Betaball. Using Finance to Evaluate. Baseball Contracts. Jamie O Donohue

Betaball Using Finance to Evaluate Baseball Contracts Jamie O Donohue 4/21/2014

1 When I negotiated Bob Stanley s contract with the Red Sox, we had statistics demonstrating he was the third-best pitcher in the league. They had a chart showing he was the sixth best pitcher on the Red Sox. - Rob Woolf, Agent

2 I. Introduction Over the past few decades, baseball has become a hotbed for statistical analysis. Sabermetrics a statistical method for evaluating Major League Baseball players - gained momentum with the Oakland Athletics and Moneyball in the early 2000 s. However, I recently recognized a need in Major League Baseball to evaluate players based not only on their performance, but also on how much teams are willing to pay them according to the market. Past statistical analyses of MLB player contracts have considered dozens of advanced performance measures, like Wins Above Replacement and Fielding Independent Pitching. These analyses, however, do not consider that teams like the Yankees are willing to pay significantly more for a player than teams like the Pirates would pay for the same player. In this paper, I use common financial and econometric practices to determine the true value of players based on their contracts. I essentially treat each MLB team as a stock and MLB at large as a market. Doing so allows me to treat each player as a project that can be undertaken or not. As one might do for a stock, I calculate the returns for each MLB team, as well as the volatility of returns, expressed as Beta. The contract of each player can be assessed with a Net Present Value analysis, which is used in the finance world to determine whether a project should be undertaken. I also use Ordinary Least Square regressions to approximate how MLB teams have paid players in the past. Based on the mathematical concept of a Random Walk, I reason that the best estimate of how teams will pay players in the future is how teams have paid players in the past. We would not expect the Pirates to spend $200 million on a player, mainly due to the fact that they have never done so in the past. Rather, such contracts are generally characteristic of teams like the Yankees, Red Sox, and Dodgers.

3 Specifically, I focus on Robinson Cano to convey my findings. Cano, who recently signed with Jay-Z s Roc Nation Sports, was reportedly requesting a 10-year, $300 million contract from the Yankees over the winter. Last September, Jon Heyman of CBS Sports wrote about how Cano is seeking to become baseball s first $30-million-a-year player. Ultimately, Cano signed a 10-year, $240 million contract in December with the Seattle Mariners for a constant annual salary of $24 million per year. Evaluations of contracts like Cano s would generally involve purely performance based measures. We do not currently have any tools that combine financial measures with baseball performance to determine whether this contract is a good idea, thus creating a need for such a contract evaluation tool. Ultimately, my purpose in this paper is to fill the need for an all-encompassing contract evaluation tool by showing how Cano s requested contract can be evaluated using common financial and econometric tools along with his forecasted future performance. II. Broad Overview of Procedure Each MLB team values players differently. A player s value is a function of both his inherent value (based on performance) as well as how the team values that performance. In this model, I use the output for salary to quantify a player s value to the team. In other words, past contracts serve as a proxy for what teams are willing to pay for players with certain levels of performance. For example, if the Mariners agree to pay Robinson Cano $24 million in 2014, they are essentially saying, We believe Robinson Cano s services this season are worth $24 million to us. The first step in my research was obtaining a cost of equity for each MLB team. This cost of equity is the rate that will be used to discount the estimated worth of a player each season. By discounting, I mean the process of expressing future cash flows in terms of their present

4 value. This is a common practice in finance as it allows one to determine the fair value of cash flows TODAY instead of when they actually occur. By obtaining a discount rate for each team, I can assess players future values in today s terms 1. After obtaining the cost of equity for each team, I created a regression for estimating a player s salary based on a variety of factors, eventually settling on one that relates player salaries to age, on-base percentage, and slugging percentage for each season. This regression yields the salary a player should expect to earn in a season, which serves as a proxy for his worth. I applied my findings to Robinson Cano, in particular, to determine whether he warranted his 10-year, $240 million contract with the Mariners. To do this, I forecasted out Cano s relevant statistics over the next 10 years, using the forecast as inputs for the regression model. I then multiplied the model output by a calculated Dollars per WAR Factor (DWARF) to obtain Cano s estimated annual worth (in dollars) he contributes to the Mariners based on his performance and the team s valuation of it. By subtracting Cano s actual salary from his worth, I perform a costbenefit analysis to find Cano s net worth for the Mariners. Because there is a unique regression for each team, about which I will go into further detail later, teams will have different valuations for the same players. To further characterize the model for each team, I discounted the player s (Cano in this case) net worth back to the present day using the team-specific discount rate. This makes my evaluation a Net Present Value (NPV) calculation such that the player s net worth is expressed in today s terms. If the NPV of a contract is positive, the team should agree to it because the present value of the player s annual benefits exceeds the present value of his annual costs. On the other hand, if the contract s NPV is negative, the team should not agree to the contract. The team with 1 In this paper, I use the terms value, worth, and benefits interchangeably. Net worth refers to the difference between a player s worth and his salary.

