[benk's Honours Paper] The Economics of Performance-Enhancing Drugs in North American Professional Baseball

Hi guys! So last semester for my Honours seminar (every student in an Honours/four-year degree has to take one) I decided to write my paper on the economics of PEDs in baseball. Have a look after the jump.

Special thank-yous to jessef, dexfarkin, Mike Andrew, Pikachu, MjwW and everyone else here who helped me whether directly or indirectly. Thanks!


The Economics of Performance-Enhancing Drugs in North American Professional Baseball

Creative Commons License
The Economics of Performance-Enhancing Drugs in North American Professional Baseball by Benjamin Klein is licensed under a Creative Commons Attribution 3.0 Unported License.

Over the past decade, the subject of doping in sports has become more and more controversial; it is an issue that evokes strong emotional reactions from casual and serious fans alike. Although the use of performance-enhancing drugs is almost universally considered “cheating,” it is unclear from an economic utility-maximizing perspective whether an individual player can rationally use steroids. This paper will detail an attempt to use economic tools to analyze whether a player is acting in an economically rational way in the decision to use performance-enhancing drugs.

This paper will analyze the issue of performance-enhancing drugs (PEDs) in Major and Minor League Baseball in four sections. The first section will briefly discuss the biological and biophysical effects of steroids on the human body and how Major League Baseball (MLB) was affected by the widespread use of PEDs in what has become known as the “Steroid Era.” The second section will discuss the economic rationality and game theory behind a player’s decision-making process to use or not use PEDs in an attempt to gain an athletic advantage over his peers. The third section will utilize Gary Becker’s theory of crime and crime abatement to analyze MLB’s much stricter drug testing policy adopted in 2005. This section will also use another perspective to explain whether the incentives and disincentives of the new policy will lead to the MLB’s intended outcome, a reduction in the proportion of Major League and Minor League players (generally young players working their way to the MLB or older players who aren’t quite good enough to play in MLB) using steroids. The fourth section will analyze how an owner of a MLB franchise would use an economically rational decision-making process in allowing the players on his or her team to use steroids.

The effects of steroids on the human body have been well-documented by medical scientists. In one major study from 1996, Bhasin et al noted that healthy male adults who lifted weights recreationally gained over three times as much muscle mass while taking steroids as did a control group given a placebo. Specifically, the group taking steroids gained 9.3% muscle mass while the control group gained 2.7%. Unfortunately, there exists a dearth of information – for obvious reasons – detailing the effects of steroids and other PEDs on the bodies of professional athletes. That said, there are several reasons why professional athletes may be able to achieve even greater gains, since they can take higher doses, take steroids for longer periods, take multiple drugs (referred to as a cocktail of drugs), or train more often than the subjects in the study. In any case, it is clear that professional athletes stand to gain some sort of biological edge by using steroids.

Biophysically, the increased muscle mass gained from use of PEDs should have a very significant effect on a baseball player’s on-field production – which directly translates into more utility as a result of money in the form of more lucrative contracts. Tobin noted that basic physics dictates that a player with 10% more muscle mass should be able to swing the bat approximately 10% faster than they would without that extra muscle mass. Similarly, that 10% increase in bat speed translates into approximately 10% increased force generated by the bat on the ball. Using physics modelling, Tobin estimated the effects of increased force on baseballs in current baseball stadiums. He estimated that the 10% increase in force could result in 50% more fly balls becoming home runs – clearly a substantial effect! Furthermore, as Harvard economist Robert Barro notes,

To a considerable extent, a team’s or athlete’s output is measured not so much by absolute skill – how far a ball is hit or how fast a race is run – but by comparisons with the skills of other performers. How much difference would it make if the longest home run went 600 feet or 300 or whether 100 metres could be run in 8 or 10 seconds? These numbers matter mainly in relation to what other athletes can do (now and in the past)

Barro’s conclusion suggests that small increases in skill or performance amongst truly elite athletes (that is, players talented enough to play professionally) can have a large effect on that player’s performance relative to his peers. As a result, if a player can hit 50% more home runs on fly balls than he did previously there would almost certainly be a significant economic incentive for him to take steroids.

