Baseball analysts often toss around dollar values of players, accompanied by an assessment of whether a team overpaid or underpaid to sign a player or acquire him in a trade. The commentary can be confusing for several reasons, including the uncertainty over which definition of value the analysts are using. To take a step back, let’s talk about the various definitions of the dollar value of a player. It seems that when the above references of “overpaid/underpaid” are made, they often refer to market value of a player. Even the definition of market value can be confusing, so we’ll come back to that later. Another way to define player value is to analyze his value to a specific team, basing it on the team’s unique circumstances, such as their revenue opportunity from improving their win total, which is driven by their market size, excess seating capacity, location on the win-curve (i.e., are they contending for a postseason berth), etc.

A third definition of value is to estimate a player’s asset value to his team. This is often a way to assess the fairness of a trade. A player’s asset value refers to the value of a team having control of the player and includes a calculation using the player’s salary, relative to some value estimate (e.g., either of the two value definitions referenced above), over the number of years he is under team control. For a simplified example, let’s say a team acquires a player making $5 million per year for two more years, but his “value” to the team is $8 million. His asset value would be 2 years X $3 million per year for $6 million (not counting the time value of money or amending his value for any risk factors). It might be considered a fair trade if the team gave up a player whose salary is $4 million per year for one year, but his “value” to the team is $10 million per year. In this simplistic example, the team would be acquiring a player and giving up a player with approximately the same value—$6 million.

Asset values can get very interesting when a player is being paid “at the market” or even above market value, as is the case with Cliff Lee. The Phillies lefty is owed a minimum of $87.5 for pitching the next 3 seasons ($25m per year + a $12.5m buyout of 2016 option). However, if Lee’s $27.5 million option vests, then a team would be obligated to pay Lee $102.5m over the next 4 seasons. There are only a limited number of circumstances in which Lee would have a positive asset value to a team. The team would need to believe that Lee was the last piece of the puzzle and the difference between possibly missing the playoffs versus a deep run into the postseason. Furthermore, they would need to believe they would be competitive over the four year span of Lee’s contract. Just reaching the postseason once, with Lee being a difference maker, would likely not foot the bill. On top of that, a team would likely need to give up a player in order to get Lee. I happen to love Cliff Lee as a player. My Starting Pitcher Ranking system has him in the top 10 of all starting pitchers this year—a year in which he’s won only 4 games! Despite my accolades for Lee, an example of a fair trade may be the Phillies giving up Cliff Lee and Domonic Brown, a disappointing, highly touted prospect with a couple of years of control remaining at pre-arbitration rates, in exchange for a low-level minor league prospect. In other words, trading Lee and a player with a low asset value (Brown), in exchange for another player with a low asset value. When assessing a player’s asset value, even the top players in the game can get “upside down” with respect to value versus salary.

Regarding the market value of players, I’ve statistically modeled the last ten years of free agent signings in order to develop a framework as to how teams value various attributes of a player, such as his age, position, handedness, recent past performance, along with several other factors. But think of this as a generic valuation, not a team-specific valuation. For example, in last year’s free agent market, my model valued Michael Cuddyer at $11 million per year for 3 years. As it turned out, Cuddyer signed a contract with Colorado for $10.5 million X 3 years. In this instance, my estimate of the market rate turned out to be very close to his actual contract value. However, if the Yankees were in the market for Cuddyer, they possibly could have valued him at a higher dollar amount, based on their unique revenue opportunities.

It’s interesting to look back at how the free agent market valued position players and pitchers over the last several years. Keep in mind there is a difference between what teams expect to pay for performance versus what they actually pay for performance, since the pay is set before the performance is delivered. I tallied all one-year free agent deals for the last eight years, capturing the player’s one-year compensation and their wins above replacement (WAR from FanGraphs). The results are listed below. It’s interesting to see the high water mark in terms of cost per WAR was 2008. Teams spent nearly $8 million per win for pitching free agents and $5.6 million per win in the position player free agent market in 2008.