5 the highest NPV for Cano s contract places the greatest value on him and should therefore be willing to pay him the most. This NPV analysis allows us to assess whether, and by how much, the Mariners benefitted from signing Robinson Cano this offseason. III. Explanation of Model Applying CAPM to MLB Teams to find the Cost of Equity In finance, the Capital Asset Pricing Model (CAPM) is often used to determine the cost of equity for a company. The cost of equity is the rate of return required to compensate equity owners for taking on risk. Applying this concept to Major League Baseball, the cost of equity can be thought of as the returns required to compensate an owner for the risk of his/her team losing value. Here, I use the cost of equity to discount the net worth of players back to presentday terms. I began finding the cost of equity by obtaining every team s value for each of the past 10 years, according to Forbes. Once I had these values, I calculated each team s annual returns, where return is equal to change in value divided by old value. Then, I took the arithmetic average of the returns across baseball for the past 10 years, using this average (11.473%) as the expected market rate of return in the CAPM equation 2. In finance, Beta is used to describe the volatility of a stock relative to the market as a whole and can be calculated as covariance (x, y) / variance (x). I calculated the variance of each team s returns across the 10-year period as well as the covariance between their returns and the average market return, where MLB is treated as the market. Once I had the Beta for each team, I was ready to use CAPM to find the cost of equity for each season. According to the CAPM equation, 2 Strictly speaking, CAPM is a specific type of one-factor model that uses a market proxy like the S&P 500 to estimate expected market return. In this case, I am actually using a more general form of a one-factor model, but will call it CAPM to further develop the comparisons between finance and baseball.

6 k e = r f + β(r m -r f ) 3. For the 2014 risk-free rate, I used the rate on a 1-year Treasury (.13%). Many analysts have predicted the long-term rate on 1-year Treasuries to reach 4%, so I smoothed the risk-free rate towards 4% in the long run to get a market risk premium for each season up to the year 2023. By doing so, each team has a unique cost of equity for each season. As I will discuss later, these rates will be used to discount Cano s net worth for each season back to present terms. Regression and Forecast Once I found the annual cost of equity for each team, I generated an Ordinary Least Squares regression to measure each player s worth, represented as a salary in dollars. To create the player sample, I used statistical data from Baseball-Reference.com for each batter under contract with the Mariners as of opening day between 2004 and 2013. I used hitters from only the Mariners in order to capture their team-specific willingness to pay for players. This provides a more accurate depiction of what the Mariners, as opposed to MLB in general, would be willing to pay Robinson Cano. Later, I repeat these steps for the Yankees and Pirates as well to demonstrate how my analysis can be applied to both a club with great financial resources (Yankees) and a club with limited financial resources (Pirates). Additionally, I used statistics only for batters because the player I am assessing in this case is a batter (Cano). Had I been assessing a pitcher s worth (i.e. Felix Hernandez), I would have used pitchers statistics instead 4. Once I had compiled all the necessary statistics, I regressed salary on more than twenty independent variables, including batting average, slugging percentage, age, games played, stolen bases, walks, and strikeouts. After trying numerous iterations, I settled on a model that regressed 3 Where k e is the cost of equity, r f is the risk-free rate, β is the Beta coefficient, and r m is the expected market (MLB) rate of return. 4 This leaves a significant amount of room for future research in the area of pitchers contracts.