The “Steroid Era” is the name given to a period from 1994 to 2004, as defined in Baseball Between the Numbers, during which steroid use in Major League Baseball was most rampant. Compared to the previous “era” (the “Canseco Era” from 1986 to 1993), players hit home runs over 20% more often and total run-scoring in baseball was over 10% higher. As a result of significant advances in biophysical supplements, the steroids taken by players – the most famous being “The Clear” – were undetectable by any testing methods in place at the time. Charles Yesalis, an epidemiologist, was quoted as saying, “the most rigorous drug testing systems have loopholes through which I could drive every M1 Abrams tank we own, and not scrape the body armour.” Even the Olympic Games were unable to catch users of steroids. Marion Jones won five medals at the 2000 Sydney Olympics and admitted in 2007 that she had used steroids, but was not caught by the World Anti-Doping Agency. Moreover, it is interesting to note that the advancements in steroid technology arrived almost immediately after the MLB’s attempted crackdown on amphetamines (“speed” or “greenies” in baseball vernacular) in the early 1990’s. After the MLB cracked down on both amphetamines and steroids, it is possible that the two substances became a sort of substitute good, a topic to be discussed later.

In 2005, MLB fully revamped its existing drug testing policy. The new policy was far more stringent than the previous policy and imposed very severe punishments for positive tests, while also incorporating new tests which allowed the detection of new types of steroids. A player’s first positive test would lead to an unpaid suspension of the following 50 games or approximately one-third of a season. Since the average 2011 salary of a MLB player is about $3 million, the first offence would cost an average player about $1 million. A player’s second positive test would result in unpaid suspension of 100 games, or about two-thirds of a season. The third positive test would result in a lifetime ban from Major League Baseball. Obviously, these punishments are not to be scoffed at.

Next, it is critical to discuss a player’s economic decision-making process in his choice to use or not use steroids, in the periods before and after the drug testing reforms. This analysis will use three different theories to evaluate a player’s decision-making process: utility-maximization and game theory, commitment theory introduced by Amartya Sen in his article Rational Fools, and Gary Becker’s theory of crime from his article Crime and Punishment. It is interesting to see whether basic utility-maximization can explain a player’s decision in a controversial situation such as using steroids. As well, it is obvious that even with a negligible chance of being caught by non-baseball authorities, some baseball players would choose not to use steroids based on a feeling of overarching “fairness” in the game. Gary Becker’s theory of crime can also be adapted to help analyze a player’s actions in the face of illegal actions with potential negative outcomes. This theory will help us analyze the decision by the MLB to implement a stricter drug testing policy, as well as to analyze a player’s reaction to that policy. The opinion of the owner of a MLB team is another important factor in a player’s decision to use steroids. Each owner has the option to condone or condemn steroid use on the team, and the decision to condone or condemn is one that will be made in order to maximize the owner’s utility.

A player's decision to use steroids would be an attempt to gain a performance advantage over other players, resulting in increased salary and thus utility. In the end, a combination of the three theories and the owner’s decision will be helpful in understanding the issues involved. Each theory is useful on its own, but together they paint a very descriptive picture of the situation.

Utility theory and game theory are the most common theories used to analyze the behaviour of sports agents in economic models. These theories can be used in models to analyze economic agents’ decisions to work or stay home, a firm’s output decision, or even a soccer player’s penalty kick strategy. These basic and robust mathematical theories will be used to demonstrate the differences in the decision-making process of a player before and after the 2005 drug testing reform.

Before the drug testing reform, a player’s decision-making process was fairly simple. Because there was no real punishment for using steroids, a player was free to collect all the utility benefits of using steroids while accepting only the personal costs, such as discomfort and medical bills. This means the decision-making process can be broken down into a maximization equation:

Equation 1

utility=[marginal benefit of using(u)]-[marginal personal cost of using(u)]

where u represents utility. Each term is written as a function of the player’s utility. The first term of the equation represents the increased income a player would receive as a result of increased performance relative to his peers, which results in increased utility. The second term of the equation represents the medical bills and other personal costs resulting from using steroids. In The Baseball Economist, J.C. Bradbury estimates these costs to a player at $500,000, though it is only crucial that the number be greater than epsilon so that the utility loss is more than negligible. This disutility figure will also be used in the game theory example.

