Batting Leadoff: Marginal Win Value and Dollars Per Win

This post originally appeared on Batting Leadoff. Batting Leadoff is a website dedicated to providing readers with premium baseball content. Posts from the site will appear regularly on the Sports Business Society Blog (view the information in the sidebar for updated information).

It is quite natural to spawn opinions on offseason moves that eventually manifest into conclusions that the general manager of Team A is a moron for signing Player B to Contract X. No matter our qualifications or level of knowledge of baseball, there are multiple times per winter us fans are left with the notion that yes, we absolutely have to be smarter than the GM of Team A.

What we do not take into consideration is that within every front office in Major League Baseball, there are dozens of bright analytical and scouting minds who are far more conversant than us. Their scouts can see how one player’s bat speed may be diminishing. Their analytical department knows how a free agent’s skill set will fit in their ballpark far better than we do. Their doctors have medical reports on players that we could only dream of seeing.

The information accessible to these bright minds is far more than we can find on MLB.TV, Fangraphs, and Baseball-Reference. Essentially, front offices make educated decisions dependent on a wealth of knowledge that the public lacks.

There are a multitude of factors that drive every transaction. The Mariners did not invest $240 million dollars in Robinson Cano because they thought he was a pretty damn good second baseman. Inside that decision came scouting insight, statistical analysis, and economic evaluation that indicated it was sensible for the Mariners to blow every single team in the market out of the water.

Of course, there are rudimentary differences in each front office’s valuation of every player. If each team valued every player equally, the market would be far different. Some teams put more weight into the scouting aspect of evaluations, while others rely on regression models to project players forward. Another large factor that is not touched on nearly enough is the marginal value that each player provides his employer.

For a number of years, analysts have looked at the contracts signed by free agents, quantified the value of the free agent, then depicted how much money the market demanded for a single Win Above Replacement ($/WAR). This number has risen annually for the past decade for reasons such as inflation and an influx of TV money among others.

The number for this off-season’s contracts was generally pegged at $6 to $7 million dollars per win. That is to say that if a team is going to sign a player who has consistently posted 2 WAR seasons (league-average), the market values him at around $13 million per season. These numbers are pretty consistent with how the market has played out so far.

However, the money per win valuation has numerous caveats that must be considered. First of all, $/WAR is not a good way to project salaries among elite players. As godly as he is, it’s unlikely that the 10-WAR man Mike Trout would be paid $70 million per year if he were on the open market. Robinson Cano posted a 6 WAR season in 2013, meaning if the market always held true, he would have found a contract that paid him an AAV of around $40 million dollars.

The second caveat is that while WAR is an extremely useful and powerful tool to evaluate players, front offices look far beyond that metric while putting a dollar sign on the value of a player. Another caveat, one which I find most interesting, is that a win is worth a different amount to every team. This in a nutshell is marginal win value.

The basic concept of marginal win value goes like this: a team filled with AAA players wins about 47 or so games in the major leagues while costing around $12 million dollars. From 47 wins on, the team is buying wins in hopes of accruing more revenue from being good. However, if the team buys one win at the market rate of $7 million dollars, the revenue added from increasing their win total from 47 to 48 is worth far less than $7 million dollars. From 47 wins on, it takes marginal analysis to decide if buying more wins is profitable for the team.

A single win carries far different value for teams who are on opposite sides of the spectrum. Several extremely smart people such as Phil Birnbaum and Nate Silver have looked at the marginal win value curve, creating the following graph to depict its true worth.

(Click to enlarge)





This graph is from 2005, so it is fairly outdated. In 2005, Silver found a win to cost around $2 million on the open market. To adjust to inflated contracts and revenue, we would simply raise the graph’s Y value to equate it to today’s contracts, keeping the shape consistent. The graph shows that it is an inefficient allocation of money to keep buying wins from around 60-85. This makes sense because barring a team slipping in one of the wildcard slots, it’s unlikely a team makes the playoffs with 85 wins.

