The question that most often arises during the off season is “how much is a player worth?” Given how cold this “Hot Stove” season has been for Pittsburgh Pirates fans, this seems like a really good time to answer that question.
Two Methods to evaluate the Pittsburgh Pirates roster in terms of worth
There are two different approaches we can take to answer that question.
The first is to find out some form of the “win-value” of a Pittsburgh Pirates player. There are a number of ways to do this that are readily available; stats like Wins Above Replacement (WAR) and Wins Above Average (WAA) seek to determine how much a player’s performance contributed to the team’s wins. While this is a very good method for comparing two different players who play different positions in determining which was “better”, it doesn’t do as good of a job during the off season when contracts, worth large sums of money are being signed.
This is where another method is needed, one that assigns a dollar value to the production of a player. This is important because team owners don’t want to sign a player for more than they can generate in terms of performance, ticket sales, merchandise, etc., whereas players would like to be paid for at least as much as they produce for the team.
Simple Economics at play
Pittsburgh Pirates fans are more likely to spend money to go watch a team, purchase team apparel, and watch games on TV if the team is winning games, which in turn means higher revenues for the team. So ultimately, what the owner wants to pay for is more wins, as they generate more revenue.
[perfectpullquote align=”right” bordertop=”false” cite=”” link=”” color=”” class=”” size=””]There are two different approaches we can take to answer that question.[/perfectpullquote]The flip side to this is that wins only generate so much revenue. For instance, if a win, on average, raises about $1 million in revenues, owners would not be willing to pay a player more than $1 million per win generated. Otherwise they would just be losing money on the deal. This is assuming they fully subscribe — in real dollar terms — to WAR or WAA.
The methodology is pretty straight forward, if we can determine the wins that a player produced and we can determine the dollar value of a win, then we can say that a player generated that many millions in revenue. Economists refer this idea a worker’s Marginal Revenue Product (MRP).
If, for instance, we say that a win is worth $1 million, and a player was worth three wins, then that player’s MRP would be $1mil per win*3wins=$3mil, thus the player should be paid roughly $3 million in competitive free agency.
The reality is far more complicated than that.
The Collective Bargaining Agreement states that a player must remain with a team for their first six years years and are only arbitration eligible for the last three years. When players sign free agent contracts there is no certainty of their future production, so that uncertainty has to be factored in, and so on.
Additionally it is very difficult to determine the exact win value of a player even between the established WAR metrics (fWAR, bWAR, WARP, openWAR). Although all of these metrics are good and reliable, each has differences in how they measure a player’s win value with some valuing pitching over hitting and fielding, while others overvalue hitting and so on.
Establishing Wins
For our purposes, WAR is not really the measurement we would like to use.
This has to do with the “replacement” aspect of WAR. As said previously, WAR is good for comparing players, what it doesn’t tell us is the total sum of a player’s contribution to wins, only their contribution “above replacement level”. That is not to say that a replacement level player does not contribute anything to wins. If you dressed me up in a Pittsburgh Pirates uniform, I would be significantly worse than a replacement level player, so a replacement level player does contribute something more to wins than just someone you pull out of the stands.
What we’re really after is how many wins above an empty 25-man roster a player contributes. In a thought-experiment way, no one pays money to go see the MLB game in a city like Columbus, Ohio because there is no team that plays there, or put in a somewhat convoluted way, they have an empty 25-man roster. If you filled that roster by putting an MLB team there, it’s likely that people would be willing to go see at least a few games and buy some merchandise and so on.
The actual analysis of this is pretty straight forward, just take the total number of team wins and regress it on factors like singles, doubles, triples, home runs, strikeouts, walks, pitcher strikeouts, pitcher walks, pitcher home runs given up, and defensive runs saved. I ultimately used two models, one that included the stats listed and the other with innings pitched, this was because the first model overweighed hitting relative to pitching, and the second model overvalued pitching to hitting. I took the average of the two to get the total number of wins contributed, that was a more moderate version.