To better illustrate the player’s decision-making process, it is possible to break the process down into a two-player game. In order to do so, there are several assumptions that must be made. The game consists of two players, X and Y, who have equal but very high levels of baseball ability or talent. Each player is an average MLB player in ability, and neither needs to worry about finding a MLB contract. They do, of course, have to worry about the size of the contract they receive. X and Y are the only two free agents in their free agency period immediately following this game, or they are the only two players who occupy a certain position (catcher, pitcher, shortstop, etc.) in that free agency period. This means that each player’s performance and contract has a significant effect on the other player’s contract. The steroids, to which each player has equal access, are undetectable and as a result the players face a negligible risk of arrest or any other civil consequence, and the steroids have an equal effect on each player’s performance. For the sake of simplicity, there are a few other assumptions. The game itself represents one MLB season, and the steroids available to the players provide their full benefit in this season. Any benefits provided by the steroids to the players in future seasons are ignored. As well, the personal disutility from steroids is assumed to be $500,000.

Creating a payoff matrix with the information available, the following is the two-person game illustrating the players' steroids decision:

Table 1

PEDs Decision

Payouts (X,Y)

Player X Use

Player X Don’t Use

Player Y Use

($2.5M, $2.5M)

($1.5M, $4M)

Player Y Don’t Use

($4M, $1.5M)

($3M, $3M)

There are three possible outcomes resulting from this game. The first and socially optimal result is that both players decide not to use steroids. Since they are equal in skill and neither player has a performance advantage over the other as a result of steroid use, each player receives an average MLB contract worth $3 million. The aggregate social utility to the players resulting from this outcome is $6 million, the highest of any of the three outcomes.

The second possible outcome is that player X uses steroids and player Y does not, or vice versa. In this scenario, the player who uses steroids receives a larger contract as a result of increased relative performance from using steroids. However, that player also incurs disutility worth $500,000 as a result of using steroids. The player who does not use steroids receives a smaller contract due to decreased relative performance but also does not incur the disutility from using steroids. The aggregate social utility to the players resulting from this outcome is $5.5 million.

The third possible outcome is that both players use steroids. In this scenario, since both players have equal performance, they receive equal contracts worth the MLB average of $3 million. However, since they both incur disutility from using steroids, each player loses $500,000 of utility and thus receives aggregate utility worth $2.5 million. The aggregate social utility to the players resulting from this outcome is $5 million, the lowest of the three possible outcomes.

The rational outcome of this game is remarkably similar to the outcome of the classic Prisoner’s Dilemma game. Each player always has an incentive to act in a way that will ultimately lead to lower social utility than if the players co-operated. Given that each player will act in his own economic self-interest, each should decide to use an undetectable steroid. However, it is worthwhile to note that these are aggregate utility estimates. It is very likely that some players would receive more benefit from steroids, perhaps smaller players who would benefit more from additional strength than would large, strong players, and others would incur greater disutility from using, for example, players with pre-existing medical conditions that could be exacerbated by the negative health effects of steroid use. Nonetheless, the Nash equilibrium of this game is {Use, Use} with payouts to player X and Y {$2.5 million, $2.5 million}.