7 salary on age, on-base percentage, and slugging percentage (Appendix A). As I will discuss in my findings, this regression yielded reasonable results for the Mariners, Yankees, and Pirates. Something to note is that I quickly realized there were several outliers in my sample of players, especially in terms of on-base percentage. In baseball, an average OBP is somewhere between.320 to.330 (Cano s lifetime OBP is.355); an OBP of.300 or below is very poor. To eradicate outliers from the model, I removed any player s season in which he earned a salary of at least $7 million but had an OBP below.300. The Pirates had no such outliers in the past 10 years while the Yankees had three. At the same time, the Mariners had ten of these outliers, which indicates to me that they have signed several risky contracts that have not paid off. Taking this into consideration, it is not surprising the Mariners have finished with a winning record only twice since 2004 and have not made the playoffs since 2001. Upon finalizing the regression model, I forecasted future statistics for Robinson Cano based on his past performance and JC Bradbury s findings on peak performance ages in baseball. In a January 2010 article for Baseball Prospectus, JC Bradbury published his findings regarding when baseball players specific skills peak. He found that players on-base Percentage and slugging percentage peak at 30 and 28.6 years old, respectively. Using these peak ages, I treated Cano s career performance as a bell curve, in which his best seasons would be centered on his peak age for each statistic. This accounts for his gradually diminishing performance as he ages into the latter part of his career (Appendix B). Assessing Net Worth After I forecasted Cano s performance for the next 10 years, I entered his statistics into the regression; the output represents a base value for the benefit of Cano s performance in terms of salary. To get a more realistic value, I multiplied the benefits by a Dollars per WAR Factor

8 (DWARF) for each team. WAR refers to Wins Above Replacement, which estimates the number of wins a player provides his team above what a replacement player (i.e. bench player or minor leaguer) would provide. The Dollars per WAR Factor, which I will calculate in the Data and Results section, expresses how the Mariners value a Win Above Replacement relative to how the market values a Win Above Replacement. The DWARF is unique, not only for each team, but for each player s contract with teams. For example, Cano s DWARF is different than Mike Trout s DWARF, but Cano s DWARF with the Mariners is different from that of his hypothetical contract with the Yankees as well. This measure helps account for market effects on player salaries; after all, the market oftentimes dictates what a team is willing to pay for a player. Cano s cost is the salary he actually earns from the Mariners. Thus, Cano s net worth is the difference between his benefit and his cost. Using the cost of equity I calculated for the Mariners, I discounted Cano s net worth back to present-day terms. If his net worth is greater than zero, then the Mariners realize a net benefit from their contract with Cano; if it is negative, then the Mariners realize a net loss. At the same time, we can compare the NPV for Cano s contract with the Mariners to the NPV if he had signed with another team. This would indicate which team benefits the most from signing Robinson Cano. IV. Data and Results Beta Calculations In finance, the Beta value indicates a stock s volatility of returns relative to the volatility of the market, which in this case is Major League Baseball. Volatility is synonymous with risk: the more volatility in a stock s returns, the more risky the stock is. A stock s cost of equity moves with its Beta value (i.e. an increase in Beta leads to an increase in cost of equity and vice versa). While the costs of equity for the Mariners and Pirates are near the MLB average, the

9 Yankees have one of the highest costs of equity across MLB, which means their team valuation returns have been highly volatile over the past 10 years (Appendix C). Interestingly enough, the Yankees value has been increasing across the 10-year period, but in an inconsistent manner (i.e. steep increases in value followed by smaller increases). The average returns across baseball decreased dramatically during 2009-2010 before increasing again in the past couple of years. This phenomenon can likely be attributed to the 2008 financial crisis, which had a particularly detrimental impact on industries like sports because they have a highly elastic demand (i.e. in a financial crisis, consumers will give up baseball tickets before necessities like food and water). Regressions In order to compare Robinson Cano s benefits to his costs, I needed some way to quantify his benefits. His costs are merely what the Mariners pay him each year, but estimating his benefits was more difficult. The best way to do this was to estimate his worth in terms of salary because his costs were already in salary terms. Therefore, I needed to find the salary Cano deserved based (1) on his performance, (2) how the Mariners have paid in the past for similar levels of performance, and (3) how the MLB free agent market is being paid in general. I generated an Ordinary Least Squares regression model to determine how the Mariners pay for different performance measures. I used statistics for all Mariners hitters as of opening day for the past 10 years to create a regression for salary in the following form: Salary = β 0 + β 1 age i + β 2 obp i + β 3 slg i 5 5 Where β is the coefficient on the variable and i is the number observation out of the n total number of observations. Salary is the dependent variable and is being regressed on age, on-base percentage, and slugging percentage.

