The Nobel Prize, Steroids and You

In what will come as no surprise to anyone who reads my writing regularly, I don't like math. I much prefer words (hence the whole teaching English and writing-a-tonnage-of-words-for-my-own-amusement-thing), but I know that math has a valuable place in the world.

That's why I read London based magazine The Economist (well, that and the snarky captions & covers). In the most recent issue, one of the magazine's Science and Technology writers explained how mathematics can solve the primary dilemma that athletes, governing bodies and fans face when they face steroid use.

Using the game theory branch of mathematics, the writer explains how and why using steroids to cheat can seem to be the only rational behavior for athletes, especially those involved in direct competition with other individuals (like the recently implicated sprinters Tyson Gay and Asafa Powell). While baseball, as a team game, is a slightly different scenario, many of the same principles hold, so consider how game theory explains the use of steroids in baseball through the following goofy teacher analogy (again, I teach English not Math, so bear with me...and if you are a math/economics person please tell me to pull down this post so I can make it actually accurate).

Say you have two players getting together for a little driveway home run derby. Let's call them "Bryan Raun" and "Moe Jauer". They'll be competing against each other and have the option to either cheat or play fairly. That means that there are four possible outcomes depending on what each player decides to do. (Symbolized in the box below by "C"s for Cheat and "F"s for Fair).
The Game Board
If the player's only goal is to win, and if cheating helps them to do so (say, by making their muscles big and avoiding injuries through some magical injection or something) , it quickly becomes clear what they should do to maximize their chance to win: Cheat. If Moe cheats, he can win or have an even shot at winning. If he plays fairly he can lose or have an even shot at winning. Only 1 of the 4 outcomes (25%) can have playing fairly end with a chance to win, but 2 of the 4 outcomes (50%) can have cheating end with a chance to win. It's simple probability: Cheat.
Option 1: The Merits of Cheating

But let's say the game isn't played just between "Bryan" and "Moe". Let's say that Bryan's crazy Uncle Bud watches them to make sure that the game is played fairly (like most used car salesmen, Uncle Bud's ethical like that). Now Uncle Bud decides that he'll watch them play and if he catches either Moe or Bryan cheating they'll automatically lose. Suddenly the strategy of the game changes, and playing fair gives you a 50% probability of getting a chance to win, while cheating only gets you a 25% chance (i.e. if Moe and Ryan both cheat, but only Ryan gets caught, then Moe wins)
Option 2: Fair Play

That might be the best way to play the game, if like Uncle Bud, all you care about is ethics. But let's pretend that Uncle Bud likes money (I know, I know...odd for a Used Car Salesman), so Uncle Bud decides to let other people watch Bryan and Moe play for a nominal fee. We can also pretend that Uncle Bud invites Mike to sell lemonade at the game and promises both the fans and Mike that the game will be really entertaining, exciting and EXTREMELY competitive. (As an added bonus, whoever wins the most might earn a little more money from fans and could be hired by Mike to tell everyone how great that Lemonade is.)

Now "Moe" and "Bryan" have even more incentive to win first and foremost, and Uncle Bud has an incentive slightly greater than fairness: he wants excitement, competition and success. So Moe and Bryan have to do some quick thinking. Does the desire to win and make money trump the desire for fairness?

Many people immersed in Game Theory have argued that the most logical decision would be to think: "I can gain so much by cheating [winning, money, more money], and Uncle Bud can gain so much by not catching me [money, more money, lots of more money] that it makes sense to cheat if I can". But there's still a few people, like, say, Moe, who would illogically decide: "you know, um...I think the risks of getting caught [losing, losing money] outweigh the benefits, so I'll play it fairly." This way only one person (Bryan) wins...right up until the moment they get caught.
Option 3: Split decision
Now the first two scenarios (everybody cheats/everybody plays fair) hit the famous Nash Equilibrium (famous in part because it helped its namesake, John Nash Jr., win the nobel prize and famous in part because it was explained using pretty girls in a Russell Crowe movie). This the point at which both people playing the game have maximized the benefit to themselves. The third and final scenario (one person cheats, the other doesn't) doesn't help either player as one will likely lose the game and money for a while, until the other player gets caught and loses everything.

Now baseball is not a two person game between "Moe" and "Bryan", and there's no amount of data that cheating automatically leads to winning or success. But, hopefully that rudimentary use of Game Theory not only explains why cheaters cheat, and why testing matters, but helps us to look at the issue that really matters.

If winning is everything
The bigger issue to me is not in understanding how or why "Moe" and "Bryan" do what they do, but in how Uncle Bud, Mike's Lemonade, and all those fans react to both cheating and playing fairly. The Nash Equilibrium could be reached if we each agree that the only thing that matters is winning. Moe and Bryan want to win so they cheat. Uncle Bud wants to make more money than the game of HORSE and the flag football game down the street, so he wants winners too. Mike's Lemonade wants champions to talk about the drink, thereby selling more lemonade, so it too wants winners. And if fans care first and foremost about beating the other guy, well...then it's all about winning...and it's all about cheating.

If fairness is everything
But, and this is a huge BUT, if we decide that it's not only in our individual interest, but it's also in our collective interest to support a fair system, then we can still reach that Nash Equilibrium. Player's might individually want to keep their jobs and avoid long term suspensions. Owners might...okay...definitely will want more money from customers and partners who trust them and longer commitments from players who won't get suspended. Companies want to support the kinds of players and sports that people love. And customers want to feel respected by owners and companies as well as having players to admire on the road to success. Most importantly EVERYONE (players, owners, companies and customers) has a collective interest in keeping the game interesting and free of embarrassing scandal. That's where we can agree that fairness trumps winning, and that's the other option for equilibrium.

Again, I know that the world of baseball is likely too big to get everyone in agreement about anything (hell, the DH debate is still a thing), but there's room for things to change, and most importantly there's room for fans to take action. Companies have already turned their back on Ryan Braun, and there's almost a unanimous boycott in place around Alex Rodriguez. Owners are leery of touching admitted users with a ten-foot pole and, increasingly, baseball players themselves are turning on those who use (As suggested by the Buster Olney story that "a pitcher drilled a hitter in a game this season, and when...he returned to the dugout, [he] explained...that he had plunked the guy because he’s a juicer -- a cheater, a PED user. The teammates who heard him understood.")

Maybe we need a town hall meeting, maybe we need a vote from the fans, maybe we need a cathartic set of admissions and tears and pleas and angry denouncements and effigies and Oprah-orchestrated-hugs, but we need an agreement about what our goals are if we want to reach anything close to equilibrium. We don't all have to agree, we can't possibly all agree...but the closer we get to agreement the better for the game, the better for the fans and the better for everyone except the cheaters.

Thank for enduring this installment of an English teacher tries his hand at Math, we now return you to your summer vacation.

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