Since MLB reformed its drug testing policy in 2005, a player’s utility maximization function is markedly different. Now, given the strict and explicit penalties incurred by a player who is caught using steroids, a rational player must consider the potential loss of utility from using steroids if he is caught. So, a player must consider all of the following: the benefits gained from steroids, the personal cost of using steroids, and also the loss of utility incurred by the unpaid suspension imposed by MLB. Therefore, a player will attempt to maximize his utility in:

Equation 2

utility=[marginal benefit of using(u)]-[marginal personal cost of using(u)]-[probability of being caught)*[loss of utility from being caught(u)]

Again, the first term represents a player’s marginal benefit from steroids as a result of increased performance. If the MLB’s drug testing reforms reduce the proportion of players who elect to use steroids, this term should be slightly larger than in Equation 1 given that only relative performance is important. The second term should be similar to Equation 1, since personal disutility from steroid use should be the same, in aggregate, as before 2005. However, the third term is potentially huge. If the testing system is rigorous enough, the probability of being caught will be substantial. As well, the salary penalty is very substantial – about $1M on average for the first offence. This figure also includes other consequences of a positive test such as loss of endorsement deals or future salary decreases as a result of teams not wanting to sign a known steroid user. Based on utility theory, the 2005 drug testing reform should have resulted in a significant decrease in the number of steroid users in MLB.

Amartya Sen’s theory of commitment as an alternative to utility theory can give another view of the issue. It is almost certain that some MLB players think it unfair in some way to take steroids. Steroids were illegal both before and after the 2005 drug testing reform, so players must have known they were taking an unapproved substance. As a result, it’s highly likely that there existed a subset of players who did not or would not take steroids even if it was in their economic self-interest. Intuitively, it is clear that artificially enhancing a professional athlete’s performance is not fair to the other athletes.

There are several negative consequences that could arise if professional athletes allowed steroid use to become mainstream, even though many of these negative consequences would not directly affect every player. For example, in a survey of high school students who admitted to using steroids, a majority said that their decision was influenced by professional athletes using steroids. Another possible consequence would be an escalating steroids “arms race.” If players use steroids (and/or other performance-enhancing drugs), some players would be inclined to seek out the newest way to gain a performance edge over their peers. This could lead to players taking new, untested and very dangerous substances. Due to the normative nature of commitment theory and a lack of suitable data, it is impossible to know the magnitude of effect of this theory on the proportion of players who elected to use steroids.

Gary Becker’s theory of crime can provide another insight into the effectiveness of the MLB’s drug testing reform. A fundamental conclusion of Becker’s theory is that if a person breaking a law is able to substitute one criminal act for another, he or she will substitute toward the offence with the lowest relative punishment:payout ratio. That said, in baseball there are only a few offences which are always punishable by unpaid suspension (teams occasionally elect to suspend their own players for disciplinary reasons). As a result, there is only one offence that could act as a “substitute good” for steroid use.

Players could substitute toward other, potentially less obviously performance-enhancing substances like stimulants. Amphetamine use was rampant in the 1970’s and 80’s as they helped players maintain focus during a long, difficult and often painful season. After the MLB cracked down on amphetamine and cocaine use in the late 1980’s, punishment for a positive test for these substances was set at a minimum of 15 days unpaid suspension, or approximately $250,000 in loss of salary for an average player. If it is assumed that players receive the lowest possible suspension on their first offence, the punishment is approximately one-quarter as severe as the first offence for a positive steroid test. Therefore, if the benefit to a player from using amphetamines is greater than one-quarter the benefit from using steroids, that player will elect to substitute toward amphetamines.

The owner of the particular MLB team is another critical factor that enters into a player’s decision with regards to using steroids. It is widely reported that owners knew that the majority of players were using amphetamines. National Baseball Hall of Fame member and former MLB third baseman Mike Schmidt wrote in his book Clearing the Bases that amphetamines "were widely available in major-league [sic] clubhouses" and that he himself used them “a couple times.” William Goldstein reported that “most [baseball executives] ignored the bowls of ‘greenies’… in many training rooms.” It is thus fair to assume that if owners had knowledge of amphetamine use by their players, they likely knew of the use of other illegal substances by their players. Assuming that owners knew of steroid use by their players, we can analyze their decision to either condone or condemn the use of steroids by their players. As well, having full executive power over all employees of the organization, when a team condemns steroids, its owners have the power to trade or even cut players who use steroids. While it seems unlikely that they would exercise it, owners would also have the power to trade or cut players who refuse to use steroids to enhance their performance.