A few closing thoughts on a player’s value to a specific team. This can be estimated by analyzing their revenues in the context of their on-field performance. I want to emphasize that statistical models of a team’s win-curve (whether from actual team financial data or estimated financials from publicly available information) is just one input into understanding a complex question: how do revenues respond to on-field performance? In much the same way statistical analysis of a player’s performance must be integrated with scouting reports, a medical assessment, an evaluation of the player’s makeup and other factors, before a complete picture can be created, the same applies to the estimation of how winning will impact revenues. Revenues are the result of consumer behavior—fans’ unique response to changes in team performance. The items that need to be considered when creating a more complete picture of a team’s win-curve are fans expectations of team performance, their motivations, and the time lag between performance and fan actions, among others.

I am not a voracious reader of baseball books. I do read them from time-to-time, but I tend to gravitate towards books on politics, current events or American history. One baseball book that I highly recommend is Intangibles: Big League Stories and Strategies for Winning the Mental Game—in Baseball and in Life. The author is my friend, Geoff Miller (thewinningmindinbaseball.com), a Mental Skills Coach with the Atlanta Braves (I also wrote the Foreword for the book, but that’s beside the point.) My point is every once in a while a “must read” baseball book comes along, and this is one of them. People who know me think that I love numbers. The reality is that I love understanding how things work and I love decision processes. Numbers, if selected thoughtfully, just happen to be an outstanding vehicle to explain how things work and to improve decision processes for big league clubs. Understanding and appreciating the mental aspects of baseball is the perfect complement to a player’s stats or a scout’s ratings of a player’s tools.

Anyone who is passionate about the game of baseball, or is connected to it in some way, wants to understand the mind of the ballplayer. What makes him tick? How does he marshal his talents during a high pressure moment to perform? How does he prepare for an upcoming encounter with his opponent? These are the types of questions discussed in Intangibles—from the vantage point of an expert teacher and the athletes and coaches he’s encountered. Many of Geoff’s stories stem from his experiences with the Pittsburgh Pirates, one of his former employers. He has a rare and unique ability to grasp the bigger picture from his various coaching experiences, and it comes through in his writing.

One of my favorite sections of the book is a discussion of a “Baseball IQ.” Miller discusses ways in which a pitcher can learn to read a hitter’s reactions to a first-pitch fastball. He discusses the six possible hitter reactions, their meaning and even some insights as to the optimal pitch sequence—all based on careful observation of the hitter’s reaction to one pitch. From the hitter’s perspective, it’s not good enough to know what a pitcher is expected to throw in a given situation. He also benefits by knowing the why. The why gives the hitter insight into the mind of the pitcher—his motivations, level of confidence, fears and insecurities, and the pitcher’s personal assessment of his own strengths and weaknesses. By knowing the why, a hitter acquires a certain intellectual intimacy with the pitcher, which may provide a competitive edge and raise his probability of success.

The Baseball IQ section also includes several multiple choice tests that can be used to assess a player’s depth of understanding of the game and also serve as a tool build his or her knowledge of various game situations. Beyond the relevance to baseball, the book is a personal training guide for the mind and can give each one of us—whether or not we are in the baseball world—tools and insights to be a better version of ourselves. Check it out. If you love baseball, you’ll really enjoy Intangibles.

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.

Building off of Part 1 and Part 2 on the relationship between winning and revenues, I’ll share highlights of my Revenue Opportunity Index—an analysis I began at the end of last season to get a better sense of the which teams could expect the greatest financial gain by improving on-field performance for the 2012 season. I initially used this to gauge who might be the most active players in the free agent market, but modified it to give an indication of the opportunity for revenue upside for this season. The index combines “raw” revenue opportunity with the expected competitiveness of the team. Raw revenue opportunity—an analysis of a team’s unrealized and potential revenues—includes a team’s ticket revenue upside, based on the current (previous season’s) attendance, ballpark capacity and average ticket prices. If a team’s average ticket price is far below the MLB average, they are deemed to have more ticket pricing upside than teams like say, the Yankees, Cubs, and Red Sox, whose prices are already far above the league average. The combination of empty seats and ticket pricing upside determine the potential for attendance revenue growth. I combine this with overall market size and an estimate of “brand strength”, which is intended to get at a club’s likelihood of realizing the attendance upside. Next, I give points for the attraction of a new stadium (Marlins). It’s been shown that the synergy of a competitive team and a new ballpark can accelerate revenues. Finally, I factor in a team’s recent postseason history—both their success in the postseason and the time since their last appearance. A recent deep run through the playoffs suggests a portion of the revenue opportunity has already been realized.