10 For the independent variables, I chose to use age, on-base percentage, and slugging percentage because this combination of variables yielded reasonable results for the Mariners, Yankees, and Pirates the three teams I wished to analyze in this paper. On base percentage quantifies how often a batter gets on base while slugging percentage quantifies the power with which a batter hits. When I started including other terms, like runs, walks, and extra base hits, the results were skewed because there was a high level of multicollinearity in which the independent variables are correlated with each other (i.e. as a batter gets more hits, his OBP will likely rise). One caveat with the model is that the variables are magnitude independent, meaning that a player with 50 at bats in a season could be worth more than a player with 500 at bats in a season. For this reason, the model should only be used for a player who has at least 100 at bats in a season. When I input Cano s 2013 statistics into the Mariners regression, his salary was expected to be $5.806 million. One might point out that this value seems drastically low for a player who received MVP consideration last season. However, this is simply the value attributed to Cano based on how the Mariners have paid players in the past, independent of current market conditions. To account for market effects, I adjust Cano s benefits with the Dollars per WAR Factor I discussed earlier. I calculate the DWARF for Cano s contract with the Mariners by dividing the model s 2013 salary output ($5.806) by his Wins Above Replacement for last season, which was 6. This yields an estimate for how much the Mariners would have paid Cano for each Win Above Replacement last year based on the model ($967,621). According to The Hardball Times, the estimated cost of a Win Above Replacement for the 2013 free agent market was $7.4 million. By dividing what the market would pay for a Win Above Replacement in 2013 ($7.4 million) by what the Mariners would have paid Cano for a Win Above Replacement in

11 2013 ($967,621), I found the DWARF for Cano s contract with the Mariners to be 7.648. I multiplied this factor by the model s benefits output (in salary terms) each season to get Cano s actual benefits to the club (Appendix D). I repeated these steps for the Yankees and Pirates to arrive at their DWARF for Cano s contract if he had signed with them. Cano s Net Worth To forecast Cano s statistics over the next 10 years, I used JC Bradbury s estimates for peak age by skill. In a 2010 article he wrote for Baseball Prospectus, Bradbury estimated the peak age for OBP to be 30 years old and for SLG to be 28.6 years old. Robinson Cano s highest OBP (.383) occurred during his 30 year-old season and his highest SLG (.550) occurred during his 29 year-old season. These findings give credibility to Bradbury s peak age estimates. In order to project Cano s statistics into the future, I divided each skill s peak age according to Bradbury by Cano s age at the time and multiplied this quotient by his peak age performance. For example, I projected Cano s SLG in 2018 by dividing Bradbury s peak age for SLG (28.6) by Cano s age in 2018 (35 years old); then, I multiplied this quotient by.550 his SLG when he was 29 (his peak year performance). This creates a bell curve with the player s peak performance at the center followed by diminishing performance during the latter part of his career. Once I forecasted Cano s statistics for the next 10 years, I used the regression model to estimate his worth for each year in terms of salary before multiplying it by the Dollars per WAR Factor. Subtracting the actual salary the Mariners pay Cano each year, we can see Cano s true net worth to the club in regards to his costs and benefits. The last step in this process is to discount his net worth for each year back to present day terms by using the Mariners cost of equity for each year, which I calculated earlier.

12 My findings indicate that the Mariners benefit by more than $198 million over the course of 10 years by signing Robinson Cano to his 10-year, $240 million contract (Appendix E). Later, I will discuss how I applied the aforementioned analysis to the Yankees and Pirates as well to provide a frame of comparison for Cano s contract. V. Implications Mariners Contract with Cano My findings support the Mariners decision to sign Robinson Cano to a 10-year, $240 million contract in December. Based on the coefficients of the model s independent variables, we can see that the Mariners pay players more for their slugging percentage than for their onbase percentage while the opposite is true for the Yankees and Pirates. The Mariners benefit from their $240 million contract with Cano every season, adding up to a positive NPV of over $198 million. This demonstrates that the Mariners made a sound financial decision by signing Cano to this contract. Even if the Mariners had paid Cano $30 million per year, as he had originally wanted from the Yankees, they still would have benefited by more than $155 million over the course of the contract. By signing him more cheaply, however, the club earned nearly $50 million more in benefits. In finance, one often tries to find the break-even point - where benefits and costs are zero and an organization literally breaks even. Retailers often use a break-even analysis to figure out what price they must charge customers to break even, given their cost structure and expected output. In this case, I use a break-even analysis to determine the highest salary the Mariners could pay Cano each year for 10 years and still not lose money. I find the break-even salary to be $49.038 million per year. If the Mariners pay Cano more than this per year, the contract NPV will be negative. If the Mariners pay him less per year, the contract NPV will be positive and

