How much did Melky Cabrera spend on his performance-enhancing drugs (PED)? I don’t mean the purchase price of the testosterone boost, but rather the impact on his next contract and future career earnings. From a purely financial standpoint, (I’ll leave the moral issue of taking a banned substance to others) was Melky’s attempt at cheating the system an economically sound choice? The answer to both of these questions depends on the impact PEDs had on Melky, the ballplayer. The post-PED, 2012 Cabrera was performing at an extraordinary level. Having already taken home the All-Star Game MVP, his .346 batting average, .906 OPS and 4.5 WAR (FanGraphs), put him on pace to have a 6.7 WAR season. His individual stats, coupled with the success of the Giants and their dependency on him to ignite their otherwise listless offense made him a viable candidate for the NL MVP award. We’ll stop short of calling his recent performance “elite”, but he certainly elevated himself into the top 10 position players in the NL, earning him the tag of “star.”

Relying on my statistical models I’ve developed of pricing in the free agent market, which Melky is eligible to enter this fall, I’ve translated his recent success into a future earnings estimate. My model includes a player’s past performance, age, position, durability, and several other factors. In the past, the model has been a reasonably accurate predictor of how “the market” values players (which should not be confused with their real “value” to teams.) Even if Melky’s torrid pace were to have slowed a bit and he finished this season as a 6 WAR player, I estimate his valuation in the upcoming free agent market would have been approximately $15 million per year for four years—a $60 million contract. To those who have not adjusted to Melky’s new level of performance, this may seem like an outrageously generous contract. But remember, last year he turned in a 4.2 WAR year, with a .809 OPS, a significant improvement over his early career performance. Also, keep in mind he would have emerged onto the free agent market with his “star” status as a 28-year old, which means a 4-year deal would take him only through his age 31 season, prior to when we would expect his significant age-based decline. What about his earnings beyond his next contract? Let’s assume his performance declines over the life of this hypothetical 4-year agreement (while MLB salaries rise) and conservatively estimate that he would earn an additional $10 million over the final phase of his career, which would begin in 2017, at his age 32 season. Let’s call it $70 million in future career earnings, had his performance not been tainted with his drug policy violation.

The more difficult task is to assess the career path for Cabrera had he chosen not to engage in PEDs. The complicating factor is his 2011 year in Kansas City, which was the first indication that he would deviate from his “old” career trajectory. In the middle of 2011, Cabrera had a major power surge. The difference between his first half and second half slugging percentage is 98 points (.423 to .521) and his OPS increased by 154 points (.735 to .889). In our scenario, let’s not give Melky the “benefit of the doubt” and instead toss out his 2011 season as partially corrupted. Let’s assume that the real, non-synthetic Melky Cabrera is the pre-2011 player—an assumption some baseball executives may make when they evaluate his free agency in the off season.  For perspective, Melky’s career from 2006 through 2010 averaged 0.6 WAR per year—the rough equivalent of Willie Bloomquist. While it’s difficult to pin down a solid estimate of Melky’s earnings for the balance of his career had he not made his step up in performance in 2011 and 2012, I’ll peg it at an average of $2 million per year for the next five years—a total of $10 million.

Using these estimates of Melky’s earnings with and without PEDs, the difference is about $60 million ($70 million minus $10 million.) Now here’s the troubling part of this issue: The only thing Melky put “at risk” (in addition to his reputation) is a portion of this year’s $6 million salary, should he get caught. His 50 game suspension, as a first-time offender, means Melky has put up a $1.8 million “security deposit” to assure that he plays by the rules. If he gets caught, he loses $1.8 million of prorated salary. If he doesn’t get caught, he gets his security deposit back and makes an additional $60 million in career earnings. This means that even if Melky had a 96% chance of getting caught, he had so much to gain and so little to lose (financially), that it would be an economically rational choice to take PEDs.

Perhaps, the Melky Cabrera situation is a “perfect storm” of unusual circumstances. First, if all of his performance increase (over his 2010 baseline) is attributable to PED usage, then the impact of the drugs on a player’s performance is likely more dramatic than anyone might have anticipated. We tend to think of “star” becomes “elite” player (Alex Rodriguez) with PED usage, or AAA player becomes major leaguer. In the case of Cabrera, we’re saying that he morphed from the 24^th guy on the roster to a perennial All-Star, which may be an exaggeration in our assumptions. Second, and related to the first point is Melky seems to be atypical in terms of the massive amount of money he stood to gain, while having so little to lose, financially. The combination of being in the final year of arbitration, while on the verge of free agency at such a young age, all contribute to the “much to gain, little to lose” situation.

However, if PEDs are capable of altering a player’s performance by as much as Melky Cabrera’s improvement, then the penalties for violation of MLB’s PED policy are likely too lenient. This leads me to consider potential enhancements to the PED program for the next Collective Bargaining Agreement that would both raise the penalty for violating the policy and lower the gains from not getting caught. The penalty for a first offender should be increased to serve as a true deterrent. Perhaps a player should have 80% of his annual salary at stake, rather than the 31% represented by a 50-game suspension. If Melky stood to lose nearly $5 million of his income if he were to get caught, he may have been far less inclined to take the risk.

On the matter of lowering the potential financial gain from improved performance, there are several directions to consider. One approach is to have a more aggressive testing protocol for players in the “walk year” of their contract—those who have the most to gain financially from illegally enhancing their performance. Since their potential financial gain is much greater than a player already working under a multi-year contract, perhaps increasing their motivation to cheat, shouldn’t their penalties also be higher? Another potential solution to the walk year issue may be to force a violator to forfeit a year of free agency. In other words, any player who violates the PED policy while in his walk year (or for that matter during their arbitration years), remains arbitration eligible for one extra year, thereby delaying his free agency by one year.

While the current PED policy is a huge step in the right direction of cleaning up the game, it seems like it’s built for a system where steroids have a only modest impact on player performance and it places too much reliance on the moral conscience of the player, rather than aligning the financial incentives for compliance. In other words, MLB is implicitly banking on players wanting to “play fair” or to place a high value on their reputation as the primary means of discouragement from violating the policy. It will be interesting to see how PED usage and penalties evolve over the next several years.