Free Agent Contracts and Auction Theory: Theoretical Implications
Imagine an auction that takes place between three bidders. The item in question? An envelope filled with money. All three bidders employ teams of analysts that attempt to ascertain how much money is in the envelope, based on a variety of evidence that isn’t important for this analogy. Each bidder thus arrives at an estimate of the fair value of the envelope. Then they place a single sealed bid. The highest bidder out of the three gets the envelope.
What bidding strategy would you employ? Here’s a bad one: Just bid what your team of analysts calculates as the expected value of what’s in the envelope. The reason this is bad is known as the winner’s curse. If each bidder comes up with an estimate of fair value and bids that number, the winner will be the one with the highest estimate of fair value. In other words, you’ll only win if your estimation of the envelope’s value is higher than everyone else’s, and since you’re always paying exactly what you’re hoping to gain, you’ll tend to lose in the long run.
Allowing for a lot of approximation, this situation describes free agency in major league baseball. Every free agent has an unknowable amount of expected future production. Teams employ armies of analysts who attempt to estimate that production. Then, armed with that knowledge, they make contract offers to that free agent, in competition with other teams.
As I said, there’s a ton of approximation and simplification going on here. Players aren’t envelopes filled with money. Team context matters. Players don’t have to accept the highest bid. Tax regimes aren’t equal, and non-monetary incentives matter, too. Contracts are complex, and there’s no requirement that they be the same number of years, have the same number of options, no trade clauses, or anything of the sort. There’s no agreed-upon universal value system; different players present different value to different teams.
But that doesn’t mean the abstracted case has no use. As we approach the trade deadline, I think there’s one clear one: dispelling the myth that teams refuse to give up much to trade for a player who just signed a big free agent deal — after all, if they valued them enough for a blockbuster, they would have just offered a bigger contract, right? That’s a great soundbite, so you hear it all the time, but it doesn’t jive with established economic theory.
The style of contract negotiation where multiple bidders submit bids and a single seller chooses one of them can be stylized as an auction. “Auction” might sound like a weird way to describe it, but if you stop to think about it, it makes perfect sense. It’s a way for multiple bidders to use their willingness to pay to differentiate themselves to a seller.
The classic auction you think of is an English auction. There’s an auctioneer, and some old people with monocles and paddles. The price keeps going up unit by unit; if you value something more than the current bid price, it’s optimal to bid more for it. In theory, the price will continue to go up until the bidder with the second-highest valuation of the item being auctioned reaches their top valuation and drops out of the bidding. The bidder who has the highest valuation then wins the auction, paying only enough to outbid the valuation held by the second-highest bidder.
A quick example: let’s say that we’re bidding for a Cal Ripken Jr. baseball card. I think it’s worth $250, you think it’s worth $200, and Meg Rowley thinks it’s worth $600. Below $200 dollars, everyone’s bidding. You drop out at $200. I drop out at $250, leaving Meg the winning bidder at either $250 or $251, depending on who bid $250 first. The bidder with the highest valuation won, and the price they paid is the valuation held by the bidder with the second-highest valuation. (A nit-picky academic aside: If you assume that bids can be made in any increment, the winning bidder will pay a fraction of a cent more than the second-highest bidder’s valuation. That’s why it’s expressed as the second-highest valuation; a bid of $250.00000001 is close enough to $250 that there’s no point in distinguishing.)
It doesn’t matter whether Meg thought the card was worth $300, $650, or $10,000. The second-highest bidder’s valuation sets the price. That’s not how free agency works. If Team A offers Player X a $100 million contract, Team B can’t listen in on the phone line and say “$101 million” only for Team A to counter with “$102 million” and so on. Relatively few offers are made. Generally speaking, they’re made without exact knowledge of what the other interested parties are doing. When Team A offers that $100 million contract, they have no way of knowing whether other teams are in the same ballpark as them. Maybe the next-highest offer is $80 million. Maybe there’s already a $130 million offer on the table.