Onto this raw revenue opportunity I overlay a team’s anticipated competitiveness. This speaks directly to the point I’ve made in the past (in Diamond Dollars and elsewhere) that certain ranges of wins have a greater financial value. If a team was expected to be hovering in the 85 to 93  win category in the NL, they were assigned a higher Competitiveness index than say the Astros, a team that was not expected to be competitive and therefore not in a position to truly capitalize on their raw revenue opportunity. A competitive team provides motivation to fans to reach into their wallets to generate revenue for the ballclub. The Revenue Opportunity Index combines the raw revenue upside with a team’s expected competitiveness. Entering the 2012 season, my Index ranked the following teams in the top quartile: the Dodgers, Angels, Braves, Blue Jays, Rangers, Marlins and White Sox. The Dodgers topped the list, having been beaten down in the latter stages of the McCourt years via declining attendance. They represented a large market, lots of unused seating capacity and reasonable ticket prices, not to mention a great brand. Combine these raw revenue factors with a team that was expected to contend in the NL West and the stars were aligned for the Dodgers to drive revenue growth for 2012, under a new revitalized ownership group. A team that is conspicuously absent from my list that was generated prior to the season is the Washington Nationals. I expected the Nats to be at least the 3^rd best team in the NL East, but underestimated their division leading pace. After escalating the Nats performance expectations, I ran an alternate scenario through my model and the Nats easily came out in the top quartile of revenue growth for 2012. On the other hand, Toronto is a team I mistakenly expected to contend for a wild card spot in the always tough AL East. Given their half-full Rogers Centre, there is tremendous revenue upside, once the Jays truly challenge for the postseason.

The Rangers have tantalized their fans with near-championships in back-to-back seasons and are realizing the value of their playoff success, with nearly a 20% increase in attendance over last year, on top of an 18% attendance increase in 2011. On the other hand, there are instances of attendance declines in the face of improvements in team performance. Sometimes the layout of the schedule can have a measurable impact on a team’s attendance. One might think the way the schedule falls over the summer and which interleague teams are coming to town has a minor impact, but I’ve seen schedules that have generated a 5% or 10% swing in attendance, independent of team performance. For example, if a team in a cold weather, northern climate (without a dome) has the Yankees and Red Sox come to town in April, rather than weekends in July and August, it can mean six or seven games with 20,000 less fans in the stands. The number of home games in various months can also have an impact. Northern cities dread April and early May games, when fewer fans are willing to brave the elements to attend. On the other hand, the Arizona Diamondbacks thrive on April games, while snowbirds are still in town, but dread July and August games when the local population base shrinks.

Two other relevant points to add about the impact of winning on revenues: First, the fans response to winning is not instantaneous, as I discussed in an earlier post. In the past, when I’ve modeled annual attendance as a function of on-field performance, I found that a combination of the most recent season and the previous season had the greatest explanatory power. Second, excess capacity is not always a positive factor for realizing revenue growth. After talking with hundreds of fans in focus groups and surveying thousands of others in quantitative surveys, it’s clear that an abundance of empty seats reduces the urgency of fans to make an advance purchase, or to buy season tickets. Their perception is “good seats will always be available.” Anything that allows fans to wait to purchase tickets, usually has a negative effect on ultimate attendance, as some fans who had good intentions to buy tickets on game day find that often “life gets in the way”, or an unfavorable weather forecast causes a change in plans.  Also, another penalty of a near-empty ballpark is that it detracts from the atmosphere and excitement of attending a ballgame, for both the attendee and the television viewer, discouraging future ticket sales.

Statistical modeling can provide insights to the ebbs and flows of team attendance, but the analysis is most effective when it includes a framework that incorporates consumer behavior. Just like the best explanatory models or forecasts of player performance must include factors that are not on the stat sheet, the same is true for attendance and revenues, or for that matter, any behavior models.

