On-Field Economics

During the hot stove season, there is a lot of discussion about which teams are major players in the free agent market and who can really benefit from the big names that are out there in any given year. Since this talk is among members of the media and the public, it’s safe to say that only the fans’ views are expressed. The narrative in Baltimore is usually that ownership is reluctant to loosen the purse strings and spring for the players that would help the team to the postseason. Understandably, this hesitance to spend like a relatively large market franchise, which the Orioles actually are, upsets much of the fan base: we all want to see winners. Fourteen years of wandering through the desert is too long to ask many of us to faithfully follow the franchise. The discussion of how much more the Orioles should, could, and would spend if the fans ran the team ends with the consensus of “more than they already do.” Rarely, if ever, is the economics of ownership considered or defended in the discussion. By rationalizing the economic reasons for the spending patterns of the Orioles, we can begin to understand why the Orioles approach labor markets and each season the way that they do. Unfortunately, this also gives a reason, but not an excuse, for the thriftiness of the franchise.

This analysis is focused only on cost and benefit of on-field product and is therefore limited to payroll and revenue generated from winning, which in itself is an approximation and not actually a direct cause-and-effect relationship. It does not include league payouts for things like national television deals and merchandise sales, nor does it include a discussion of regional sports networks and broadcast rights fees. These are all important topics and are necessary for understanding the economic decisions made by franchise ownership, but I believe it’s best to start with the basics before muddying the water with cash influxes from sources that make (sometimes) independent decisions. I intend to cover these topics and try to piece together exactly where the Orioles get their money in a future article, scheduled for completion in early February. For now, all we need to know is that every owner makes money on their teams. If an owner were to seek benefit maximization from their on-field investment, how many wins would they chase? And the all-important follow up question: how much does that cost?

Discuss ownership economics as it pertains to marginal cost and marginal benefit on the BSL forums.

As most people that have followed baseball in the post-Moneyball era understand, each win is not created equal. Theoretically, each win during the Orioles season is worth a different amount of revenue based its relation to the likeliness of the team’s playoff appearance. In this way, the 90th win of the season is worth more than the 60th because more people are likely to attend or watch the games of a winning and playoff-bound franchise than a middling one, making the broadcast rights fee that the organization can negotiate increase. For applications of this model, it is assumed (often incorrectly, since broadcast rights fees are part of a long-term contract) that the rights fee can be renegotiated on a regular basis.

In addition, the Baltimore Orioles’ 90th win is worth a different amount of revenue than the New York Yankees’ 90th win, which is worth a different amount of revenue than the San Diego Padres’ 90th win. If we assume some equal proportion of each franchise’s television market watches a 90-win team, the total number of viewers of the Yankees is very different from the total number of viewers of the Orioles. In a league in which television revenue reigns supreme as a revenue generator, the actual number of eyeballs to TV sets tuned to baseball games matters a lot. When we take into account that demographics and preferences matter a lot to proportional viewership, the equation changes further: San Diego offers beaches and great weather even during the later months when its team would near the 90-win mark, likely cutting into the percentage of residents that would tune in for Padres games. In New York and Baltimore, the tradition and history of the city’s teams, the brutally cold weather, and the lack of awesome beaches, could push the percentage of residents willing to spend time watching the broadcast baseball games to levels above the league average for 90-win teams.

These two considerations together help to explain why teams on the extremes are willing to spend more money to acquire top-flight players. The Yankees, for instance, play in the largest market in the country in terms of total population, have a history of winning that attracts casual fans, exist in a geographic climate that pushes people indoors without much to do besides watch baseball, and have a number of other advantages working for them already that push the marginal value of a win above that of league average and all other teams in Major League Baseball.1

* * *

Focusing on Baltimore, it’s possible that fans’ disillusionment with the free agent market and the winter meetings is often stemming from an inability or lack of desire to see Major League Baseball franchises as if they were owners themselves. Speaking as a fan, I want to see a winning franchise and I don’t care what it costs because I reap significant benefit and incur very little cost of fandom. I buy a few tickets here and there and $2.14 per month to subscribe to MASN. I have almost no skin in the game for substantial return on investment; as long as I feel that watching an Orioles game on TV is worth $0.10 and a trip to the stadium is worth $10, I’m making out just fine.