Before I get into the meat of my argument, it’s worth making one thing clear: Money isn’t a proxy for anyone’s value. There’s no way around modeling it that way in these simple abstractions, but they’re just that: abstractions. They aren’t a perfect mirror for the real world. To come up with a model, you have to have some kind of single-unit measure of value, and I’m using dollars for the sake of simplicity. That’s not real life. The optimal amount to offer someone in exchange for their services playing baseball doesn’t say anything about their “worth”; it’s just economic (and free agent contract) shorthand.
Let’s return to free agency. The best way to describe these negotiations, for the purposes of defining a generic game, is a first-price sealed-bid auction. In this style of auction, bidders submit a single sealed bid without knowledge of other bids. The seller then selects the highest price and sells the good to that bidder for that price. It’s not quite a perfect fit – negotiation happens after bids have been submitted, and teams frequently submit multiple offers over time – but it’s a good first-order approximation. And the established strategy is decidedly not “bid what you think the good being auctioned is worth.”
Let’s talk about why. Assume our three-bidder envelope scenario from above. Further assume that the value of the envelope is $100, and that the three teams bidding for the envelope have analysts who independently calculate their own expectation of that value. Those calculations are randomly distributed around $100, with a standard deviation of 15 percentage points.
In the case where each team bids 100% of their calculated value, they each win a third of the time (obviously). On average, the sale price is 112.7% of $100 – oof! Imagine being one of those teams of analysts and suggesting this plan to your boss. “We’re going to bid in an auction. We’ll win a third of the time. On average, we’ll be overpaying by 12.7%. Oh, and we’ll only pay less than the envelope is worth 12.5% of the time that we win.” This is an obviously abysmal plan.
The clear problem here is that you shouldn’t bid an amount such that you’ll never be excited about winning. If you always pay 100% of what you think a thing is worth, the only way you end up winning is if a) you undervalue the item in question and b) both of your rivals in this game do as well, and by more than you did. That doesn’t happen very often. A better strategy is to bid an amount lower than you think the item is worth, but still close to the value, so that you can still win some percentage of the time without paying vastly more than its value.
To do a bit better than broad generalizations, I wrote a Python script that simulates this auction. That’s where I got the 112.7% number, as well as the 12.5%. That’s with each of the three teams bidding 100% of their calculated value in the auction. To figure out alternative strategies, I can just change the bid.
For example, if Team A bids 88.8% of its estimate while the other two teams bid 100% of theirs, things change meaningfully. Now the results look like this:
| Team | Bidding Strategy | Hit Rate | Average Price Paid | Bargain% |
|---|---|---|---|---|
| A | 88.8% | 14.0% | 104.6% | 32.7% |
| B | 100% | 43.0% | 110.6% | 17.9% |
| C | 100% | 43.0% | 110.6% | 17.9% |
A quick explainer on the columns: bidding strategy refers to what percentage of their calculated fair value a given team bids in the auction. Hit rate is how frequently a given team wins. Average price paid is what percentage of true value (100%) each team pays, on average, across all its winning bids. Bargain percentage is the percentage of winning bids that provide positive value, i.e. where the winning bid is less than 100%.
Now, Team A’s strategy looks meaningfully better to me than their two rivals. They’re winning auctions less frequently, sure, but winning wasn’t so great when it was almost never a good deal. If this is a repeated game (many auctions over time), like free agency, you’d expect Team B and Team C to rein in their strategies. What if they, too, started bidding 88.8% of their estimate in an attempt to rein in costs?
| Team | Bidding Strategy | Hit Rate | Average Price Paid | Bargain% |
|---|---|---|---|---|
| A | 88.8% | 33.3% | 100.1% | 51.2% |
| B | 88.8% | 33.3% | 100.1% | 51.2% |
| C | 88.8% | 33.3% | 100.1% | 51.2% |
That 88.8% figure wasn’t chosen at random; it’s the ratio that, in this example, produces an expected cost of roughly 100% for each bidder if they all follow the same rule. Roughly 50% of the time, the price paid ends up being a bargain, which follows logically. If you want to counter the winner’s curse, you have to bid less than your expected value, and that holds for everyone involved in the bidding.