However, the theory states that at 86 wins, the value of the revenue a team makes from extra ticket sales or whatever revenues are driven by playoff excitement begins to exceed the money you are paying for a win. Looking at the graph, you can see that you acquire surplus value buying wins from 85-95 because the marginal value is higher than the $2 million dollar cost of a win in 2005. From 95 on, the value decreases due to the fact that you likely have the division title in the bag and spending money to win upwards of 100 games is rather gluttonous.

There are uncertainties when using marginal win value to dictate your offseason. It is extremely hard to project how many wins a player is worth, especially with the volatility of pitchers or injury-risk players. That, along with other possible variations, makes it extremely difficult for a team to forecast its win totals while entering a season.

The standard deviation between true talent and performance is about six wins in the best projection models, meaning that a team with the talent of an 81 win team could win anywhere from 75 to 87 games. That being said, marginal win value is absolutely something that front offices take into account when deciding if it is profitable to keep spending on their club.

In Part 2, I am going to take a look at some of the most questionable moves that were made this offseason, and try to find each front office’s motives behind the moves. While marginal win value is going to play a large role in this exercise, I’m also going to use a number of other explanations to decipher why these transactions were made.

A lot of this piece was made possible by the fantastic work of people such as Dave Cameron, Lewie Pollis, Phil Birnbaum, and Nate Silver. These articles are fantastic reads and quite informative. Special thanks to Matt Swartz for the correspondence and help in equating Silver’s 2005 graph to the inflated contracts of this offseason. 

This post originally appeared on Batting Leadoff. Batting Leadoff is a website dedicated to providing readers with premium baseball content. Posts from the site will appear regularly on the Sports Business Society Blog (view the information in the sidebar for updated information).

Daniel Schoenfeld is a senior in high school in Evanston, Illinois. He plans on studying business economics while pitching in college next year. He is interested in scouting and statistical analysis, and hopes to use Batting Leadoff as a platform to break into the industry. He’s currently working on a large scale project detailing the indicative factors involved in injury projection of pitchers and is always willing to learn and share. Contact him at dschon711@aol.com and follow him @DanielSchoe. 

ILRSBS Goes to Phoenix: Part III

The team taking in the beautiful Phoenix skyline.

This is Part Two of a three-part series following the ILRSBS Case Competition team's trip to the SABR Analytics Conference in Phoenix, Arizona. (Click here to read Part One, and click here to read Part Two.)

When all was said and done, Hudson, Mike, and I were happy with our research and preparation. As we went to sleep at 3am, Phoenix time the night morning before presenting, we knew we had put all the effort possible into the case. Using an already overused sports analogy, we left it all out on the field.

Our team was scheduled to compete first that morning, at 9:30 sharp. In front of three judges from teams such as the Texas Rangers and Cleveland Indians, we were ready to make our pitch as part of a 20-minute presentation and 10-minute Q & A. Perhaps the most eye-opening part of the trip was just being able to stand in front of a room of extremely intelligent people and watch them as they listened to what we had to say. They truly did care, and the passion they have for the game was on full display. Often times we have these “epiphany” moments in our lives when we say, “How sweet was that?” I know I can speak for the three of us that one day, looking back; this certainly may be one of those moments.

Our team wound up finishing as the runner-ups in the Undergraduate division, as the eventual champions from NYU took first place. In the graduate/law division, Pepperdine University took top billing. For a three-man team, we were extremely proud of our accomplishment, and while we would’ve loved to win, the experience and learning we were able to participate in was recognition enough.

In addition to the Diamond Dollars Competition, the three of us were fortunate enough to interact up close and personal with some of the leading minds in the entire industry. Through various panels, and networking sessions, Hudson, Mike and I were able to meet top executives in Jed Hoyer, Rick Hahn, and Jerry DiPoto. Brian Kenny of MLB Network was one of the panel moderators, and throughout the conference we were able to connect and speak with various professionals from companies such as Fangraphs, Baseball America, Baseball Prospectus and other Major League clubs such as the Colorado Rockies, Texas Rangers, Cleveland Indians, and more.

Executives Daniels, Hoyer, and Hahn.

