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%.
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%.
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