What Impact Did Steroids Have on Alex Rodriguez’s Home Run Performance?

Following yesterday’s post, I received an e-mail from an interested reporter asking me if it was possible to compare Alex Rodriguez‘s performance versus expected performance during his admitted steroid seasons.

Something about the wording of his e-mail stirred me to think about a better way to look at this than what I had previously done. The procedure is simple, I use Baseball-Reference’s “Neutralize Stats” tool to convert A-Rod’s home-run rate (HR/AB) performance to a consistent baseline. Then I use my estimates of aging from a study to be published in Journal of Sports Sciences (working paper version) to examine Rodriguez’s neutral career aging trajectory.

The table below lists A-Rod’s career performance neutralized for park and era effects—these are not his actual numbers, which are polluted by ballpark and era effects—as well as a correction for natural aging. The “Aging (v. Peak)” column reports the percent difference from his projected peak HR/AB. I base the aging progression towards his peak using the mean of his age 23 and 24 performances to project his peak HR/AB performance of 9.18% at age 30. It’s interesting to note that A-Rod’s peak HR/AB performance occurs at age 31 at 9.37%.

Year	Age	Neutral	Aging 	Pred.	Neutral	Pred.	Neutral HR
		HR/AB	(v.Peak)HR/AB	HR	HR	- Pred. HR
1994	18	0.00%	-67.63%	2.97%			
1995	19	3.18%	-56.73%	3.97%			
1996	20	5.63%	-46.79%	4.89%			
1997	21	3.94%	-37.80%	5.71%			
1998	22	5.98%	-29.77%	6.45%			
1999	23	7.91%	-22.70%	7.10%			
2000	24	7.41%	-16.58%	7.66%			
2001	25	8.12%	-11.43%	8.13%	51	51.07	-0.07
2002	26	8.91%	-7.23%	8.52%	55	52.56	2.44
2003	27	7.53%	-3.98%	8.82%	45	52.72	-7.72
2004	28	5.98%	-1.70%	9.03%	Gain	01-03	-5.35
2005	29	8.28%	-0.37%	9.15%	Gain	01-02	2.37
2006	30	6.00%	0.00%	9.18%			
2007	31	9.37%	-0.59%	9.13%			
2008	32	6.84%	-2.13%	8.99%			

The reporter also noted that A-Rod claims to have quit taking steroids after a 2003 spring training injury; therefore, we might not want to include 2003 as a steroid season. Thus, I include his 2001–2003 and 2001–2002 total gains in home runs. As the table indicates, 2003—the season in which we know he tested positive—he hit nearly 8 fewer home runs than expected. He hit almost exactly as many home runs as expected in 2001 and 2.44 more than expected in 2002.

So, what were A-Rod’s steroids worth? 2.37 home runs over two seasons, or a little over one home run a season. At least, that is the estimate based on the method I laid out above; however, it’s probably best to say that there was no observed effect. It is possible that the steroids did give Rodriguez a boost, and this may have helped him through an injury or some other factor that my estimate does not account for. It’s also likely that he hit more home runs than expected through random chance. Given the general swings in the play of the game, it is very difficult to separate true performance changes from random swings in performance. The deviation here isn’t large enough to say much.

The important finding is that the statistical record doesn’t reveal an obvious spike in home-run performance by Alex Rodriguez during the time when he admits to using performance-enhancing drugs.

Addendum: The reporter mentioned above is Carl Bialik, who now has a post up on the subject at The Numbers Guy.

Further Addendum:
For those who have asked why posted this brief analysis, see Thomas Boswell’s latest.

Rodriguez may have taken performance-enhancing drugs for only three years — never before, never after.

For one thing, his statistics, as we’ll show, indicate that he may be coming clean. He averaged 33 percent more homers in his dirty Texas years — from 2001 to 2003 — than in the other 10 full seasons of his career. That’s a huge leap, similar to the numbers that first incriminated Barry Bonds in many baseball minds….

In his three years in Texas, from 2001 to 2003, he averaged 52 homers vs. 39.2 everywhere else. The jump was even bigger when compared to his previous five superstar years in Seattle, when he averaged 36.8 homers.