Franchise ownership is a different animal. There are plenty of different types of owners, given labels that represent the extremes: hobbyists and investors. The idea is that hobbyists are different from the average fan only by money and that their goal is to craft a winning franchise because they’re just like us and want to have fun and that investors are penny-pinchers that get in to make money and sell the team later at a profit. In reality, every owner is some combination of the two. Think of it more as a spectrum, where some owners like to win more than others, and some owners want to deposit more money in their personal bank accounts than others. An example of an owner that attaches a high value to winning is George Steinbrenner. An example of one that attaches a low value to winning is Jime Crane. In either case, the goal of ownership is still to maximize profit, only profit is determined by more than money. In this way, each franchise can still be evaluated as an investment vehicle that (ideally) generates positive returns for the owner while taking into account the fact that some owners like winning.

Economists have a word for the value that an individual attaches to happiness: utility. Utility can really be measured in any unit, since it’s more of a concept than a fact. To turn this spectrum into part of an economic model, we can measure utility as a dollar value and say that each owner has determined a value of utility that he attaches to each win his team adds during a season such that the benefit of a marginal win is given by the following:

MBW=MRW+MUW

Assuming that an owner derives $1,000,000 worth of utility from every win, we can adjust the marginal revenue graph to reflect a fluctuating marginal benefit throughout the course of a season:

Average marginal benefit of each win, based off of Nate Silver's Baseball Between the Numbers

Average marginal benefit of each win, based off of Nate Silver’s Baseball Between the Numbers, adjusted for inflation and a $1M translation for marginal utility of a win.

* * *

Marginal cost of a win is even more difficult to price because wins can be acquired through drafting and developing, trades, and the free agent market. To get a rough idea of what teams are paying for wins, I divided marginal payroll by marginal wins to determine marginal cost per marginal win. This figure is obviously biased down because of the talent and contributions of young players and the hefty contracts of older players. The median marginal cost per marginal win in 2012 and 2013 is $2.625 million. As a side note, many of the league’s worst teams payed the most for their wins above replacement in 2013: the Cubs, White Sox, Astros, Yankees, and Phillies all paid more than $4 million per win. Take that figure with a grain of salt because those teams could bring their MC/MW figure down by simply winning more games.

Combining the marginal cost and marginal benefit curves gives the following graphic:

Marginal revenue, benefit, and cost curves using league-average figures.

Marginal revenue, benefit, and cost curves using league-average figures.

This marginal benefit curve is unusual in that typically, marginal revenue is above marginal cost and slopes downward due to diminishing returns on production. Here, we can see that fielding a playoff-caliber team is the only way to approach profitability with on-field product alone. Including marginal utility means that it requires more wins to reach benefit-maximization, which makes sense: if an owner likes winning, he will be willing to lose money getting to an even higher win total.

This graph shows the high cost of a bad team: Franchises that fall under .500 are, using average prices, overpaying for each additional win that they accrue. It visually shows that it’s sub-optimal for teams to pay more than an average of $2M per win if they can’t reach the 84-win mark. Teams that generate positive benefit for each win strictly from their on-field product (read: not from league payouts, luxury tax distributions, merchandise sales, etc.) are competitive. As expected, the franchises that operate as benefit-maximizing are those that win enough to be eligible and likely to make the playoffs.

Keep in mind that the cost of wins 0-48 is about $13.5M, the cost of a team of league-minimum contracts. Every win up to number 49 is essentially generating a free net benefit for the franchise. Major League Baseball also has all sorts of revenue-sharing procedures in place to protect teams that fall below .500 from losing money.

Profit maximization isn’t what it sounds like. Rather than building the absolute sum of all profits to its highest level, the goal of profit maximization is to incur costs until the point at which the cost of one additional unit is exactly equal to the revenue derived from one additional unit. The production of one unit past that point may still generate positive revenue, but ends up taking away from the firm’s profits because it costs more than it’s worth. Baseball franchises tend to operate as benefit maximizing firms that incorporate the fun of winning into this calculation.