Below is a chart of the more important stats and their impact on wins (note: the Pitching stats for a pitcher getting a strikeout, and giving up a walk and giving up a home run are denoted with a “d” at the beginning for “defensive”)
| Outcome | Win Value |
| Single | 0.03 |
| Double | 0.04 |
| HR | 0.15 |
| SO | -0.02 |
| BB | 0.02 |
| dSO | 0.03 |
| dBB | -0.04 |
| dHR | -0.16 |
| DRS | 0.06 |
What this means is that a batter hitting a single contributes about 0.03 wins, where as a strikeout by a batter costs a team about 0.02 wins and so on down the line. So, hypothetically, if all a player did all season was hit 10 home runs and struck out 10 times and did nothing else, that player would be worth 13 wins:
10*0.15+10*(-0.02)=1.3 wins
The Pittsburgh Pirates’ top wins producers in 2017 were a pretty unsurprising bunch:
| Name | Wins |
| Gerrit Cole | 6.75 |
| Andrew McCutchen | 6.34 |
| Josh Bell | 6.29 |
| Ivan Nova | 5.04 |
| Josh Harrison | 4.89 |
Cole and Nova were both good pitchers who added a lot of value by staying healthy and pitching a bunch of good innings. McCutchen, Bell and Harrison were the biggest stars of the offense and were reflected as such. Additionally, it seems as though Josh Bell is poised to be the new face of the franchise, posting nearly the same number of wins as McCutchen, in just his rookie season.
The Pittsburgh Pirates’ worst producers weren’t particularly shocking either.
| Name | Wins |
| Alen Hanson | -0.38 |
| Gift Ngoepe | -0.44 |
| Phil Gosselin | -0.48 |
| Joaquin Benoit | -0.56 |
| Antonio Bastardo | -1.02 |
What is a bit shocking is that in just 9 innings pitched Antonio Bastardo managed to single handedly be worth an entire loss. Putting that into perspective, Tyler Glasnow, who labored through much of his 62 Major League innings last year, only registered -0.23 wins, or between 1/5th and 1/4th of a loss.
[perfectpullquote align=”right” bordertop=”false” cite=”” link=”” color=”” class=”” size=””]The reality is far more complicated than that.[/perfectpullquote]This model is pretty accurate too; if we sum up every player’s Wins generated, we get a total of 74.4 wins. Since the Pirates ended up with 75 wins on the season, we can be confident that this model works and chalk the last 0.6 wins up to luck or random variation.
We can think of the wins that a player generates as their “product”. While perhaps not as tangible as say, a factory worker’s widget production, fans pay more to see a team that produces more wins, in the same way that a consumer pays more if they are buying a larger quantity of said widgets. Since this is the number of wins that each individual produces, economists refer to this as their marginal product.
How much is a Win Worth?
The next step is to find a dollar value of an individual win to include into this calculation. To do this, I pulled the revenues for teams as reported in the Forbes MLB team valuations, from 2013-2016, the most recent year that we have data for, and adjusted the 2013-2015 years to the 2016 mean. I also used 2010 US Census data and 2011 Canadian Census data to get a rough approximation of population of the cities and surrounding areas as a proxy for the team’s market size.
Controlling for the population of the team’s market, a win is worth about $1.45 million to a team on average. Since we don’t have 2017 numbers yet, we’ll assume the average annual growth in revenues between 2013 and 2016 of about 10% which pushes this number up to $1.6 million per win.
Since we now know how much a win is worth, and we know how many wins each player produced we can define their Marginal Revenue Product (MRP) as the number of wins they produced multiplied by the value of a win.
First off, here’s a table of the various important outcomes, their respective win-value as well as their MRP:
| Outcome | Win Value | MRP |
| Single | 0.03 | $50,000 |
| Double | 0.04 | $70,000 |
| HR | 0.15 | $246,000 |
| SO | -0.02 | -$30,000 |
| BB | 0.02 | $27,000 |
| dSO | 0.03 | $42,000 |
| dBB | -0.04 | -$67,000 |
| dHR | -0.15 | -$248,000 |
| DRS | 0.06 | $102,000 |
To put that into perspective, for whatever it’s worth, a homerun hit is worth roughly the median home selling price in the US in 2017, and a home run given up costs a team roughly that same amount.