Perhaps the highlight of our week, however was getting to meet a fellow Cornellian that each of us one day hope to aspire to. Speaking with Rangers General Manager Jon Daniels was surreal. His advice was not only invaluable and thoughtful. Our two takeaways from him for were to watch as much baseball as possible, and to stay humble. As he put it, the game isn’t big on “self-promoters.”

The three of us with fellow Cornellian, Jon Daniels.

When all was said and done, the three of us had an amazing time. After a quick red-eye flight home, accompanied with a daylight-savings-time-change, we found ourselves back in reality of Cornell life.

As the inaugural Cornell case competition team members, a certain sense of pride exists in what we were able to accomplish. We look forward eagerly to next year when we send a few more students and continue to prove that the Ivy League knows its baseball.

Here are quick takes of our trips from my team members:

“It was a tremendous opportunity to be able to go to the SABR Conference and present our case in front of a group of highly regarded individuals within the baseball community. The conference itself was much more intimate and laid-back than others I had been to which allowed me the opportunity to speak with several Major League GMs, MLB Network Analyst Brian Kenny, members of the baseball analytics community, and a host of executives within Major League baseball. The only drawback to the conference, or more plainly the city of Phoenix in general, was the dearth of carne asada steak” –Mike Parnell

Outside the beautiful Chase Field in Phoenix.

“Participating in the SABR Case Competition was a great experience. The opportunity to spend a few days working on such a fascinating case was awesome, and getting to present our work to MLB industry leaders was truly amazing. The conference brought together hundreds of forward-thinking baseball brains, and so many people brought great ideas to the discussion. Being a part of that conference was so much fun, and although we didn't win the competition, I can’t wait to go back next year.” –Hudson Belinsky 

Oh, and we also got to take in a few WBC games!

We hope you all enjoyed this look into our trip to Phoenix. We look forward to making this event a key part of the organization moving forward. For any questions, comments, or suggestions, please email me at gmc74@cornell.edu.

ILRSBS Goes to Phoenix: Part II

This is Part Two of a three-part series following the ILRSBS Case Competition team's trip to the SABR Analytics Conference in Phoenix, Arizona. (Click here to read Part One.)

As mentioned previously, in projecting Mike Trout, we had an amazing talent on our hands. Looking at his WAR totals gave us a Hall of Fame type player, someone who would continue to produce at an MVP level into his early 30s. It became pretty clear to us that there would be no team with the resources available to trade for this type of player, so we turned our focus to figuring out what type of contract offer we could confidently extend to Trout.

$440,000,000 was the value of Trout’s production value to the Angels, yet, this number failed to account for risk. In any long-term agreement, each side takes on inherent risk. There are many circumstances in which the deal could turn out poorly. Injury, and lack of performance are the two main factors, yet in this case we also needed to account for the value of making life-changing money. Essentially it all boiled down to the guarantee of big money in the face of various risk factors.


After trying a couple different strategies, our team decided on generating a regression equation to determine a “discount rate” to Trout’s production value. We compared recent (since 2000) contract extensions, and examined the service time that each player had accumulated at the time of signing. After looking at the player’s production value ($4.5 million x WAR total = Expected Production) we plotted a regression against the service time at the time of extension. Our belief was that the more service time, or the more “established” a player was, the closer the player’s actual contract would be to his expected production value.

The extension data that helped us create our Regression.

Using the regression data we came up with the following equation: Discount Rate = -0.14511x + 2.000839. Plugging in the service time, we were able to establish a fair contract offer for Trout. Our offer to Trout would be eight years for $140 million, yet we would be willing to accept an offer up to $204 million over that time. With an agreement in this range, the Angels would lock-up an (projected) MVP-caliber player into his age 32 season. They would secure a face of the franchise, and they would not have to break the bank or mortgage their future success or payroll flexibility. From Trout’s perspective, he would get life-changing money, his first big contract that would now be guaranteed, even in the face of injury or lack of performance. 



Like the old game, Deal or No Deal, the more risk present, the more of a discount applied. By examining recent extension data, we confirmed our intuitive belief that this was the case. While players may be leaving some money on the table by taking extensions early on in their careers, they do so in order to receive security and peace of mind. In the end, the “Trout dilemma” boiled down to this issue of tradeoffs.