* * *

Peter Angelos

Peter Angelos

Now, Peter Angelos is often seen as a tightwad. It could be that he simply doesn’t care so much about winning; that he falls farther on the investment side of the spectrum. He might even like winning, just not as much as he likes turning a profit. If the utility he gains from a marginal win is less than $1M, the wins that would generate a net positive benefit change.

In 2013, the Orioles had a marginal payroll of $78,798,333 – that is, pay on top of the cost of fielding a replacement-level team at league-minimum salaries. That payroll generated 37 wins above replacement at a rate of $2,129,684 per marginal win. Based on our previous marginal benefit curve that includes utility and adjusts for inflation and metro area, the on-field product of the Baltimore Orioles earned $73,985,270 in marginal benefit. That’s astoundingly close to an equilibrium between marginal cost and marginal benefit.2

The question for the front office is how many wins are needed to maximize benefit from the team. For that, we can use an Orioles-adjusted marginal benefit and marginal cost curve, assuming that Peter Angelos doesn’t care about winning at all:

Baltimore Orioles Marginal Revenue/Marginal Cost Curve

Baltimore Orioles Marginal Revenue/Marginal Cost Curve

Note that this is a simplified graph. The Orioles would in fact be turning a major profit on each marginal win Manny Machado and Chris Davis are worth because they’re vastly underpaid for their ability, while the team would be losing money on Nick Markakis. Working with average cost gives a graph that is a lot easier to read.

If we assume that the first 48 wins are neutral and that that don’t generate any net benefit or loss (which is most likely the case; any surplus or deficit there is likely trivial), we can put an exact number on the numbers of wins it takes for the Orioles’ marginal cost to equal its marginal benefit. At a rate of $2.129M per win, the Orioles would ideally fall around 95-96 wins to maximize benefit to the owner. That’s 95 wins with a marginal payroll of about $100M or a total payroll of about $113.5M. If Angelos were to love winning and treated each win as if it was worth an extra $1M in utility, the Orioles would be aiming for 100 wins every season. These numbers are relatively similar for each team, and it’s why we often see hobbyist owners3 willing to put more money into their teams and aim for more wins. The marginal revenue gained from each win does vary significantly, and in large markets like Boston and New York, can be high enough to justify enormous payrolls.

So why don’t we see the Orioles gunning for 95 wins every season? Well, those last few wins are hard to come by. How much an owner can really draw benefit from his or her team depends on how well his general manager constructs a program that develops players well. If the Orioles were trying to add wins to their 2013 squad and reach the 95-win mark, they would have to be significant players in the free agent market or be unusually strong in developing talent at the minor league level that can contribute to Major League wins either through performance or as trade candidates. If the Orioles were to add ten wins through free agency, they would pay through the nose both in dollars and compensation picks given up. 95 wins is the profit-maximizing mark only if the team is paying just over $2M per win.

None of these figures include revenue sharing payouts and other money the league gives teams and owners, which make it a lot easier to take losses from the on-field product. The Orioles don’t need to hit 95 wins to maximize profits because Major League Baseball subsidizes the cost of ownership and virtually ensures that every owner will be receiving a positive return on his or her investment.

It’s fairly widely accepted that a win costs $7M in free agency. The Orioles will never pay that, and the reason is right on the marginal benefit graph: even if Peter Angelos thought wins were worth $1M in utility, not even the 90th win, the most valuable win around, is worth $7M in Baltimore. If we assume that the team would be willing to spend exactly as much as each of those ten wins brings in, they’d be working with a budget of $41M for ten wins, and that’s only in order to add wins and break even on those additional wins. They wouldn’t be willing to give $4.1M for the 86th win though, and if a win in free agency costs $7M, they just won’t find a player willing to play at that cost. To make money on those wins and cut into the losses they incur getting to 85 wins, the Orioles would have to pay less than each of those wins brings in.

While plenty of 1- and 2-win players would jump at the opportunity to make $2.7M adding the Orioles’ 86th win, that player only makes sense to hire if he’s taking the place of a 0-win player. Since you can only put so many guys on the field, the Orioles would have to find someone willing to sell chunks of 3 or 4 wins for less than $10M that can take positions currently occupied by replacement-level or 1-2 win players. For the O’s, there just aren’t that many positions to fill.