This isn’t what economists call a stable equilibrium. Now that Team A’s rivals are bidding less aggressively, Team A can bid even less aggressively than the rivals and capture some expected profits, at the cost of winning the auction less frequently:
| Team | Bidding Strategy | Hit Rate | Average Price Paid | Bargain% |
|---|---|---|---|---|
| A | 85.0% | 25.2% | 97.3% | 62.3% |
| B | 88.8% | 37.4% | 99.3% | 54.5% |
| C | 88.8% | 37.4% | 99.3% | 54.5% |
Now, on average, is this deal worth it for Team A? If all they care about is maximizing excess value, sure. If they’re targeting some minimum amount of value added – imagine this past year’s Giants, who had money to spend and wanted to add some talented players with it – being more passive than breakeven might be a bad strategy, because it has a chance of leaving you with nothing.
Interestingly, Team A bidding less aggressively makes Team B and Team C’s outcomes look better, even with a static bidding strategy of 88.8%. As Team A gets even less aggressive, things continue to look rosier:
| Team | Bidding Strategy | Hit Rate | Average Price Paid | Bargain% |
|---|---|---|---|---|
| A | 75.0% | 8.7% | 90.0% | 88.4% |
| B | 88.8% | 45.6% | 97.6% | 60.6% |
| C | 88.8% | 45.6% | 97.6% | 60.6% |
Maybe that’s a Tampa Bay style of strategy. Come in low, knowing you’ll usually miss. When you do hit, you’re probably clearing a good deal. On the other hand, if one of the bidders gets extremely conservative, maybe it makes sense for another bidder to get aggressive to take advantage:
| Team | Bidding Strategy | Hit Rate | Average Price Paid | Bargain% |
|---|---|---|---|---|
| A | 75.0% | 7.2% | 90.5% | 87.3% |
| B | 92.0% | 52.9% | 100.0% | 51.7% |
| C | 88.8% | 40.0% | 56.7% | 57.7% |
Team A’s timid bidding means that the winner’s curse is lessened. Plenty of times, Team B will win not because it has the highest valuation, but because Team A just isn’t competing enough. That opens room to get more and more aggressive in bidding relative to modeled value. Now Team B is winning the auction a full half the time without losing money on average.
You can play around with this style of analysis endlessly. Team C might actually have room to get less aggressive themselves at this point, since they’re generally going to beat Team A anyway. If they back off, they can win a ton of auctions while still getting meaningful positive value on the ones they win:
| Team | Bidding Strategy | Hit Rate | Average Price Paid | Bargain% |
|---|---|---|---|---|
| A | 75.0% | 9.7% | 89.5% | 89.5% |
| B | 92.0% | 63.0% | 98.6% | 57.0% |
| C | 83.0% | 27.4% | 94.0% | 74.2% |
If teams have to act without knowing their rivals’ strategy, there’s no strong-form equilibrium to be found. Game theorists have calculated what’s called a Bayesian-Nash equilibrium for one form of this auction when auction valuations are drawn from a continuous uniform distribution, but that’s not what we’re dealing with here. In any case, the right behavior for a given team depends on the behavior of others, but in every case, the optimal bid is less than 100% of calculated value.
This makes sense intuitively. Imagine a GM winning the auction to sign an impact player. If the “every team bids up to its indifference point” crowd are correct, that GM’s reaction should be just that: indifference. “I like my team the same as I liked it before signing Bryce Harper because I made a bid of exactly what I am willing to pay to the point where his deal has no surplus value.” That seems dumb on its face. Teams don’t bid for free agents because, if their bid is accepted, they’ll be indifferent. They do it because they want to add that player at that price. They’d prefer to win as opposed to lose the bidding. Otherwise they wouldn’t bid that much!
If teams are acting as economically rational actors, they should rue missing out on free agents fairly often. To leave yourself room to come out ahead, you have to sometimes miss on bargains. Teams are no fools. They understand this concept. I’m willing to wager that, some significant fraction of the time, teams see the terms for a free agent who just signed and think “Ooh, we missed on that one.” When you’re bidding in the dark, that has to be the case if you want to pick a winning strategy in the long run.
