One of the main rules we consider when choosing between fantasy baseball leagues is how players are assigned to teams at the start of and throughout the season. While drafting remains the most popular way to set initial rosters, auctions are the most popular alternative. Auctions are also the dominant method for acquiring free agents in high-stakes leagues like the NFBC. The influence of auctions on fantasy baseball prep materials shows up predominantly in how we quantify player value. We use dollar amounts to represent player values rather than round equivalents in part because it makes identifying tiers of players easier, but also because it can be directly mapped onto how one should think about pricing players in an auction format where every player is available to every team. Auction values inform how to bid in an auction, but there’s more to an auction than knowing your values. This article aims to provide an introduction to relevant parts of auction theory and apply them to some common decisions faced by fantasy baseball managers.
Common Types of Auctions
For this article, I’m going to take as given that managers have identified an expected dollar value return for each player before the season begins. I’ll also assume that, for free agent auctions, managers have identified the expected value of a player in terms of their free agent acquisition budget (FAAB). How a manager transforms that dollar value into a bid should depend on the auction’s rules. Fantasy baseball auctions are usually one of two types: an open-cry, ascending-bid (“English”) auction or a sealed-bid, first-price (SBFP) auction.
The English auction is probably what comes to mind when you imagine an auction. A group of potential bidders calls out increasing prices they’re willing to pay, perhaps subject to a minimum increase between bids. For our purposes, I’ll use the most common bid increment of $1. Whoever bids the most wins the good and pays the auctioneer the amount of the final bid. If we ignore the possibility that the last bid is a “jump bid,” where the bidder increases the bid by more than the minimum increment, the winning bidder pays the second-largest bid plus a dollar. This is true whether the winning bidder is slightly more optimistic than the second-place bidder or wildly more optimistic about the value of the player. Despite paying the amount of the final bid, these types of auctions are functionally “second-price” auctions. In certain settings, although I’ll argue later that fantasy baseball does not qualify as one of them, an English auction is equivalent to a sealed-bid, second-price (SBSP) auction where bidders submit bids to an auctioneer who gives the player to the highest bidder at the price of the second-highest bid plus a dollar. The distinction between the two is whether the bidding happens publicly or privately, and therefore whether bids convey information to other participants in the auction.
The other relevant type of auction for fantasy baseball is a sealed-bid, first-price auction. In an SBFP auction, all participants submit a private bid to the auctioneer. The auctioneer awards the player to the highest bidder, who pays their bid as the price. Free agent bidding in many leagues, including high-stakes leagues like the NFBC, is conducted via SBFP auctions. The main distinguishing feature between SBFP and SBSP auctions is that the amount the winning bidder pays for the player is their own bid, not a function of the bids of other participants. If you’re curious, there is an open-cry equivalent to the SBFP auction called a “Dutch” or “clock” auction, but these are less relevant for our immediate purpose.
Information in Auctions
To know how to bid, we have to be careful about where our estimated dollar values come from. The easiest type of auction to analyze is one in which a bidder’s valuation of the item is independent of the other bidders’ valuations. These are called “private values” auctions. The archetype of a private values auction is an auction of a painting where the buyer has no interest in reselling the art, but merely derives some pleasure, determined by their taste, from looking at it. Importantly, there’s no uncertainty in a private values auction: we can determine our own willingness to pay for a piece of art without reference to any external information. English and SBSP auctions are equivalent in a private values setting. In a private values English auction, it is always best to bid so long as the price is less than your value for the player. In private values SBFP auctions, as opposed to SBSP auctions, you should never bid up to your value. Bidding your value in an SBFP auction guarantees you cannot get any positive return on your investment. Shading your bid below your value reduces the probability that you win the player, but gives you a positive return when you do win, leading to a positive expected return on your bid. Unfortunately, private values is not an accurate description of auctions in fantasy baseball.
When we auction a player in fantasy baseball, we’re buying a bundle of statistics and position eligibility that would be the same for every fantasy team in the league. In a points league, that bundle of statistics is worth the same amount of points for every team. This situation is called a “common values” or “interdependent values” auction. The challenge we face is that we don’t know what those statistics are going to be until the season has been played out; we’re facing uncertainty in how to value the player being auctioned. The archetype of a common values auction is an auction for the right to drill for oil in some unexplored oil field. There is a true amount of oil available, which is unknown to the bidders until they start drilling. Fantasy baseball auctions are somewhere in the middle, although closer to the common values end of the spectrum. If you’re facing a decision that’s constrained somehow by how you’ve constructed your roster thus far, a player may be more valuable to you than to the rest of your league based on your build. That margin is a private values component, but the player’s actual performance is the same across teams.
In common values auctions, auction theorists usually think about bidders as having “signals” of the true value of the good up for auction. In fantasy baseball, projections are signals of the true value of a player. No projection system, even if it made zero error in aggregate, will nail every player’s performance. Instead, projections are positively correlated (we hope) with the actual performance of each player. However you choose to combine projections to generate an estimated dollar value for a player, that estimated dollar value is your signal. Since you’re here, it’s likely the case that you’re going to rely a little more on PLV-powered projections than the rest of your league; that’s one source for how your league can come to different signals of a player’s value.
The Winner’s Curse
The winner’s curse is the most famous idea associated with common values auctions. Andrew Friedman gave a succinct explanation of the winner’s curse shortly after joining the Dodgers, saying, “If you’re always rational about every free agent, you will finish third on every free agent.” If teams use the same sort of dollar-per-WAR or other valuation methods for free agents, then the largest contract offer a player receives will be driven by which team has the strongest positive signal about the player. Even if each team’s signal is statistically unbiased, the maximum signal will be (on average) an overestimate. In other words, players end up getting the best offers and signing with the teams that are most likely to have overestimated their future performance. The same is true in fantasy baseball.
When bidding and winning a player, you receive the information that no one else valued the player as highly as you do. The logic of the winner’s curse tells us to reevaluate whether you got a good deal on that player and to reduce your expectations for the rest of the season. In FAAB bidding, the only additional information we get is that everyone else’s signals were smaller than the winning bid. In the English auction we use to allocate players at the start of the season, we gain even more information because we can see the price at which each other team decides to stop bidding. While a hyper-rational textbook bidder could perfectly adjust for the new information, it’s unlikely that MLB or fantasy teams are doing so perfectly.
One way to consider the magnitude of the winner’s curse is to compare average auction values (AAVs) to the value each player returns at the end of the season. As an illustration, consider the outfielders who were drafted in the first two rounds last year. The AAVs below are derived by mapping each player’s average draft position to the equivalent average auction value from the first 25 NFBC auctions this season. The end-of-season values come from the Fangraphs auction calculator.
Assets from Freepik | Featured Image by Justin Redler (@reldernitsuj on Bsky/Twitter)