To maximize an owner's utility, the decision to condone or condemn steroids is rather similar to a player’s utility function in deciding to use or not use steroids. An owner wishes to maximize utility in:

Equation 3

utility=[marginal benefit of condoning(u)]-[marginal cost of condoning(u)]

The only cost to choosing one action is the opportunity cost. In this case, the opportunity cost is the next best possible action, that is, the action not taken. Therefore, costs can be ignored in this equation since the cost terms cancel one another out. If the equation results in a positive number, the owner will gain utility from condoning steroids and will do so. If the equation results in a negative number, the owner will gain utility from condemning steroids and will then rationally condemn steroid use by the team.

The marginal benefit to an owner of condoning steroid use by the team would be composed of extra revenues brought in by an increased level of performance by the players on the team. If an owner condones steroids, the players on his or her team will perform at a higher level than they would without using steroids, ceteris paribus. As a direct result, the team should win more games. There is a known positive correlation between a team’s record or winning percentage and in-stadium attendance. As Michael C. Davis notes in the paper “The Interaction between Baseball Attendance and Winning Percentage: A VAR Analysis”, “winning has a substantial and long-lasting effect on attendance, as all ten teams showed a significant increase in attendance.” This increase will directly result in increased revenues for the team through increased ticket sales, and will likely also result in increased revenues from increased television broadcast earnings. As a result, an owner can receive substantial utility gains from condoning the use of steroids by the team’s players.

The marginal benefit to an owner of condemning steroids, on the other hand, offers a less clear utility gain. An owner may feel that using steroids, or other performance-enhancing drugs, is unfair and diminishes the sanctity of the game. In this case, commitment theory may play an important role in an owner’s decision-making process. That said, the clear utility gains to an owner from condoning steroids suggest that owners would be highly likely to condone steroids on their own teams on an individual basis.

Empirically, the data paints a very different picture than the one offered by utility theory. As established earlier, utility and game theory dictate that the vast majority of players should use steroids. If players do not use steroids, they run the risk of losing a great deal of income to other players who enhance their performance using steroids. However, the data shows that only six percent of players took steroids before the 2005 drug testing reform. Analysis of that six percent of players in Baseball Between the Numbers shows that the overwhelming majority of players who did test positive were marginal MLB players or MLB prospects playing in the Minor Leagues. Using the economic tools that have already been used to analyze the issue, there are a few possible explanations for these unexpected data.

The difference between the marginal benefit and marginal cost of steroids likely varies as a player’s salary increases. At a low or average salary, it is likely that the marginal benefit outweighs the marginal cost fairly substantially. However, if a player is already earning a very large amount of money, the added utility from additional income would be less than if the player is earning closer to the league minimum salary. Strictly decreasing marginal utility is a critical assumption in economic models, and this model is no different.

Figure 1

As demonstrated graphically, a player who already has a high salary receives less utility from an absolutely valued equivalent amount of income than does a player who has a low salary. A player receives the same amount of utility from an increase the size of range “i1” as he does from the range “i2”. Since range “i2” is much larger than “i1”, the graph demonstrates that at a low income level, an increase in income results in a much higher increase in utility than the same increase in income at a high income level. For this reason, it makes intuitive sense that marginal MLB players would be more likely to use steroids than established Major League players.

Another possible explanation for why so few players elected to use steroids is that commitment theory played a significant role in players’ decision-making processes. Given that the mathematical models of steroid use predicted that a much larger proportion of players would use steroids than is shown empirically, it is likely that players’ own sense of fairness caused them not to use steroids. Furthermore, assuming that players themselves knew which other players used steroids, the lower the proportion of players using steroids, the less socially acceptable it would be among other players to use steroids. In this way, a very large proportion of players who didn’t use could have created a culture that directly or indirectly shunned users. This could cause players to feel that using steroids was unfair and to decide against using them, even if using steroids would have been economically rational for those players.