For a variety of reasons, this abstracted example isn’t a perfect reflection of free agency. I picked three teams rather than four or five arbitrarily. I don’t have any particular reasoning behind my 15% standard deviation selection; the real variation in projections is likely smaller than that, though I don’t have access to team valuation models to say that with any certainty. Cut the variance term from 15% to 7.5%, and the bidding strategy that produces no excess value moves up from 88.8% for each team to 94.5%. There’s nothing special about those numbers; I’m just using them to show how the math works rather than saying they exactly represent reality.
The very concept that every team has a consistent valuation framework is probably wrong; they all no doubt have some version of it, but players output hits and runs and strikeouts and walks, not dollars. It’s all very indirect, and different teams probably handle that process in extremely different fashions. Should you account for marketing value? Blocking a prospect? A team’s place on the win curve?
A marquee player changes the equation even more. Sure, in theory you’re playing a repeated game, and making good decisions in the long run adds up. But each free agent is unique. You don’t get to bid on Harper 15 times and look at how you did in aggregate; there’s only one of him and he’s not a free agent every year. That might cause teams to diverge from “optimal” long-run behavior; players aren’t fungible, and there really might be no replacing the guy you miss. What are you going to do, trade for him?
I also don’t think that the calculations are done on the terms I’m describing here. Teams almost certainly don’t calculate up some grid of expected production value and discount from there. I assume it happens more organically: A GM goes to their team of contract specialists and says something along the lines of “come up with a contract offer for Player X that will make us happy if we sign him.” More or less wiggle room might get added based on how badly the team needs that particular player, whether the owner is a fan, or whatever other factors you can think of. Game theory never needs to explicitly come into the discussion.
I’m not claiming that I’ve solved the equation. I don’t think I ever will, in fact. Probably, no one can solve this problem perfectly. But I think the general conclusion is inescapable. Teams absolutely expect to get a positive benefit when a free agent accepts their contract offer. A meaningful fraction of free agents sign deals that pay them less per contribution than some arbitrary fair value, normalized across all free agents, would suggest. Mathematically, it just has to be that way.
What should you take away from this article? It’s basically this: stop thinking that a free agent contract is a perfect reflection of exactly what the league, as a whole, thinks a given player’s contributions are worth. Nothing about the way free agency works suggests that conclusion – it’s a logical fallacy. It feels like any auction should find the fair value of the thing being auctioned, but that’s not how it works. Auctions find the auction clearing price, which generally includes some expected profit for the buyer.
Enough competition can erode that expected profit to roughly zero, but even then, an expectation of zero implies that about half of the time, the buyer will be getting a bargain. Other teams know that, and while “what did this guy get in free agency” is a useful data point for working out a player’s value in trade, it’s definitely not the end of the argument. If you want to figure out what teams would give up to get a player, don’t just lean on precedent. Start from first principles and figure it out. The shortcut of “oh they were a free agent so I can assume they are being paid perfectly efficiently” just doesn’t work.
Ben is a writer at FanGraphs. He can be found on Bluesky @benclemens.
As an A’s fan, I can tell you with supreme confidence their free agent strategy of “Nope.” is never meaningfully better than any of their rivals.
/s
I’m impressed you’re still an A’s fan.
where’s the sarcasm?
I mean, “Nope.” might be a better FA strategy than “Let’s give half a billion dollars to the rotting corpses of Albert Pujols & Anthony Rendon.”
This is a great article. Thanks for writing / sharing, I love the mathematical underpinning and the framework you used, even if it can never perfectly capture every nuance!
Auction theory is severely tested in real world situations. For example, in a real English auction, many bidders will bid beyond what they intended because they get caught up in the excitement of the chase and want to win. (I’ve seen similar things happen in negotiations, where a deal breaks down because someone feels like they need to “win the deal”. While we are supposed to deal with these things dispassionately, unfortunately, being human, most of us let ego or adrenaline get in the way. Auction theory (and in particular the types of auctions like free agency where information is imperfect as to what other teams are offering is imperfect at best) says that usually sellers do better. But Scott Boras, knowing this, pushed this too far this year, probably costing his clients money in the long run.