13 beneficial for the club. Seeing as this amount is obscenely high, it would be unlikely that the Mariners would ever lose by signing Cano. The question then becomes, By how much can they possibly gain? The cheaper they can sign a player, the more they gain and the more money they have to spend on other players. Yankees and Pirates Contracts with Cano Now suppose the Yankees and Pirates decide they want to sign Robinson Cano. Their valuations for Cano is different from the Mariners valuation because they have different budgets and different needs, similar to how a company would value projects differently (i.e. Wal-Mart would likely pay much more for a storage warehouse than a local convenience store would because Wal-Mart has greater resources and needs). To assess the Yankees and Pirates valuations for Cano, I needed to generate regressions for how they value players, just as I had done for the Mariners (Appendices F & G). I also calculated their DWARFs and costs of equity as I had done before in my first analysis (Appendices H & I). Of the three teams I analyzed, the Mariners had the lowest annual cost of equity, which impacted the Net Present Value of Cano s contract favorably. My findings for Cano s contract with the Yankees and Pirates help shed some light into the effectiveness of the model. According to the NPV analysis, Cano s 10-year, $240 million contract is worth $119.378 million for the Yankees but only $.875 million for the Pirates (Appendices J & K). This intuitively makes sense since the Pirates, unlike the Yankees, cannot afford to spend much money. As I mentioned earlier, however, Cano s contract yields a positive NPV of more than $198 million for the Mariners. The fact that the Mariners benefited more than the Yankees by signing Cano makes sense because they were the ones who ended up signing him. Since the Mariners valued Cano the most, they offered him the most lucrative contract,

14 resulting in his signing. My findings, which were in accordance with the actual outcome, help give credence to the entire analysis. When looking back at the results, I tried to figure out why the Mariners have a higher valuation for Cano than the Yankees. Intuitively, the reason is probably that the Yankees have other superstars in their lineup, like Derek Jeter and Mark Teixeira, making the loss of Cano less detrimental to the team. The Mariners have fewer established Major League hitters and would therefore place more value on Cano s performance. In regards to economic success, Cano gives the Mariners a superstar to attract fans, sponsorships, and television contracts. By signing a player of Cano s stature, the Mariners are likely to further increase their revenue in the coming seasons. It is a little more difficult to discern why the Mariners have a higher valuation for Cano s contract from a technical standpoint. One impact is the cost of equity, which for the Mariners is only about two-thirds of that for the Yankees. A lower cost of equity results in higher present values for annual net worth because they are discounted at a lower rate, which compounds each year. For example, Cano s net worth in 2023 is being discounted at a rate of 9.029% for the Yankees but only at 6.383% for the Mariners. The Mariners have a lower cost of equity because their valuation according to Forbes has been less volatile over the past 10 seasons when compared to that of the Yankees. Another technical reason Cano is worth more for the Mariners is that they have a higher Dollars per WAR Factor than the Yankees. This indicates they have likely been paying less than the Yankees for each Win Above Replacement during the past 10 years 6. Since I multiplied the benefits of the contract each season by the DWARF, the Mariners actual benefits after 6 Keep in mind that I removed outliers from the model. Had I kept the outliers in the model, the Mariners DWARF would be more similar to the Yankees.

15 adjustment are greater than the Yankees benefits. Furthermore, the model for the Mariners indicates that they pay more for aging players than the Yankees pay. The age coefficient for the Mariners regression is 2.9% of the coefficient for SLG and 5.4% of the coefficient for OBP. On the other hand, the age coefficient for the Yankees regression is 3.5% of the coefficient for SLG but only 1.1% of the coefficient for OBP. In other words, age appears to be a more powerful variable in the Mariners regression than in the Yankees regression. Since age always increases, it offsets decreases in Cano s OBP and SLG for the Mariners, but not for the Yankees. This in turn drives up Mariners benefits as Cano ages, but causes benefits for the Yankees to decrease. At first glance, one might be surprised that the Yankees had a lower valuation for Cano s contract than the Mariners. After careful analysis though, one can see the reasons, both intuitive and technical, for why the Mariners receive more benefits by signing Cano to a 10-year, $240 million contract than the Yankees. VI. Limitations of Model One of the major limitations of the model is that the Random Walk concept does not necessarily hold true in Major League Baseball free agency. Recall that in finance, the Random Walk says that the best estimate of a stock s price today is the price yesterday. In other words, future prices are based on past prices. In this paper, I have assumed that teams will pay future players similarly to how they have paid players in the past. However, this may not always be the case, especially when organizations have undergone significant management or ownership change. Similarly, it seems we are in a transitional era for baseball contracts. Prominent agents like Scott Boras and developments in the most recent Collective Bargaining Agreement have contributed to an era of generally higher salaries across MLB. If I were to write this paper again in 10 years, my findings would be much different.

