR the following year. Margin of increase: 22 HR
  • Davey Johnson went from hitting 5 HR in 1972 to hitting 43 HR in 1973. He hit 15 HR the following year. Margin of increase: 38 HR

And, in case you’re a visual learner, here’s a nice compact graph for comparison:


All of these other six players had similar (if not greater) jumps in production to Barry Bonds. Are we going to ridicule and crucify them for cheating too? Of course not, so why are we doing so for Bonds? If it sounds nuts to accuse Davey Johnson or Roger Maris of going nuts on steroids, it should sound equally crazy to do the same to Bonds. Why is he not simply the most productive home run hitter who has ever lived? After all, someone has to come out on top.

Since I am generally not a fan of small sample sizes and just so there is no accusation of cherry-picking my own data, let’s take a look at a study of power spikes throughout baseball history. In his excellent article on the subject, Nate Silver defines a Power Spike as the scenario in which “a player is an established major league veteran, at least twenty-eight years old, with at least 1000 plate appearances (PA) accumulated between his previous three seasons; and the player improves upon his established home-run rate by at least 10 HR per 650 PA, in a season in which he had at least 500 PA”. After normalizing offensive levels across all eras to the same baseline (Silver uses the 2004 AL), he finds that Power Spikes from 1994-2004 were no more or less common than they were in any other era (graph). Perhaps you take umbrage with the standardization of offense, arguing that the raw numbers of home runs hit in 2004 was due to exogenous factors not present in other eras (i.e. steroids), and that this greater number of home runs led to more Power Spikes rather than the converse. Thus, Silver re-runs the numbers without the normalization, but this time breaks out the results into separate buckets for differing established power rates (i.e. the number of home runs the player hit before his Power Spike). While Silver does find that non-adjusted Power Spikes have occurred more frequently from 1994-2004 than in prior eras, this increase is attributable entirely to players whose established home run rate was 10-30 HR per year (graph).

Why more Power Spikes for this middle tier of players? It’s a good question. As I suggested earlier, perhaps there was generally a greater focus on power hitting, or maybe this just happened to be a period of high offense that we really ought to normalize when comparing to other years. The culprit certainly doesn’t seem to be steroids, though, since those with the most to gain by using steroids – either via marginal benefit (players with no power suddenly proving they can hit home runs in the big leagues) or added production (power hitters who already hit many balls very far suddenly making more of those balls go over the fence) – did not experience any abnormal jumps in power. To reiterate: power hitters in the “Steroid Era” did not have any more Power Spikes than they did in any other era.

Let’s return to Bonds for a look at one more graph. Here is the same chart of his home run totals, but with his stolen base counts in each year (plotted on the right axis) added:


Notice that his stolen base numbers plummeted right around the time he is accused of having taken steroids. While stolen bases are an admittedly imperfect measure of speed, this phenomenon is particularly problematic for Bonds’s accusers given that steroids have been shown to increase the “burst” performance of muscles, specifically aiding activities like sprinting (Husak and Irschick, 2009). Rather than evidence of steroid use, I see here a player whose skill set changed over time. Consequently, he did what all great players do: adjust. I believe the Bonds recognized his speed was declining quickly, and so he transformed himself late in his career from a player who relied on a power/speed combo to a player who focused almost exclusively on performance at the plate.

As for that amazing 2001 season, I want to suggest a causal factor that is very simple and yet incredibly hard for many people to accept: luck. There are so many factors that contribute to the outcome of a plate appearance beyond the batter’s swing: the pitcher, the defense, the umpire, the wind, the batter’s concentration, fatigue experienced by both teams from a long season, and so on. To suggest that one single factor – mind you, a factor that has not been proven to have any substantial impact whatsoever – is responsible for the whole of Bonds’s performance that season seems to me to be the height of absurdity. I generally dislike intangible clichés like “momentum”, but I do believe we saw a Bonds who was locked-in for the entirety of that season and who got the benefit of a few lucky breaks without much going wrong. Rather than reaching to write off his accomplishments, we ought to take a step back and appreciate an all-time great player performing at the height of his powers, recognizing that the confluence of factors leading to that performance will likely never occur again—and not because baseball is now a “clean” game.

Indeed, those pointing to one-time spikes in power production as evidence of steroids tainting the game are crossing a bridge that logic cannot support. If steroids caused an initial jump in power for a player, why did that level of power production not continue? Assuming that these players were taking steroids and that the steroids had a demonstrable impact on their performance, you would expect the players to continue using and their level of performance to remain at that level. Clearly, for players like Bonds and Brady Anderson who did experience single-season power spikes, that was not the case. The more sensible premise is that steroids contributed to a gradual but noticeable uptick in power output that sustained itself for several years until steroids no longer became prevalent in the game. Yet, if you accept that supposition, you must throw out drastic single-season power spikes as evidence of your case—you cannot simultaneously possess and consume your cake. At that point, deciding when steroids became prevalent enough to affect the league as a whole, which players were using steroids at which points, and separating the benefit of steroids from the natural development in batting skill and normal year-to-year fluctuations becomes an exercise in guesswork with no more legitimacy than suggesting that a countrywide shift in climate patterns led to thinner air from 1985 to 2005. Cloaking arbitrary accusations with an air of authority is no substitute for rational logic.