The revenue generated from the Pittsburgh Pirates top producers looks like this:
| Name | Wins | MRP |
| Gerrit Cole | 6.75 | $10,806,000 |
| Andrew McCutchen | 6.34 | $10,150,000 |
| Josh Bell | 6.29 | $10,069,000 |
| Ivan Nova | 5.04 | $8,056,000 |
| Josh Harrison | 4.89 | $7,832,000 |
At first glance these numbers seem exuberant, but keep in mind; this doesn’t take into account what these players are actually being paid.
Rent
Using payroll data from Spotrac to see what these players are actually paid, then subtracting it from what they actually produced we can see either the surplus value or cost that they generated for the Pirates organization. This is an idea economists refer to as their “rent” which is defined as the marginal revenue product minus the wages paid.
| Name | Wins | MRP | Rent |
| Gerrit Cole | 6.75 | $10,806,000 | $7,056,000 |
| Andrew McCutchen | 6.34 | $10,150,000 | -$4,058,333 |
| Josh Bell | 6.29 | $10,069,000 | $9,520,000 |
| Ivan Nova | 5.04 | $8,056,000 | -$360,666 |
| Josh Harrison | 4.89 | $7,832,000 | $82,000 |
You can see that, according to this model, McCutchen and Nova were overpaid by $4 mil and $360,000 respectively, whereas the young guys, Bell and Cole who are either on their rookie contracts or in arbitration, have contracts are well under what the free agency market would value them at. Harrison’s contract was worth pretty close to the actual value he generated, despite the fact that he was injured and missed out on the last several weeks of the season.
This model has a few key limitations to consider when viewing this information. The first is that we can’t measure the real value of stardom from a player like McCutchen. McCutchen generates value solely because he is a super star, people want to come to Pirates games or tune in on TV just to watch him play, people want to buy and wear his jerseys because of he is a star, and so on. All of these factors result in more revenue from ticket and concession sales, TV revenue, and merchandise sales, meaning that someone like McCutchen has an actual MRP that is likely greater than just the one calculated above.
The other key limitation is that we don’t have a way to quantify what their presence on the team does. For instance, Nova was a consummate professional on the mound, taking the ball every five days, putting in his innings, and acting as a stabilizing force for this young pitching staff. We don’t know and can’t quantify the leadership value of players like Nova, or McCutchen, or Freese, which may very well be extraordinarily important to a team winning tight baseball games or turning a season around, but is never factored into the wins that they themselves generate.
All that being said, this is an estimation that we can work off of by theorizing the value of leadership, stardom, and things of that nature, on top of what we can actually quantify.
25 of the 46 athletes who played for the Pirates in 2017 were a net-loss for the team. No player was more of a negative value than Antonio Bastardo, who cost the team $8.1 million; $6.5 million in his contract and an additional $1.6 mil because of his poor performance.
The 5 biggest losses of last year:
| Name | Wins | MRP | Rent |
| Antonio Bastardo | -1.02 | -$1,636,000 | -$8,136,000 |
| Francisco Cervelli | 1.38 | $2,214,000 | -$6,786,000 |
| Andrew McCutchen | 6.34 | $10,150,000 | -$4,058,333 |
| Joaquin Benoit | -0.56 | -$893,000 | -$3,474,992 |
| Daniel Hudson | 1.73 | $2,775,000 | -$2,725,000 |
Bastardo and Benoit were just bad last season, Cervelli was a negative value as a result of being injured and unable to produce, McCutchen just didn’t quite produce to the level that many would have liked, but as I said earlier, was likely not that big of a financial loss for the team, and Hudson is just overpaid.