Economic theory and game theory usually work fine if the sample size is big enough. But these sample sizes are painfully small. (And most economic theory barely works in the real world).
Self-bargaining also seeps in during the heat of the moment. “I’m already at 100, what’s 105”, even if you made a decision beforehand that you were going to go to 100 tops. And once you’re at 105, is 110 really so much more?
Anyone who’s played fantasy baseball in an auction format can attest to this phenomenon.
Bingo.I have played a FFL auction league for close to 30 years & while you can have your valuations, it is easy to go over those..& quite frankly, you almost have to.
If you don’t go over, you miss out on all of the top 5 QB’s, top 10 RB/WR, etc & end up with a bunch of mediocre players & about 25% of your budget unused. & when you get to the point where there is only one “sure thing” left, that guy is the most overpaid.
Scarcity is a bitch..only so many stars to go around & if you miss out on them, you’re on the path to mediocrity.
There are definitely ebbs and flows in the auction format as to when guys are getting overpaid. For example in baseball, you really really do not want to be bidding on the last “sure thing” closer. As you said, scarcity is a thing.
Inflation is also a thing over time. I look at the dollar rankings given to players on Yahoo, and I honestly don’t know what leagues those analysts are playing in. Way too low at the top and way too high on the lower middle end. Nobody’s paying $10 for mediocrity, they’re saving that money, picking up a $1 guy, and putting the $9 toward their top picks. Now rinse and repeat with multiple guys.
This and then some. We “let ego or adreneline get in the way” Or affection. Or fear. Or frustration. Or sleep deprivation. Or distraction. Or or or…emotions, motivations, or…heck, bodily sensations. “Being human” doesn’t need the modifier “Unfortunately.” We just are.
Your concluding sentence could be your header instead of tucked in parentheses at the end. “Most economic theory barely works in the real world.” (Though perhaps it’s overstating the case since my impression is the discipline has moved on since I was in school 100 years ago and Milton Friedman and rational choice theory ruled.)
(Okay, I haven’t taken more than Macro and Micro over 40 years ago so have at me all you economists.)
Maybe I’m misunderstanding the article, but common-value, sealed-bid, first-price auctions have a symmetric equilibrium. It’s not a closed-form solution, but one could calculate the optimal bidding function for any set of parametric assumptions on the signal-generating process. I don’t think I can format math here, so I can’t just copy-paste the proposition and proof, but it’s Proposition 6.3 in Krishna’s Auction Theory, Second Edition.
These are not common value auctions. While there will be correlations among values, they could vary significantly from team to team.
Ben is contending in the article they are common-value — an envelope with $100 is worth $100 to each of them. I’m just referencing his assumption, not making a claim.
Agreed, but I’d go even further to make the claim they’re closer to common value than private value on that spectrum. There’s both private value and common value components, but surely we agree that the majority of a player’s performance is common across which team they sign with.
I also think Ben doesn’t need the common values assumption to make his point – “bid the expected second order statistic conditional on my value being first” is a symmetric BNE in a sealed bid first price private value auction. Bidding your value is weakly dominated in first price auctions in the private values setting..
Yeah I agree that we’re almost certainly closer to common value world than private value world. And yes, I agree that if the point of the article is that “a player making 20 million this year doesn’t mean that his expected contributions are valued by his team at 20 million”, you could make that point using a private values auction.
Reading this made me curious if there is every a feedback loop for bidding from agents to teams around contracted terms. I know they likely keep bids close to the chest in order to maximize the value of subsequent bids, but do agents ever tell GM’s something like “you’re about 10 million short” or whatever the number is in order to push teams to adjust their bidding strategy? I understand that a lot of this bidding happens in a vacuum without knowledge of competing bids, but I also know that it may be in an agents favor to play teams against each other during the bidding process to increase maximum value. Or do teams just simply not tolerate this back and forth?