Guaranteed contracts can also get in the way. If the Orioles were to cut a 1-win LF making $2M in order to sign a 3-win LF to a $10M deal, they’d really be adding 2 wins at a cost of $4M for each. They’d still be allocating $12M to the left field position, and only getting a total of 3 wins for it! The Orioles had a hole in left field following the 2013 season, though, and a multi-win player was available. Shin-Soo Choo signed with the Rangers for a backloaded contract worth just $14M each in 2014 and 2015. Based on the marginal revenue the Orioles would be expected to get from a 4-win player, they should have been willing to pay $14M for his services.

* * *

Shin-Soo Choo deep in thought. (September 27, 2013 - Source: John Sommers II/Getty Images North America)

Shin-Soo Choo

The issue with signing Choo is that his signing makes bad business sense in the long run. The Rangers are paying him $20-21M for his age 33-37 seasons. While he might not decline quickly, he would have to better his output at the end of his career to be worth those figures at all. The Orioles weren’t going to get Choo on a 2-year, $28M deal when he was the second-best free agent available, and that contract would only increase the team’s win total while breaking even on those wins anyway. That doesn’t even begin to erase the losses the team incurred in getting to 85 wins in the first place! To actually realize profit on those additional wins, the team would have to pay Choo less than $14M for the next two years and probably less than $10M for the following five years. That’s not a particularly competitive offer.

Clearly, the best way to make money with on-field product is paying players below their market wage. Failing that, it’s to sign 1-2 win players at positions that aren’t currently occupied to contracts worth less than the wins that they add to the team. There are two ways to do that, if no regular targets are available: identifying market inefficiencies that leave 1-2 win players available for $2-4M or taking risks on recovering players. Both of these methods are playing the lottery, albeit with better odds (hopefully, if your analyst is good) in one scenario.

Why Peter Angelos is seemingly only willing to allocate $100M to payroll is something I’d like to explore further, in trying to understand his own finances from the Orioles and MASN altogether, including league payouts, merchandise distribution, and ticket revenue. Revenue distribution helps profitability, and works in such a way that depresses the number of wins needed to act as a profit-maximizing organization. What we need to keep in mind is that Peter Angelos has requested a profitable baseball team from year-to-year. His aversion to long-term contracts is not for payroll flexibility, at least not primarily. Instead, it’s to ensure that he’s never locked into an under-performing, overpaid team that won’t generate a profit.

And that’s okay, even if it doesn’t mesh with what fans want. It’s his money to try to capture a return on, and I’m willing to help because I gain utility just from watching the team. Maybe we can look forward to Angelos wanting to win in old age, like many owners before him, and translate his marginal benefit curve up by a few million dollars per win.

I plan to answer any questions received in response to this article as part of a look into the additional money swirling around the Orioles. Until then, join the discussion of franchise economics on the BSL forum to share your thoughts, questions, and ideas.


It’s at this point that I encourage you to forget about the Yankees, who operate on an entirely different plane than every other team in baseball. The team lost $50M in ballpark revenue by fielding an average, cost-conscious lineup in 2013, representing a weird and rare instance in which the team literally has to spend money to attract people to the ballpark in the hopes to break even at all.

If Jim Johnson had saved the average 95% of his opportunities, the Orioles would have ended the season with an additional 6 wins. The marginal benefit earned by the Orioles in this scenario would be $106.28M. While that would indicate a payroll that was sub-optimal in that it payed too little, remember that many Orioles had breakout seasons that were as difficult to predict as Jim Johnson’s 9 blown saves.

And old owners. It’s incredible how old age turns so many long-term owners into fans that really just want to have some fun.

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About the author


Patrick Dougherty   

Orioles Analyst

Patrick is the co-founder of Observational Studies, a blog focused on the analysis and economics of professional sports. The native of Carroll County graduated with a Bachelor’s degree in Economics from Loyola University Maryland. Patrick works at a regional economic development and marketing firm in Baltimore, and in his free time plays lacrosse.


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One Response to On-Field Economics

  1. Pingback: Baseball Blogs Weigh In: Middlebrooks, Burnett, Orioles – MLB Trade Rumors

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