The 5 biggest surpluses of last year:
| Name | Wins | MRP | Rent |
| Josh Bell | 6.29 | $10,069,000 | $9,520,000 |
| Jameson Taillon | 4.76 | $7,620,000 | $7,064,500 |
| Gerrit Cole | 6.75 | $10,806,000 | $7,056,000 |
| Trevor Williams | 4.58 | $7,328,000 | $6,784,000 |
| Chad Kuhl | 4.56 | $7,299,000 | $6,749,000 |
Again you’ll see all of these players are either on rookie contracts or arbitration eligible. In fact the first contracted player that was worth positive rent was Gregory Polanco generated about $4 mil in surplus and sat at the 8th most rent generated. This has a lot to do with the structure of the CBA, and probably impacts free agency as teams with a lot of surplus from young players can afford to take a loss on top free agents and still come out with a profit.
In total the Pittsburgh Pirates organization netted about $24 million in surplus in 2017. While initially that seems like a lot of money that the Pirates can spend in free agency this off season, keep in mind that, all else equal, the salaries paid next year are only going to go up and that surplus will shrink, unless some veteran players are moved. That doesn’t account for any other expenses of the team like the payroll for coaches and staff or taxes paid. Realistically, the actual amount available for free agency is probably around $10 mil, which can net you a nice player to be sure, but not a super-star.
A reason why decisions are excruciatingly slow?
What makes this topic so interesting during the hot stove season is that it gives us a better understanding of why teams make the decisions they make. For instance, Cervelli’s negative value means that a team would only be willing to take him on via trade, if the Pirates ate some of the money. Chris Stewart, who cost the team $1.5 mil, had almost no chance of having his option picked up when the option of Diaz, who generated $1.2 mil in surplus, is already there. The Pirates are asking so much for Gerrit Cole because, beyond just being the team’s leading win producer, he is also a huge rent producer.
It’s not perfect, however; Wade LeBlanc was a $2 mil surplus and was non-tendered, where as George Kontos was a loss of $64,000 but will still be back for next season. Some of that has to do with LeBlanc having more innings pitched as a Pirate so it’s not a perfect science, but it is still really insightful.
[perfectpullquote align=”full” bordertop=”false” cite=”” link=”” color=”” class=”” size=””]At first glance these numbers seem exuberant, but keep in mind; this doesn’t take into account what these players are actually being paid.[/perfectpullquote]If we evaluate the rents and MRPs of players across the league, we can make judgments on trades. If, for instance, Cole is going to be worth about $14 mil in rent over the next two seasons, and whoever he is traded for generates $16 mil during their time with the Pirates, the Pirates would be on the better end of the deal, even if it is over a longer period of time.
This isn’t the complete modeling of the baseball labor market by any means. For one thing, not all wins pay the same, teams that are closer to contention for their division or a Wild Card spot, tend to generate more revenue as the fan base is excited. In other words, fans will pay relatively little to see a team go 63-99 over 62-100, but will pay a lot more for a team to go 92-70 and make the playoffs over 91-71 and miss them.
This results in an “S” shaped revenue curve where revenue per win is flat and small for teams out of contention, then rises rapidly as teams come into contention, then flattens back out as teams run away with a playoff spot. As such teams are willing to pay more for wins when they expect to be competing for a playoff spot, versus out of contention, or running away with it.
There is also a problem of accounting for uncertainty in a player’s future production when signing them to a contract in the present; that uncertainty has to be factored in when using MRP as a predictor of the contract they will be signed to. We can use this model to analyze trades and contracts, as a way of quantifying how good a GM is at signing and trading players to their team’s benefit. These topics will be addressed in future articles.
For now, this should serve as a primer as to the type of calculus going on in the front offices across the MLB during this hot stove season. Teams are trying to maximize the rent they receive from the players they sign; while minimizing the potential losses should a player fail to produce. This is put in tension with the player side who want to maximize the amount of money paid to them. This results in, on average, players being paid slightly less than the value they produce, and teams can use that surplus to address weaknesses on the club’s roster.
Below is the full list of each Pittsburgh Pirates’ player’s win-value, marginal revenue product, and rent generated in 2017.
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