After hitting 42, 42 and 41 homers in his last three years in Seattle, he hit 52, then 57 in his first two years in Texas. Granted, the Ballpark is a launching pad. Rodriguez slugged .666 there in three years vs. .576 on the road. But that’s still worth only a few extra homers a year, not 12 or 15.

24 Responses “What Impact Did Steroids Have on Alex Rodriguez’s Home Run Performance?”

  1. Willy says:

    Hey JC, 

    Would neutralizing for era effects possibly be a problem? If as A-Rod said, everyone was doing it. Wouldn’t that be present in the era effects? Many claim that athletes feel the need to take steroids to keep up with the competition. If enough people are taking steroids to create an era effect, then neutralizing for it will make a large part of the performance increase (assuming that it exists) that would be attributed to steroids disappear. Right?

    Or am I misunderstanding what an era effect is?

  2. JC says:

    Possibly. It measures A-Rod relative his peers in any given season. If his use fluctuates along with use in the league then it could hide an effect. Over a two-to-three year period in an era that likely had constant use, I think it it’s unlikely to be an issue here. I’d be more concerned that he used before and after he stated he used having a bias. Here, I’m assuming he’s clean before and after, and that’s all you can do.

  3. Tim says:

    JC – Two questions.  (1) You are looking at hr/ab.  Is this the statistical at-bats, or plate appearances?  If A-Rod thought that PEDs could help him hit home runs, couldn’t he actually be less selective at the plate and therefore walk less?  It would be interesting to see the rates rerun with hr/plate appearances.  (2) Also, if theoretically, PEDs help a player recover faster from injuries, it would be interesting to see how his playing time changed for those three years. 

  4. JC says:

    1) AB = AB
    Here are his neutralized walk rates. Nothing stands out.

    Year PA BB rate
    1994 59 8.47%
    1995 149 4.03%
    1996 677 7.98%
    1997 638 6.27%
    1998 748 5.88%
    1999 572 9.09%
    2000 672 14.73%
    2001 732 10.11%
    2002 725 11.59%
    2003 715 11.61%
    2004 698 11.46%
    2005 715 13.43%
    2006 674 12.91%
    2007 708 13.70%
    2008 594 11.11%

    2) He played a lot during all three years in Texas, missing only one game. He played every game for the Mariners in 1998 and for the Yankees in 2005.

  5. Rumit says:

    Hey, great work. I’ve been of the opinion for a while now that the PED thing has been blown way out of proportion and that there’s very little hard evidence suggesting that they actually  have a dramatic impact on performance. But, I wonder, if that list of 104 players became available, could the question be answered conclusively? Because, then we’d have a set of 104 players who we know were juicing and a second set of ~600 players who would likely have significantly less users (this is assuming that there is a relatively small percentage of guys who were using and tested negative). Would this be a large enough sample to do a one year comparison and measure the performance difference between users and clean players?

  6. JC says:


    Sure, you could do it. A similar analysis was done with the Mitchell Report players by Jonathan Cole and Stephen Stigler, and they found no evidence of an ergogenic effect.

  7. David says:

    This analysis makes sense for A-rod, but how do you explain Brady Anderson’s HR total of 50 in 1996, when his next highest career year was 24 in 1999.  He also hit 0.637 in slugging that year, 0.160 higher than his second highest season.  Yet his strikeouts remained steady between 1995 – 2000, so he wasn’t “swinging for the fences” on every pitch.  Was he the one guy where steriods helped him a ton?  Or was it something else?

  8. CR says:

    I assume you are taking A-Rod at his word that 01,02,03 were the only years he used. If you are correct with your formula then why do athletes use PED’s? If PED’s had little to do with his power numbers why did McGwire’s and Bond’s HR  numbers jump off the table?

  9. JC says:


    So, I guess Roger Maris used steroids, then. After 61, his next highest HR totals were 39 and 33. The only-game-in-town arguemnt is a tough one to win, especially when we look at strange distributions. Things that seem weird happen randomly every day.

    There is zero evidence that Anderson used, and I think it is wrong to jump to the conclusion that he used steroids without further evidence. The fact that he had a good year isn’t sufficient evidence to convince me.