Isn’t this what agents do? An “agent” acts, it’s not like the player is just totally passive in all this. My understanding is that it’s a lot of check-ins between front office members and agents rather than anything formal.
That’s kinda what I thought which makes me think that it’s not so much as a blind auction (since there is a revision loop to the bidding process) and more of a competitive bidding process.
just watch “ Hard Knock “ NYG episode concerning Barkley. It supports your theory. Back and forth etc. an agent isn’t doing his job if he isn’t pushing that envelope.
I would be very surprised to learn that FA bids/contract negotiations operate like a sealed bid auction.
Offers and terms get leaked publicly with some level of frequency by both teams and agents, so I strongly suspect that there’s a significant level of communication between the parties that we never learn about.
I bet they are closer to the sealed auction bids than people think. Teams have gotten burnt by misinformation so much. Boras kept implying that he was having serious discussions at his proposed price points all off season and none of the teams paid him any mind and stuck to their price.
One strong reason to think this is because in the environment that Ben describes, the auction format that maximizes revenue to the seller (so the auction format that maximizes a player’s contract) is the English auction. Basically, the player has an incentive to tell every team what the other offers are truthfully. Obviously, they also have an incentive to inflate the other offers when reporting them, but if you think that agents do this quite a bit, they have some reputation-based incentives to not do so.
if I recall my auction theory correctly, expected revenue is the same regardless of whether the auction is first-price or second-price, English or Dutch.
True, the way to increase expected revenue is to set a reserve price (an optimal auction, Myerson ’81 https://faculty.econ.ucsb.edu/~garratt/Econ177/Chapters5and6.pdf). Which might correspond to free agents going unsigned when the season starts—you could think of, say, Jordan Montgomery saying he wouldn’t sign a contract for less than some reserve and hoping there was one team that would offer it (ofc there are more complicated dynamics at play with the ability to then change that reserve price, negotiate and sign at the start of the season).
That’s true in certain cases! The most common auction format that gets taught is one where everyone has symmetric and independently distributed private values — in that case, you have revenue equivalence across the auction formats.
Here, though, if we’re assuming interdependent values and affiliated signals, that revenue equivalence principle doesn’t hold.
Right, teams bid on free agents to fill a need and they know most of the 26 guys on the roster are paid well below what they’re worth.
Front offices in free agency are less concerned about high fiving a “bargain”. MLB is already set up where the best player in the universe can be making the league minimum. Mike Trout won an MVP on the league’s minimum wage. Judge and Alonso hit over 50 homers while earning pennies on the dollar. Even guys who are in their final year of arbitration are only earning about 80% of what they’re actually worth.
Yes? I agree. But this seems to imply that there are teams kicking themselves for not signing a player at a bargain price. Maybe later in the offseason when they’ve committed a bunch of money to random guy A and Matt Chapman signs for the same amount of money they’re annoyed, but I don’t think teams worry about missing out on a specific player. If they haven’t gone after a guy, it’s because they have a backup plan that they’re comfortable with.
The reverse scenario is much more likely to be true–a player gets an offer notably beyond what another 28-29 teams will pay. The most extreme examples are a meddling owner wants to make a splash and pays whatever it takes. But typically if an agent thinks that another team would be willing to pay their client more money then they do something about it. This is why it seems a lot more likely that a consensus value is likely to be under the final signing price and not over it. In other words, free agent deals definitely can have negative trade value the moment they are signed, because in a lot of situations (but not always) if a team wanted to take the player at that price they would have offered a deal at that level.
I disagree that “FA deals definitely can have negative trade value the moment they are signed.” I know I write this every trade deadline, but Trade Value is much more tied to the player’s forecasted WAR (say zWAR for example or Steamer WAR) than it is to Surplus Value. You can always send a bad contract back to mitigate the money.
