All of the discussion about performance enhancing drugs in recent weeks (namely: Alex Rodriguez) has caused me to think a lot about why players choose to use PEDs in the first place. Obviously their goal is to get an edge on the field, but is it really worth it considering the drug testing policies put in place by Major League Baseball? Don’t they realize that they’re going to be tested multiple times over the course of a season? According to section 3A of Major League Baseball’s Joint Drug Prevention and Treatment Program, each MLB player is tested at least twice during the season: at the start of spring training and at a random date in the season. I’ll refer to these as “mandatory tests”. In addition, there are 1,400 drug tests performed randomly on players throughout the season and off-season. I’ll refer to these as “random tests.”
Generally speaking, players should never expect that they won’t be tested. The only time a player could potentially fall through the cracks would be after his mandatory, in-season test. At this point, he just has to dodge whatever remains of the 1,400 random tests. The issue is that he would have no idea whether any given test is his one mandatory test or one of the 1,400 random tests (I’m assuming MLB wouldn’t disclose this information to the player). Using some basic probability, I decided to figure out just how likely it was that a player would be tested again once he’s been subjected to 2 tests—one at the start of spring training and one at some point during the season.
Essentially, the odds a player will be tested again after being tested in-season is:
P(The in-season test was random) + P(The in-season test was his mandatory test) x P(Having to take at least 1 random drug test between now and the end of the season)
Where P() can be read as “the probability of”.
All of these probabilities change as the season progresses to account for the number of days left in the season. Obviously, a player’s less likely to avoid all remaining random tests on April 1st than he is on August 1st.
The odds that any one test is the mandatory test are extremely high: greater than 99% for most of the season. So once a player’s been tested in-season, he can basically assume that his only remaining threats are the random tests. Here’s the distribution. Click to embiggen.
The graph runs from February 11th through October 31st which corresponds to the “champion season” defined in the treatment program. The probabilities are based off of the instance that the player received his first in-season drug test on the corresponding date on the X-Axis. Unsurprisingly, it becomes less and less likely that a player will be tested again as the season progresses. I’m assuming the tests are administered uniformly throughout the season since the document outlining the drug program doesn’t specify otherwise.
One thing that I didn’t account for in this model was off-season testing. However, off-season testing only consists of 225 random tests. Spread out over all MLB players, the odds of being hit by one of these fairly slim (~17%). Plus, it’s probably safe to assume that practically all players would come up clean on the tests later in the off-season as the spring-training test date approaches. In case you were wondering, the probabilities don’t change much after a 2nd or 3rd in-season test. This is because there’s such a high probability that the first one was the mandatory test.
Of course, there are ways to cheat on drug tests. One popular way is by using “designer steroids” that are only traceable in a person’s system for a short period of time, if at all. Players probably haven’t done the math, but they do have general idea of their odds. If a player’s tested on or after June 20th, he has a less than 50% percent chance of being tested again. Even if he is, he may have good reason to believe he could dupe the test by using some chemically doctored drug.
So when do a player’s odds reach a point where the risks outweigh the reward? How certain would player need to be that he won’t get caught to risk juicing? Obviously, every player’s situation is different, but there are certainly instances when it’s a risk worth taking. For fringy players, it could be the difference between making a few million playing baseball or returning to an impoverished country. We’ve also seen well established players who are financially well-off get dinged in recent years. So the choice isn’t always financially driven.
As much as MLB has done to crack down on PED’s in baseball, players are obviously still pushing the envelope. The obvious solution would be to test more frequently. Here’s what would happen if MLB doubled its random testing from 1400 to 2800. Click to embiggen.
This would certainly help. The odds of being tested again are clearly significantly higher through the majority of the season. It wouldn’t clean up the issue completely though. Aside from the fact that the odds of being tested are still low later in the season, designer drugs reduce the probability of getting busted even further.
The bottom line is that as long as players have reason to believe they won’t get caught, some are going to try to get away with it. Even if they were tested every day, at least a few players would probably use substances that are theoretically undetectable. Nonetheless, more random tests could help to mitigate the problem. Assuming players weigh the risks in a way similar to the actual probabilities, more frequent testing would go a long way in discouraging players from using.