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SQ Featured Article: Baseball Free Agency and Auction Theory

As the MLB enters winter meetings and the free agency period heats up, there have been a flurry of signings–some of them seemingly good, others that probably left you scratching your head. There are a lot of factors that go into signing a free agent, ranging from the number of potential suitors to the scarcity of players at the given position in that year’s market. It can be tempting to look at these signings from the perspective of a single team using an approach that looks at team finances, need, and historical prices. Evaluating a transaction, however, should involve many more factors than this somewhat one-dimensional approach allows. Auction theory, on the other hand, goes a long way to explaining the behavior of free agency markets and provides a more complete set of criteria upon which free agency signings can be evaluated; the following paragraphs lay out the basics of auction theory and explain its application to free agency markets.

The first thing to note for those new to auction theory is that not all auctions are created equal: they come in flavors that include first-price auctions, second-price auctions, all-pay auctions, etc. Common to all auctions, however, is the principle that each of the parties participating in an auction (in this case the teams bidding on a player) theoretically has an ideal bidding strategy that serves as a best response no matter what the other bidders do. Each bidding strategy depends on the value of a player for a given team as well as the type of auction in place. Unlike standard auctions however, each team has high degree of information about the other bidders preferences and player values, based on their knowledge of that teams structure and their prior “bidding” history.

Most free agency markets work like an ascending first priced-auction, meaning teams bid as the price goes up until all but one team drops out, at which point bidding ceases and the they pay their bid. The player may use other teams’ bids as leverage to get a higher bid, so values are not sealed. Each player has a minimum value at which they are willing to work which functions as the starting price, at which point the lowest bid becomes the de-facto reserve price. What’s different about FA versus a standard auction is that if a team’s first bid is below the players minimum working value, than they could be insulted and less likely to listen to future bids from that team– or even exclude them from the auction entirely. Another primary difference is the asymmetric information that exists among teams in relation to a given player: teams have limited knowledge of the player’s physical characteristics, injuries, tendencies, and mental health, giving teams that have hired the player recently a significant advantage. Familiarity can even lead to a price discount if the player feels more comfortable with that team, or the team knows about an injury that other teams might not. In this case, teams have an incentive to keep that information to themselves to use as leverage against the player. Even though the “informed team” might not have the highest initial bid, if the information is revealed then other teams will lower their bids and thus the player’s selling point past what the informed team originally offered. In most cases the player would rather take the low-ball offer than risk the collapse of the bidding market, in which case the final bid might be even lower.

Timing in these auctions also has a lot do with the final bid price. In some cases it is advantageous for a player to sign with a team relatively early, before the big money teams drop out of the auction. In other cases a player may wait in the hope that teams continue to drive up the price to the point the player is signed for much higher than his true value. In general, when it comes to starting-caliber players, teams have the same preferences (i.e. they rank the players in the same order) and thus once the bidding for one player surpasses a team’s willingness to pay, they will immediately move on to their next choice. This can prove problematic for big name players that draw out bidding for a long period of time and run the risk of having the market cut out from under their feet, as in the case of Edwin Jackson.

As a general rule, the players of mid-to-low value in a given year’s market will sign sooner because, while multiple teams may value them, it is much more likely that a team will choose to reallocate their funds to another player that would provide them a bigger “profit” (in the sense of the player value, factoring in team needs, versus that player’s costs) than a higher value player. There is also the case where a mid-tier player is overvalued initially and so has an incentive to sign before the market is set.

Additionally there is a subset of players to whom the “Dutch descending auction” is more applicable. With such an auction, there is an initial high price that slowly goes down until one team agrees to pay at that price, at which the point the auction is over. These are your players like Michael Bourn who claim to be looking for a five year, $100 million dollar contract. Since the Vernon Wells fiasco, teams have been less likely to even consider absurd demands of that nature. Bourn will have to lower his price little by little until one team agrees to pay that price, at which point he will sign. Teams have an incentive to wait for his value to be lowered over time– but if they wait too long there is a chance he will sign with another team and their opportunity will be lost.

To illustrate the points above, let’s look at a few of the recent signings and evaluate them using this framework. The first singing is B.J. Upton, who was the biggest name on the market outside of Josh Hamilton. Hamilton, however, is on a different tier in terms of bidding and perceived value, so he doesn’t really factor into this auction. This is a case where history has affected the perception of a player, with Andre Either’s five year, $85 million contract being the highest for a player of that tier. Either was widely considered to be overpaid, which made the auction for an Upton a descending bid auction. With the Phillies possibly in the market with their fairly deep pockets, the Braves acted quickly to snag Upton at a five year, $75 million contract in anticipation of Bourn’s departure. Based on the measure of Upton’s dollar value added over the past few years, this is a reasonable contract; however Upton’s peripherals are worrisome despite his tremendous natural talent.

A more traditional signing, in the auction sense, was Mike Napoli, who was in a unique position because of his higher defensive value as a first baseman than at catcher, but it his great hitting that overshadowed both. His wRC+ average for his past two years starting for the Rangers is 145.5, which is excellent for a catcher and good for a first basemen. Keeping Napoli at 1B puts less stress on his body and should keep his hitting consistent, which is probably the Red Sox’s rationale. Though Napoli was fielding multiple bids, it is likely that the Red Sox were one of the few offering three years at that level of value. Bidding stopped there because even if other bidders had higher per-year values, projecting a 31-year-old player with a body type that doesn’t typically age gracefully at age 35 is a risky proposition. You’d think that Napoli’s archetype as a “power hitter’ would allow him to wait longer and accumulate value as many of the other options dried up, leading me to think that the Sox had far and away the best bid on the table. In that sense, they may have overbid. But at the same time they may have put off other bidders, some of whom may have reached that total incrementally, by offering so much so quickly. In other words, the strategy may have been viable because, if the Sox had offeredless initially and slowly raised their bid, other teams may have stayed in the auction.

The last case we’ll look at is Ryan Madson, a top tier relief pitcher with a killer changeup who sat out the last year because of an injury. Madson took a one year deal last year in a poor market for relief pitchers in the hopes of striking rich this year, but instead was lost to Tommy John surgery. Previously, with his stuff and performance that indicated graceful aging, he would be in for Jonathan Papelbon money. But it was not to be. Instead this was essentially another ascending auction where values were known (everyone could use an elite relief pitcher), but level of risk that each team was willing to take on was not. Thus it was more a sealed bid auction, where bidders submit their values all at once and the highest bid is chosen. It is not advantageous for teams to reveal their risk tolerance, and so Madson chose the bid that had a higher risk but with a return closer to what he could have received pre-injury. Such an auction incentivized participants to bid their risk-adjusted value because overbidding could be costly with a lower expected value, and underbidding could result in a loss of the player because of the sealed bid format.


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