Part 3 – Should We Care?

By now, I hope it has been demonstrated that those asserting with certainty that steroids had a definite impact on the game of baseball are no more credible than your run-of-the-mill conspiracy theorist. However, let’s put that aside for a second. If we do assume that many players were using steroids to some significant effect, should this change our evaluation of the game during this period? Ought we to ban steroids and stigmatize their use simply because they create a dangerous and slippery slope for future athletes? The answers to these questions are far murkier than you might initially suppose.

First, it bears pointing out that the question of whether steroids are even bad for you at all is hotly debated. Both Bhasin et al. and Storer et. al reported no adverse side effects from their studies of how steroids affect the body. The review of scientific research conducted by Hartgens and Kuipers also discusses the side effects of steroids in detail. While the results of the reviewed studies are often in conflict, Hartgens and Kuipers do find that steroids impact the reproductive system (by shrinking the testes and sperm counts, and by causing gynaecomastia), the cardiovascular system (by increasing cholesterol levels, although the effects may be mitigated by the generally good cardiovascular health of athletes), the liver (although negative effects are only found with orally ingested steroids), and behavioral health (although results are often self-reported and impossible to separate from other mental health issues found in people who use illegal drugs). However, there are two important things to note from these findings: the samples studied, and often the number of those impacted within those samples, are too limited to draw conclusions for the public at large; and most importantly, almost all of these side effects reverse themselves once steroids are no longer used. We routinely accept and even applaud athletes who trade possible long-term consequences for short-term gains in performance—think of all the athletes who get cortisone shots or painkillers in order to play through some injury. Why should we fear athletes’ use of steroids to boost their performance, especially when any adverse side effects are neither certain nor long-term?

It is true that steroids can have a much greater negative impact on adolescents; their skeletal structures are usually not fully formed enough to handle the added muscle mass conferred by steroids. Should we be concerned then that our children will emulate athletes and inadvertently cause themselves harm? I’ll let Mr. Walker handle the specifics, but the short answer is no. A relatively small proportion of children (less than 20%) identify an athlete as their role model, and those that do actually tend to use all drugs less frequently than their peers. The real issue of drugs in baseball has nothing at all to do with steroids. If anything, it is the criminally under-reported and widespread abuse of “greenies” (amphetamines), of which there is substantial anecdotal evidence.

What about the argument of “unnaturalness”: that we must take the accomplishments of the “Steroid Era” with a grain of salt because they were achieved via an exogenous factor not present in any other period in baseball history? Unfortunately, this position creates the slipperiest of slopes because you can make the very same argument about many other innovations in athletics that are not looked upon in a negative light. The advances in medical science and nutrition knowledge that help athletes like Steve Nash and Mariano Rivera perform at a high level late into their careers were unavailable to earlier generations; should we then automatically deduct credit for modern-day athletes’ accomplishments because they’re able to play better, longer? Stephen Strasburg and Adrian Peterson rebounded better than ever from injuries that would have ended the careers of players in previous eras—are we to argue that they are cheating because they took advantage of newly available medicine in order to extend their careers? If the answers to these questions are no, it is difficult to see the point at which the use of steroids crosses the line. Who are we to argue that steroids are bad, but platelet-rich plasma therapy and carefully constructed diets are not? Is it even possible to non-arbitrarily draw a line in the sand?

I don’t purport to have good or satisfying answers to any of these questions, but I do know that they can easily be asked and debated. Moreover, I know we ought to be deeply suspicious of anyone who definitively asserts that steroids are a stain on sports that ought to be expunged. Indeed, as we have seen time and time again, anyone who claims with certainty that steroids have perceptibly impacted the game of baseball flies in the face of everything we can learn from medical science, mathematics, historical data, and logic.


2 thoughts on “Blind Men Only See Black Skies

  1. Owen says:

    Raphael, Justin, and probably no more than three other readers: Justin’s slanderous and incendiary “counter-arguments” in this article are every bit as baseless and indefensible as Mr. Walker’s original assertions. I have begun my response, which I had hoped to post promptly, but this will be impossible, as I have already written some 1700 words describing the depth and breadth of this mis–nay–DISinformation and haven’t even begun to critique section 1.3 yet.

    As my schedule becomes more busy over the following weeks, do not expect my response to be so mind-bogglingly snappy as my prior article, published within a mere 36 hours of Justin’s original comments (AND I played golf in-between).



  2. Justin says:

    Ball don’t lie.

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