Some thoughts on Barry Bonds’ and the alleged lack of proof of PED use.

When I was playing serious poker, my required reading list included the works of David Sklansky and Mason Malmuth. Sklansky first opened my eyes to the use of my math background and MIT education to gambling.

Sklansky’s writing inspired this article. But it isn’t about poker. Sklansky came up with an idea for the use of Bayes’ Theorem that I had never seen before, and I will use it here in analyzing Barry Bonds.

We all can agree that Bonds has never failed a test. He did admit to taking steroids, just not “knowingly.” We can also agree that the evidence of the effect of steroids on baseball performance is sketchy to non-existent. At least scientifically. From a mathematical perspective the link, as far as Bonds is concerned, is very solid, based on an a theoretical application of Bayes’ Theorem.

Thomas Bayes was a mathematician who developed one of the great theorems of mathematics, Bayes Theorem. If you want to read about it in detail, click the link. For our purposes though, the basics of it are below.

Bayes’ Theorem is a way to figure out conditional probabilities. An example that is often cited is the “false positive.” Suppose that 0.5% of women at age forty who participate in routine screening have breast cancer. 90% of women with breast cancer will get positive mammographies. 10% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography. What is the probability that she actually has breast cancer?

Out of 10,000 women, 50 have breast cancer (0.5% of 10,000); 45 of those 50 (90%)have positive mammographies. From the same 10,000 women, 9,950 will not have breast cancer and of those 9,950 women, 995 will also get positive mammographies (10% false positive, as specified above). This makes the total number of women with positive mammographies 995+45 or 1,040. Of those 1,040 women with positive mammographies, 45 will have cancer. Expressed as a proportion, this is 45/1,040 or 0.07767 or 4.3%.

The surprising implication is that if a woman (given these parameters) has a positive mammography she is still unlikely to actually have breast cancer!

Sklansky, in discussing this idea in his book Poker, Gaming and Life, uses Bayes’ Theorem to opine that if two unlikely events that are apparently unrelated occur at the same time, they probably are related even if we don’t know it yet. He gives, among others, the example of Stephen Hawking. Hawking has lived longer than anyone else with Lou Gehrig’s disease. He is also one of the smartest people in the world.

Here we have two unlikely events that are apparently unrelated. The incidence of Lou Gehrig’s disease is low. It just happens to occur in one of the world’s smartest men, and then that person just so happens to live longer than anyone else with the disease. Either this is a huge coincidence, or these two items are related in some way, and we just don’t know it yet. He writes that it is much more likely that they are related than not.

So, how does this apply to Barry Bonds?? Bonds has arguably had a singular career since the age of 35. No other player has had such a tremendous career after that age. By analogy, his post-age 35 career is similar in the above example to Stephen Hawking’s survival with Lou Gehrig’s disease. He has played better than anyone else after age 35.

Now we know that there is a tremendously low probability that a player will achieve what Bonds did after the age of 35. In fact, we also know this to be true even given Bonds previous performance. We also know that Bonds admitted to taking steroids, only he claims that he didn’t do so knowingly (this may be the most improbable of all of the probabilities I have mentioned here!) It doesn’t matter for the purposes of this exercise.

So, is it a coincidence that of the very few players who have been proven to actually have taken steroids, he has had the most singular career after the age of 35?? If we apply Bayes’ Theorem as Sklansky suggests, then the answer is clearly no; it is much more likely that his performance was the result of PED use than not; they are related. These are two unlikely events occurring at the same time. The Sklansky use of Bayes’ Theorem says that they are related and we just can’t/haven’t proven it yet.

In my personal opinion, I am willing to bet that Bonds’ performance was significantly affected by his PED use, and that science, if it investigates, will eventually prove that baseball players are significantly helped by PEDs even though baseball is a game of skills more than a game of athleticism.

A few related points. First is that this speculation is independent of the science as it stands now. No one can seriously argue that science has proven that use of PED’s makes on a better player. And there are many ways one can gainsay this proposition. But it is my belief that science will one day prove this to be true; for now I am speculating that it is true based on this use of Bayes’ Theorem.

Second: No matter what is proven in the coming years, this use of Bayes’ Theorem shows that Bonds’ post age 35 performance was at least in part, if not largely, the result of his PED use. We can argue about how much, but based on the use of Bayes’ Theorem above I don’t think anyone can legitimately assert that he was either not helped at all (I am rebutting the position of those that say that hitting a ball is not like other athletic feats, and so Bonds’ may not have been helped by PEDs) or was only helped by a minimal amount.

Third: We do not know when Bonds actually took the “cream” and the “clear.” Allegedly, he took it at least in 2003, per his leaked grand jury testimony. However, a much more likely scenario is his alleged decision to use it in 1998, according to Game of Shadows, the now infamous book. I am not saying anything about the truth or falsity of the allegations in this book.

Am I singling out Bonds?? In a way, yes, but what I have written is equally applicable to Sosa or Palmeiro or McGwire, especially as proof that they did take steroids despite their denials. This use of Bayes’ Theorem establishes that Bonds would not be the home run king were it not for steroid use. Regardless of the lack of scientific evidence right now, it is much more likely than not that Bonds’ record is the result of steroid use.

Why is this controversial? I am not sure it is in the sense that we all think that Bonds’ was helped to some degree. However, if this use of Bayes’ Theorem is considered then it is clear that those who believe that it is speculation to assume that Bonds’ was helped by PEDs are incorrect. His career totals and achievements are the result of PED use.

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