Moreover teams focus on maximizing Wins in their playoff window. The Rays probably win every year in Surplus Value, but their goal is to win the World Series. Thus, I agree totally with your comment below that I don’t believe teams underbid for a lot of FA’s hoping they’ll win. Most FA’s get what Ben Clemens projects them to get. I think we only find a few “bargains” every FA season, but a lot more of “hmm, that contract needs a lot to go right for the team not to regret it.” Still, if you’re a team in your playoff window, you’ll take that shot.
More generally, I just don’t think the model of how teams behave in this article makes any sense. What probably happens is that the front office gets a budget from ownership while the front office decides how many wins they want to add. And then the front office tries to add that number of wins with the resources they have available. There are good reasons front offices want to save money, because they want to ensure that they have more resources to work with if they need to. What looks like “isn’t competing enough” is just the banal observation that they think there’s a better way to get to their desired win total than getting caught up in landing a particular player.
I like the piece. Interesting and different.. Hypothetical if you are a contending team: You won 85 games last year, just short of playoffs. Your key pieces will be back. You had a hole at, say 3rd, a Replacement-Level Killer. There’s a 3QWAR FA 3rd baseman available. Do you jump in early and overpay?
You are adding a second value: a premium above market value representing your need at the position. I think the idea is that your need impacts the bidding strategy, so to answer your question: maybe?
Good reply, Thanks
Is this premise true at all? I have always more or less taken it for granted that there’s a lot of (effectively) collusion between front offices, as well as wink-and-nudge communication by the agents, and that their bids against each other are far, far less than “blind.”
I don’t think that anyone who reads FanGraphs ever believed that “a free agent contract is a perfect reflection of exactly what the league, as a whole, thinks a given player’s contributions are worth.” We all understand that free agent contracts are heavily influenced by which large market teams are active, what they need, how many alternatives are available at that position, and owners occasionally doing something completely irrational.
We discuss contracts as an approximation for market value simply because that is useful for comparisons, but we all understand that some contracts are bargains and some are an albatross. Orioles fans remember how Scott Boras convinced Peter Angelos to offer more than twice as much as any other organization did for Chris Davis, a mistake that has crippled the team’s payroll ever since.
That risk assessment is another factor in any serious discussion of contracts, as small market teams can be undone by one massive mistake, whereas the Yankees and Dodgers can afford to offer more than they believe a player should get.
I think the price other teams pay in the recent past has a profound effect. I wonder how much money Mike Trout has not only cost himself but cost others by not holding out for free agency not once but twice. That also explains why owners hate the idea of the truly most wealthy people joining their club. Cohen’s spending spree has not been beneficial to the Mets, but it could help drive up prices. Look at Wheeler’s recent deal.
I think Ben’s analysis is very good, but we should also consider that these negotiations are not performed in a vacuum. If Paul Goldschmidt signs for 5/$130 million, you can bet your ass that Freddie Freeman is going to want and expect more, no matter that WAR projections say (which were hilariously wrong in that case anyway).
I personally would have been thrilled to get a great player for exactly what I think he’s worth. I doubt the Phillies regret outbidding everyone for Bryce Harper, the Yankees for Gerrit Cole or Aaron Judge, or the Dodgers for Freddie Freeman or Shohei Ohtani.
On the other hand the Red Sox should be kicking themselves for not outbidding the world for Mookie Betts. Angels signed Trout for a huge amount and it hasn’t worked out but it wasn’t a bad move, or at least I don’t remember anyone saying so at the time.
It’s not about getting the best deal. It’s about adding the most franchise value. Getting Aaron Judge for 20% more than the Yankees paid is still better than not getting Aaron Judge.
I absolutely make my best offer immediately and then concede if it’s not good enough. I’m happy with whom I’ve hired. That I paid 50% above “market” is fine. I have the right person and they’re not looking to leave.
“The optimal amount to offer someone in exchange for their services playing baseball doesn’t say anything about their “worth”; it’s just economic (and free agent contract) shorthand.” – You didn’t need to include this statement, but you did. Thank you for that.
Thanks for the article, Ben.
What does ZiPS have to say about this? I agree with your logic but my gut sense (which obviously could be very wrong!) is that players don’t usually sign tremendously below their ZiPS-implied value over the life of a contract.