  10. JC says:

    There is not much I can do but take A-Rod at his word. As for Bonds and McGwire, I have written quite a bit about them over the past few years. It’s too much to go into here, but you could find some potential answers if you poke around the site. A big reason for the change in these two players is that they played in an era when HR were low, and then suddenly jumped The change occurred for many players other than McGwire and Bonds (did Griffey use?) almost overnight in 1993, and I think changes to the ball and expansion had a lot to do with this rise. This doesn’t rule out steroids, but had steroids never been invented I think the post-1993 HR explosion would have happened anyway.

  11. a says:

    Arod says he started the PED after signing the huge contract with Texas because he felt pressure to live up to the conract. By that same logic, i don’t see how he could have stopped after being traded to the Yankees. Where would there be more pressure? Texas or new York??
    I say the reason there is little difference between the years is that he used before and after ’01,’02,’03.

  12. CR says:

    I don’t disagree that a jump in HR’s would be expected with the ball, expansion, and parks getting smaller. Don’t you have to admit that an explosion by so many players in the same time frame seems a bit odd? I still would like to know why a lot of people say steriods/PED’s don’t help that much or are not proven to help. If this is the case, why did/do so many players take them? These PED’s make you stronger, faster, and recover quicker from injuries. HGH actually improves eye sight. Isn’t Bonds the the perfect example of how these help? Before he was suspected of using he was a great player. After a body change and using he was arguably the best hitter to ever play the game.

  13. Alex says:

    Arod was great without roids. Theres no doubt in that

  14. Ken says:

    JC, you’re making strong assumptions here about when he started particularly as that impacts how you deal with aging.  If you assume his progression from 94 to 98 was natural, and everything after that is drug-enhanced up to 2007, his predicted peaks are lower, and he gains a lot from their use.  Obviously that is cherry-picked, but it’s really quite hard to use 2001-2003 as anything close to a firm limit given the absence of reliable testing (particularly of blood).  You’re essentially saying that steroids have no effect on the basis of a proven liar’s word, but they would appear to have an effect if he’s lying about his dates (which seems more plausible to me).   I’d be hesitant to clear steroids of effects on this basis alone.

  15. JC says:

    You’re essentially saying that steroids have no effect on the basis of a proven liar’s word

    I am? I believe there is strong scientific evidence that anabolic steroids have an ergogenic effect. I also stated in the post that he could be receiving a benefit and that it doesn’t show up in the numbers. I can’t help it if he is lying, I’m just trying to see how the data shakes out if he is telling the truth.

  16. Jason says:

    We have an endpoint here.  A-Rod says he quit using steroids in spring training 2003, and there’s at least supporting evidence that he hasn’t been using any PEDs since 2004 because he hasn’t failed any tests.   That endpoint rests on a much firmer foundation than the alleged starting-point, which depends entirely on A-Rod’s questionable veracity.  Why, then, did you not address his declining performance since he says he quit steroids?  

    He fails to match his expected totals every year from 2003-08 with the exception of 2007, when he exceeded it by about one home run.  Over that time period he has fallen about sixty home runs short of his expected total, roughly ten a year.  Perhaps that’s what A-Rod’s steroids were worth.  Rather than no effect, your study suggests Alex has been fibbing in saying his drug use only began in 2001.

  17. Doubter says:

    Your numbers are based on assuming that Arod was only taking steriods 2001-2003.  Call me a doubter.  He lied, he lied, he lied.  When he got caught he minimized and blamed.

    Neither you nor Arod can prove that he was clean from the beginning of his career until 2001 or from 2003 to the present, therefore your analysis proves little.  Maybe the Feds will raid Boras and we’ll learn a little more.

  18. JC says:


    I appreciate the sentiment, but please, don’t refer to this—or anything I write here—as a study. 🙂 It is a blog post looking at some data using a few assumptions. These numbers are going to flop around by their nature. I wouldn’t draw much from them. I was just curious if anything obvious would jump out. Nothing did. To be honest, I was surprised at how closely the numbers matched up.

  19. JC says:


    Good grief.

    From #2

    I’d be more concerned that he used before and after he stated he used having a bias. Here, I’m assuming he’s clean before and after, and that’s all you can do.

  20. JMO says:

    Amphetamines, Cortisone, Steroids, et al…I’m having a difficult time understanding the cutoff point “between competitors looking for an edge” and “cheating.”


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