There are several important findings I can add to my previous post on the financial payoff from reaching the postseason, as well as the overall impact of winning on revenues. There are clear exceptions to this largely valid model, with the Tampa Bay Rays at the top of the list of exceptions. The absence of a suitable ballpark facility in an acceptable location have aborted this virtuous cycle of playoffs, followed by a jump in revenues. Despite leaping from a 66-win team in 2007, to averaging 92 wins for the next four seasons, including a World Series appearance as a 97-win team in 2008, the Rays have shown little gains in revenue—far below what any MLB-wide models or analysis would expect. Interpret this to mean there needs to be a baseline of underlying factors that make for a healthy franchise. Despite one of the best leadership teams in all of MLB, the payoff from winning in Tampa is nowhere to be found. This is not conclusive evidence that the Tampa/St. Petersburg market cannot sustain a big league club, but a confirmation that the Rays’ stadium situation is untenable. The stadium is poorly situated in a part of the metropolitan area away from the population center. The perfect storm of a devastating economic climate, lengthy drive times to the ballpark, and a generally unappealing facility, all served to inhibit attendance and revenue growth following a highly successful four-year run, including three trips to the postseason.

A more general pattern I’ve discovered and quantified is the distinct time lag in how fans respond to a winning team during the season, particularly if the success was not anticipated. If a team with modest fan expectations gets off to a hot start, attendance may take months to respond. For the fan, the time lag allows for validation. A 15-5 start in April is a good sign, but a 45-30 record in June means a lot more to a skeptical fan. Even when a fan makes an affirmative decision to come out to the ballpark, there is another time lag to fit the event into his/her busy schedule. So, a strong April and May, on average, might trigger a June decision, which may materialize into a July or August visit to the ballpark. While teams constantly ask fans to be patient as they build toward competitiveness, the reverse is also true. Teams need to be patient in their expectations of fans response to winning. (Incidentally, broadcast ratings for game telecasts seem to rise more quickly, with little lag, as TV viewing presents fewer obstacles than planning a trip to the ballpark.) The most interesting aspect of this phenomenon is a team’s inability to monetize a strong second half performance, should it fail to land in the playoffs. A strong July, August, and September is commingled with the events of the following offseason to shape fans perceptions and expectations of the club’s outlook, while a strong April through June, converts enthusiasm more directly into July, August, and September revenues.

The addition of the second wild card will alter the probability of reaching the postseason at various win totals. The sweet spot on the win-curve—the 86-91 win range in the NL and the 89-94 win levels in the AL—carry an even higher probability of reaching the postseason, in the new playoff system. It represents the most likely range of wins for the new (2^nd) wild card qualifier. However, we still need to see how the wild cards are treated by fans under the new structure. While I love the new playoff format, because it truly provides advantages for division winners and handicaps wild card entrants (see my earlier post), it may change the financial payoff from reaching the postseason. How will fans and the media treat the new wild cards? Is the one-and-done play-in game viewed as a “trip to the postseason”, or more like a 163^rd tie-breaker game to get into the “new” postseason? In the old playoff format, it seemed that fans and the media treated the eight teams as near equals. In the new format, I could envision four strata of playoff teams—wild card losers (losers of the play-in game), wild card winners, #1 seeds and the remaining division winners—with each strata carrying different levels of fan expectations about their ultimate postseason success.

From my perspective, there is an enormous gap between winning a division and earning a wild card, in the new system. For the last seventeen years we have used the term “wild card” in baseball to mean something very different than what it now means. In the new system, it’s the right to flip a coin after 162 games to see if you advance into the final eight—the old playoff format. A team that wins the coin flip earns the right to enter the tournament, but their ace starter will move to the back of the rotation, because he just pitched in the play-in game. Even though on paper the wild cards are a big disadvantage, it may take several years of poor showings by wild card entrants to alter the mindset of fans and dampen their enthusiasm. Maybe this is one instance when a small sample size works to the advantage of a team, as fans remain stuck in the old mindset and continue to reward clubs for earning a wild card. For Part 3 on this topic, my next post will discuss a “Revenue Opportunity Index” I’ve developed, comprised of various factors, to estimate which teams have the most to gain (financially) by improving their performance on the field.