I know ZiPS isn’t the final say on these things (gasp!) and that there are many kinds of valuation models out there — but it would be interesting to see if the contracts players sign usually come at a discount, what that amount typically is, and whether it’s evolved over time.
Both state and county taxes come into place here too. A $100 million contract with San Francisco is significantly less for the player than the same contract in Texas.
Lived experience shows that for the most part the very rich care about other factors more than state/local taxes, and the construction of the “jock tax” also mitigates this, along with other aspects such as marketing opportunities and preferences such as culture, weather, etc.
This is the kind of thing that matters to some players a lot more than others. Greinke really didn’t want to play in California for this reason but for others the dollars are more about feeling valued than take home pay.
I’m not sure I agree with the premise that players have an equal value to each team. Depending on where a team is on the win curve and the size of their market, each marginal win will have a different value for them. On top of that, you’ve got different levels of positional need and any number of other baseball-related factors.
To take one extreme example, Matt Chapman surely had much more value to the Giants than he would have had going back to the As this year. The Giants were at a crucial point on the win curve with a large potential revenue and could expect a few wins to significantly increase their revenue this year, while the As would have gotten fairly little difference to their attendance and revenue from a few extra wins. The Giants had rational reasons to work from a higher estimate of Chapman’s value to their team, even with a better 3rd base situation than the As.
This was just so good. As an econ grad, it’s always a joy to read articles like these. Very easy to follow and comprehend. Great work!
This is an interesting concept, but I’m not really sure what the overall point or conclusion is here.
You’re starting with a flawed metaphor/abstraction, acknowledging immediately that it doesn’t apply well, and then ending with “aha, I told you it was flawed!”…?
Well yeah… I’m not the one who brought it up, bro!
I don’t think you can extrapolate your auction example to free agency.
There are many pools of free agents: the stars, the old guys, the non tenders, the coming back from injury. Valuation methodologies will very widely. Then there is tenor. This isn’t a one price clears all market. There’s number of years which is also a huge variable. There are lesser issues as well (tax rate, geographic location, etc). Thus the solution is a combination of a multitude of factors (see: Correa C)
Then you have the issue of suitors. Some guys have the whole league interested (Yamamoto) and others have no one (Pham)
I’d hazard that the market established is pretty much the correct valuation. There are a few contracts that end up being wildly high or low but the vast majority look like they get it about right
I’d say the process is more like buying a house where the seller gets “sealed bid or bids ” and then tries to cajole other buyers into a bidding war or at least a second offer. I think the mechanism also ensures pretty fair results most of the time
Love the intersection of analytics with business strategy here. I do have three comments/questions for consideration:
*As noted by others, there is an information market for free agents – agents and media insiders. It’s not perfect for sure, but teams do have some insights into the marketplace.
*Second, contract structure will play some role too. For example, increasingly players are looking at tax strategies in their contract structures (see Ohtani’s deferred money). The willingness of a team to enter into creative contracting is also an increasing factor beyond money.
*Finally, a larger point. Maybe I missed it or misunderstood it, but I’m not sure an auction captures the entire value of free agent signings as a proxy. One key component of a signing is not only that you get the value of the player’s services (i.e. win the envelope), but that you deprive competitors of their services too. Let’s take Harper – your example. When Philadelphia signed him, they didn’t only get his envelope of performance for 13 years – they deprived the Nationals and perhaps the Braves and others from getting those services as well. That deprivation value can be significant as it is in the NL East now.
Your model appears to look at winning the auction as the singular game being played. In baseball, it is only a part of a larger competitive framework. So, looking narrowly at winning the “envelope” could be understating the value of a signing within that larger competitive framework.
For me, the better proxy is the game of Monopoly. Limited money, scarce properties, known values, and buying properties deprives your opponents of their future rent stream. There are a million Monopoly strategy posts, but buying lesser properties not often landed on for less money as an efficiency play (let’s call it “Monopolyball”) isn’t often touted as the best way to win.
As others have noted, in life your best purchases are often the ones you think at the time are overpriced. Thanks again for an interesting read.