16 Moreover, the regression for each team has a fairly low R 2 value, meaning the independent variables do not have a very high amount of explanatory power in the model. I tried to adjust the model to attain a higher R 2, but because of multicollinearity and other factors, the results did not make sense. Likewise, a few of the independent variables were not significant at a 95% confidence interval. This could be caused by the fact that certain important variables were omitted from the model, which in itself is a limitation. My regressions include only three independent variables and are therefore not comprehensive. Other potentially important variables to consider in future models are stolen bases and Ultimate Zone Rating, which is a widely used defensive statistic. Players may also contribute non-baseball benefits that are difficult to quantify, like popularity and leadership. While these contributions are palpable, they are not included in my current model because of how difficult they are to quantify. In the future, I would look to build more variables into the model. VII. Summary and Conclusion In this paper, I have demonstrated how common financial and econometric principles can be used to assess Major League Baseball free agent contracts. Combining the use of financial tools (i.e. Net Present Value analyses and Ordinary Least Squares regressions) with the calculation of Dollar per WAR Factors, I showed how the Mariners benefited more than the Yankees and Pirates by signing Robinson Cano to a 10-year, $240 million contract this past offseason. The fact that Cano eventually signed with the Mariners gives the model more credibility and encourages me to develop it further in the future. If front offices across Major League Baseball incorporate similar techniques into their evaluations of player contracts, they will be able to make more educated, intelligent decisions.

17 VIII. Appendices Appendix A Salary Regression for Mariners (STATA Output)

18 Appendix B Graphical Forecast of Cano s Statistics 0.600 0.550 0.500 0.450 0.400 0.350 OBP SLG 0.300 0.250 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Age Note that the decline in statistics is smoothed over the next 10 years. In actuality, the decline in statistics would likely fluctuate over the next 10 years instead of being so smooth.

Appendix C Cost of Equity 19

Appendix D Mariners Annual Benefits from Cano Contract 20

Appendix E Mariners NPV Analysis of Cano s Contract 21

Appendix F Salary Regression for Yankees (STATA Output) 22

Appendix G Salary Regression for Pirates (STATA Output) 23

Appendix H - Yankees Annual Benefits from Cano Contract 24

Appendix I Pirates Annual Benefits from Cano Contract 25

Appendix J Yankees NPV Analysis of Cano s Contract 26

Appendix K Pirates NPV Analysis of Cano s Contract 27

28 Acknowledgments I gratefully acknowledge the support and generosity of Professor Michael Hemler in the Finance Department at the University of Notre Dame. He read several versions of Betaball, providing me with valuable feedback to improve the paper each time.

29 References Bradbury, J.C. How Do Baseball Players Age? 11 January 2010. Baseball Prospectus. 19 November 2013. Forbes Valuations for the 30 Clubs in Major League Baseball. Bizofbaseball.com. 16 November 13. Heyman, Jon. Cano asks for $300 million contract from Yankees. 26 September 2013. CBS Sports. 1 December 2013. MLB Team Values The Business of Baseball. Forbes. March 2013. Web. 16 November 2013. New York Yankees Compensation. BaseballProspectus.com. 16 November 2013. New York Yankees Statistics. Baseball-Reference.com. 16 November 2013. Pittsburgh Pirates Compensation. BaseballProspectus.com. 16 November 2013. Pittsburgh Pirates Statistics. Baseball-Reference.com. 16 November 2013. Seattle Mariners Compensation. BaseballProspectus.com. 21 April 2014. Seattle Mariners Statistics. Baseball-Reference.com. 21 April 2014. Swartz, Matt. Methodology and Calculations of Dollars per WAR. 27 March 2014. Hardballtimes.com. 21 April 2014.