Angel's owner Arte Moreno will ultimately hold the
final decision on what to do with Mike Trout.

As a final piece to our presentation, we analyzed how the Angels could reasonably fit Trout’s contract into their current salary structure and obligations. By doing this, we also found that the distribution of money to Trout could vary year-to-year. In doing this, the Angels would maintain competitiveness (as a projected 90-win team) and still be able to retain their star at a fair price.

Check back tomorrow to hear how our team did and to hear about some of the other experiences from our weekend in Phoenix.

ILRSBS Goes to Phoenix: Part I

Hello, Phoenix. Hello, SABR.

This is Part One of a three-part series following the ILRSBS Case Competition team's trip to the SABR Analytics Conference in Phoenix, Arizona.

Just two weeks ago, three members of ILRSBS were able to take part in a unique opportunity. The 2^nd annual Diamond Dollars Case Competition in Phoenix, Arizona provided a platform for Mike Parnell, Hudson Belinsky, and myself to showcase just what Cornell and the Sports Business Society is all about.

Held as part of the SABR (Society for American Baseball Research) Analytics Conference, our case tasked us with developing, answering, and presenting our recommendations for a real-life baseball operations question. Last year, the case dealt with a “buy or sell” type question surrounding the Washington Nationals. This year, the focus was all on one of baseball’s most intriguing players: Mike Trout.

Yes, baseball’s most popular, mystifying and perhaps soon-to-be loved player was the focus of our entire case. You can imagine the excitement that came over our three-man team upon learning that we would be tasked with developing an appropriate contract extension for Mr. Trout. How fitting it was that days earlier, the real life Angels decided to renew the reigning AL MVPsuperstar at just $20,000 above the league minimum. As you can imagine, our first recommendation was simply, don’t do that!

Mike, Hudson, and Gabe working on the plane.

But in all seriousness, after receiving our case on Sunday morning, Mike, Hudson and I had four days to put together a cohesive 20-minute presentation on which to be judged. In the case, which was actually set following the 2013 season, Mike Trout went off for a 8.4 WAR season in which the Angels fell to the world champion Nationals in six games. In this scenario, the Angels would have one more season of Trout under cost-control as well as three years of control in which he would be arbitration eligible. Trout would become a free agent in 2017.

Placed in a position to advise Jerry Dipoto, the Angels GM, our team had to develop a contract proposal. Our three options were to trade Trout, to extend him over the short-term, or to provide him with a long-term extension. Playing into this decision would be our expected production of Trout, the value in dollars that he would be worth, the construction of the team around him, and the risk involved in such a contract. With the facts established, we set out to develop the best decision possible.

Through the next 4 days, we slogged through the massive amounts of data and processes needed to make our case to Mr. Dipoto. I’ll spare you the details, and just hit on two of the major highlights in our process.

The first is the manner in which we decided to project Mike Trout’s production for the next ten seasons (through age 32). As a team, we developed models for players similar to Trout in the three facets of the game, hitting, base running, and defense. Our samples were different for each of these categories, but they included players that met specific criteria for a player of Trout’s caliber and production. After developing an “aging curve” for a player such as Trout, we developed a Monte Carlo simulation to help predict the results for 10,000 seasons of Trout based on the previous three seasons’ production (weighted 45%, 30%, 25%). We continued the process until we wound up with ten seasons of Mike Trout production. What we got was one of the best players of all-time. To boil the numbers down a bit, Trout put up the following WAR (Wins Above Replacement) totals for the years 2014-2024: 8, 11, 11, 8, 11, 9, 9, 8, 8, 8, 7. Wow. Just. Wow.

Yes, Mike Trout, you are that good.

After we took Trout’s production value, we then assumed each win to be worth $4.5 million on the open market. Multiplying this number by his production we determined his value to be worth approximately $440,000,000 over the course of ten seasons.

Of course we couldn’t reasonably give Mike Trout $440,000,000, could we? Check back later this week to find out how we accounted for risk, what our final proposal was, what the judges thought, and how we spent the rest of our time in Phoenix!