I have asked myself whether Barry Bonds used performance enhancing drugs (PEDs) numerous times during the last 10 years. Finally, I decided to go to work answering the question, or at least to build a framework whereby anyone with a calculator and the conviction to make assumptions can answer the question.
The answers provided by the method I propose are not absolute. They are only probabilistic but they are a start and, I believe, a good place to begin serious analysis of whether Barry Bonds used PEDs.
The question I seek to answer is: did Bonds use PEDs, given his unusual career path? Let me define the career path in question as one in which a hitter's four best seasons by OPS occur after age 35, and the worst of those four seasons is better than the fifth best OPS season by .100.
Barry Bonds' four best OPS seasons occurred consecutively, from 2001 to 2004. His OPS values those seasons were 1.379, 1.381, 1.278 and 1.422, respectively. His fifth-best season by OPS occurred in 1993. His OPS that season was 1.136, which is .142 below his 2003 OPS of 1.278.
Not only are all those OPS values hugely rare, the occurrence of the four best at such a late stage of a career is ludicrously rare. One might say inconceivable.
The framework I propose employs Bayes' theorem, a very useful and powerful theorem used all over the place by statisticians.
To use the theorem, we need a few numbers or probabilities. This is the stage where I need to make some assumptions. My assumptions follow:
The probability a major league player who played at some point between 1990 and 2005 used PEDs: 1/10. Call this A.
The probability a player who used PEDs would have a career peak like Barry Bonds' peak I described above: 1/1,000. Call this B.
The probability a player who never used PEDs would have a career peak like Barry Bonds' peak that I described above: 1/1,000,000. Call this C.
Then, applying Bayes theorem, whose definition can be found in Wikipedia and many other reputable websites and statistics texts, we get the probability of Bonds using PEDs, given his career peak.
A*B/((A*B)+(1-A)*C) = .0001/(.0001 + .0000009) = .00001/.0001009 = .991
According to my assumptions, there is a 91.7 percent likelihood Barry Bonds used PEDs. Feel free to plug in your own numbers for A, B, and C. The only restriction is that the numbers must be values between zero and one.
In other words, his bizarre career shifts me from the baseline assumption of a 10 percent chance he used PEDs to the belief that there is a 99.1 percent chance he used PEDs.
My assumptions are purely for illustrative purposes. I have no idea what B and C might be. I think somebody, maybe Jose Canseco, could supply a reasonable number for A.