From time to time, DraftMVP’s blog features guests who have done some interesting and valuable thinking about sports, analysis and decision-making. We’re proud to share with you excellent writing on the Steroids situation (which we talked about here) , A-Rod (who we talked about here) and Game Theory (which we clearly need to write about). This comes to you from Guest Blogger and friend of DraftMVP: Apurva Desai.

Apurva blogs about sports, life and his own musings at http://apurvadesai.com/ and you can reach him via e-mail at apurva.desai@yahoo.com

The recent revelation that baseball superstar Alex Rodriguez tested positive for steroids in 2003 has rocked the sports world and reignited the seemingly never ending steroid saga. But really, should anyone be surprised.

The late Ken Caminiti admitted in a Sports Illustrated story that he had used steroids during his 1996 MVP season and had indicated he doesn’t regret using them to get ahead. He further said, “It’s no secret what’s going on in baseball. At least half the guys are using [steroids],” says Caminiti. “They talk about it. They joke about it with each other. … I don’t want to hurt fellow teammates or fellow friends. But I’ve got nothing to hide.”

Later, Jose Canseco, in front of Congress and in his book “Juiced- Wild Times, Rampant ‘Roids, Smash Hits, and How Baseball got Big”, claimed that 80 percent of players used steroids and that MLB owners condoned steroid use because they felt a deluge of home runs would help win back the fans after the strike wiped out the 1994 World Series. While Canseco is clearly not the smartest bulb in the box, much of what he says has proven to be true.

I personally believe that the 50% to 80% figure is much more accurate than the 7% that MLB reported after their 2003 testing. The reason why the 50%+ clearly makes sense to me is all about game theory.

The classic game theory prisoners dilemma example is presented as follows (as shown in Wikipedia): Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (defects) for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act? The classical prisoner’s dilemma can be summarized thus:

In this game, regardless of what the opponent chooses, each player always receives a higher payoff (lesser sentence) by betraying; that is to say that betraying is the strictly dominant strategy. For instance, Prisoner A can accurately say, “No matter what Prisoner B does, I personally am better off betraying than staying silent. Therefore, for my own sake, I should betray.” However, if the other player acts similarly, then they both betray and both get a lower payoff than they would get by staying silent. Rational self-interested decisions result in each prisoner’s being worse off than if each chose to lessen the sentence of the accomplice at the cost of staying a little longer in jail himself (hence the seeming dilemma).

Now, if I apply the game theory matrix to two competing professional baseball players who have two choices- 1) take steroids vs 2) not taking steroids. Let’s assume this is during the early 2000’s when there wasn’t a steroid testing program, steroids were readily available for all of the players if they wanted it, and the players lifetime livelihood depends on their income from baseball (which is the case for the majority of players who don’t have college educations nor many other skills). The major downside is long-term health issues as the likelihood of suspension and arrest weren’t high due to the absence of the testing program.

In this game, for each player in terms of on-field performance and monetary reward, the best result he can get when not taking steroids is to be at a competitive balance with his peers which is the worst result the player would get when taking steroids. Furthermore, the risk if he did not take steroids when his peers did was to have a competitive disadvantage which could cost him his spot in the major leagues, reduce their salary potential or worse, limit their earning potential to minor league salaries. Now of course, as the matrix indicates, taking steroids is linked to long-term health impacts. The bottom line though for the majority of these players is that the chance to ensure their major league salary would clearly offset the risk to his long-term health—the payoff of having a competitive balance or advantage would be greater than avoiding unknown long term health risks. Given that the majority of baseball players are not superstars who are on the fringe of staying in the major leagues vs being in the minor leagues or out of the game, during that period without real testing and penalties for taking steroids, it is easily understandable why more than 50% of players would be taking steroids.

The harder question is why players such as Barry Bonds and Alex Rodriguez would begin to take steroids after they had already become superstars without the benefit of steroids (allegedly— don’t know for certain). These players place in the league was already guaranteed, their contracts were already amongst the highest in the league, and their performance already granted them All-star status. These players really didn’t have as much incentive to take steroids and risk their health as the common average player. However, greed, personal ambition to be the best in the game in this era or any era, and to live up to large contracts they had already earned may be reason for top players to have taken steroids in an era when there weren’t penalties for steroids.