The reform of drug testing in MLB worked as predicted by Gary Becker’s theory of crime and the mathematical models. While the figures may not be precisely correct given the clandestine nature of steroid use, they are the most reliable data available. In an MLB "feeler test" administered before the drug testing reforms, designed to determine how widespread steroid use was in baseball, the number of positive tests was about six percent (around 200) positive results. In the year following the MLB’s drug testing reform, around two percent of players (around 70) tested positive for steroids. Since the reform introduced much harsher punishments for positive steroid tests relative to other offences, this outcome is precisely what Becker’s model predicted. According to the most reliable data available, MLB was definitely able to induce a significant proportion of players to stop using steroids. Unfortunately, as unreliable as the data for steroid users is, the data for stimulant and illicit drug use is even worse, for obvious reasons. For this reason, it is practically impossible to determine whether or not players are substituting towards amphetamines, other stimulants, or other unknown substance use in an attempt to gain a performance advantage. This knowledge would be very helpful in determining if the players’ reaction to the MLB drug testing reform followed the predictions of Becker’s model exactly.

Major League Baseball owners, as well, behaved precisely as the model predicted. Given the substantial potential gains from condoning steroids, it took an immense public outcry over the rampant steroid use in the MLB for owners to agree to a new drug testing policy. Because of the outcry, owners faced a new utility-maximizing scenario. Considering the potential positive publicity that would result from agreeing to a new drug testing policy, owners would agree to the policy and attempt to capture the highest possible revenues through attendance and television ratings. As well, if all owners condone steroids, then on the whole, each team would be gaining the same amount of benefit from steroids and owners should be indifferent between condemning and condoning steroids. Given the positive publicity generated by a new drug testing policy, owners would agree to condemn steroids league-wide.

This paper has investigated the economics of the decision-making process of a Major or Minor League baseball player in deciding to use or not use steroids. In doing so, game theory and utility theory as well as Amartya Sen’s commitment theory and Gary Becker’s theory of crime were used to illuminate the issues at play. As well, a MLB team owner’s decision to condone or condemn the use of steroids was investigated. All told, it is necessary to use all four of these economic tools to gain full understanding of the issues involved.



Bouton, Jim, and Leonard Shecter. Ball Four. New York: Collier, 1990. Print.

Bradbury, J. C. The Baseball Economist: the Real Game Exposed. New York, NY: Dutton, 2007. Print.

Click, James, and Jonah Keri. Baseball between the Numbers: Why Everything You Know about the Game Is Wrong. New York: Basic, 2006. Print.

Schmidt, Mike. Clearing the Bases: Juiced Players, Monster Salaries, Sham Records, and a Hall of Famer's Search for the Soul of Baseball. New York: HarperCollins, 2006. Print.

Journal Articles

Becker, Gary S. "Crime and Punishment: An Economic Approach." Journal of Political Economy 76.2 (1968): 169. Print.

Bhasin, S., T. W. Stoerer, N. Berman, C. Callegari, B. Clevenger, J. Phillips, T. J. Bunnell, R. Tricker, A. Shirazi, and R. Casaburi, “The effects of supraphysiological doses of testosterone on muscle size and strength in normal men,” N. Engl. J. Med. 335, 1–7, 1996.

Davis, Michael C. "The Interaction between Baseball Attendance and Winning Percentage: A VAR Analysis." International Journal of Sport Finance 3.1 (2008): 58-73. UM Research Board. University of Missouri. Web. 25 Nov. 2011. <>.

Sen, Amartya Kumar. Rational Fools: a Critique of the Behavioral Foundations of Economic Theory. Print.

Tobin, R. G. "On the Potential of a Chemical Bonds: Possible Effects of Steroids on Home Run Production in Baseball." American Journal of Physics 76.1 (2008): 15. Print.

Newspaper Articles

Goldstein, Warren. "Steroids, Steroids, Everywhere." Huffington Post 13 Dec. 2007. Print.


Major League Baseball’s Joint Drug Prevention and Treatment Program." Http:// Major League Baseball. Web. 25 Nov. 2011. <>.

Stenson, Jacqueline. "Kids on Steroids Willing to Risk It All." MSNBC, 3 Mar. 2008. Web. 25 Nov. 2011. <>.

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