Auctions are an integrated part of a lot of fantasy baseball leagues. Many drafts are arranged as auctions in which owners engage in bidding wars to acquire players. This is typically done in the form of a so-called English auction, where one owner announces a starting bid and others then beat that amount incrementally. However, auctions are also sometimes used when deciding the distribution of free agent players. Normally these auctions are sealed-bid auctions, in which every owner only gets to submit one bid without having any knowledge about the actions of the others.

This article seeks to describe a certain type of sealed-bid auction, namely Vickrey auctions (also known as second-price sealed-bid auctions). In regular sealed-bid auctions the winner of the prize (i.e. the fantasy player) is simply the owner with the highest bid, and the price he has to pay equals his bid. This, however, opens the door for speculation. The simple rules of Vickrey auctions erase the incentive to not bid according to your true evaluation of the player.

The scope of this article only encompasses sealed-bid auctions, but the conclusions in the section titled “True Value” actually apply to all kinds of auctions.

Rules

The rules of a Vickrey auction are simple: Each owner submits a sealed bid in the form of free agent money (FAAB), and the player auctioned is then awarded to the owner with the highest bid. The trick is that the price which that owner has to pay is not equal to his own bid but, rather, equal to the next-highest bid in the auction.

If there is more than one “highest bid”, the league will have to devise a tiebreaker rule. For example, the player could be awarded to the team which is lowest in the overall standings of those highest bidders (the price paid being that team’s bid).

A common variation is that the auction winner has to pay $1 more than the next-highest bid. More on this later.

One might suspect that the rules for Vickrey auctions would open the door for even more speculation about the preferences and tactics of the other owners. However, this is not the case as I will demonstrate shortly. First, it is necessary to describe exactly what is meant by “value”.

True Value

A crucial concept in fantasy baseball is that of context. We all know that position scarcity matters a lot and most owners know how to adjust their bidding according to their current needs and even the needs of the other owners.

What most people fail to realize, however, is that the term “value” actually goes well beyond just those considerations. Many owners will enter a draft day auction with the belief that the first player announced is worth $15 but then actually end up getting him for $18 simply because “you wanted him badly and you didn’t ridiculously overspend”. This may seem like a very human act, yet it is quite risky and very unscientific – and, frankly, unnecessarily dumb.

I will now introduce the concept of a fantasy player’s Estimated True Value (ETV for short). I just coined that term for this article, so don’t Google it or tell it to your kids. This concept applies to all sorts of auctions. A player’s ETV is what you estimate is the value of the player all things considered. Those last three words are to be taken quite literally. Here are some of the considerations that enter the picture when determining a player’s ETV:

1. Your estimate of the mean of the player’s statistics from this point of the season and out relative to your current roster’s production (“mean” is a term from probability theory which, in essence, means “the expected result”).
2. Whether you play in a keeper league or not.
3. Your place in the league standings of each individual fantasy stat category and the gap to the nearest competitors in each category.
4. The other owners’ place in the category standings (i.e. can you hurt a rival by acquiring the player).
5. Position scarcity.
6. Player pool scarcity (i.e. if there are only few useable players left in the free agent pool, and you know the other owners are also interested in them, the higher demand will inflate the price).
7. The cost of not getting the player (i.e. if your only catcher has landed on the DL you might be willing to give up more in order to have a healthy line-up for the following week).
8. Your remaining FAAB (i.e. if you only have few free agent dollars left, you will lose flexibility by spending them all on one free agent).
9. Your personal risk profile (i.e. you may want to pay a little extra for established veteran players with a more certain skill set, or you may want to pay a little less for injury-prone players that could potentially yield zero value for you, or you may want to pay more for youngsters with very high ceilings). This can essentially be viewed as the price of the standard deviation (another term from probability theory).
10. Etc.

I am sure you will be able to add more points to the list. The basic idea is that spur-of-the-moment irrational evaluations are disregarded when dealing with a player’s ETV. Everything should be taken into account on beforehand.

Obviously, it is very difficult to put a price tag on many of the elements listed above. The weighted mean of a player’s stat lines can be gleaned from projection systems such as PECOTA, from experts like Mike and Cory on MLB Radio’s Fantasy 411, or from gut instincts and experience. The rest of the points are harder to quantify and the methods for this lie beyond this article’s scope. However, the important thing is that you – in some way – include all these considerations when describing a player’s value. They should not be regarded as external factors which have more to do with “intangibles” than the process of player evaluation.

It can be quite illustrative to make an analogy to the stock market. When deciding which shares to invest in, a stock broker also has to make an estimate of the expected yield of each share. He also must adjust for the volatility of the stock, his remaining amount of money, his own risk profile, and the cost of not investing at all, for instance. Stock brokers do not face the same problem with scarcity that fantasy owners do but that doesn’t make the analogy less relevant. The important thing is that he has to adjust for a number of factors and that he does this on beforehand when deciding whether to buy or to hold on to the money. Using this analogy, it will be easy to realize the following four points about a player’s ETV:

1. It is (almost) solely based on your own evaluation of the described factors. Therefore, ETV’s will vary, sometimes greatly, from owner to owner. Note, though, that the player pool scarcity is affected by the other owners’ evaluation of the player.
2. ETV’s can change quickly. For example, if a number of players of the same skill set as the player in question are suddenly gone (due to injuries or aggressive bidding), the player’s price will likely rise sharply.
3. You would never want to pay more than the ETV for the player, simply because – all things considered – that would be an expected net loss for you. Now, the player may get hot, or he may go stone cold, but you expect him to not be worth the investment.
4. You are completely indifferent between not getting the player and buying the player for an amount equal to his ETV. Go back to the stock market analogy: If you are offered a share for $10, and you have estimated that share’s value to be $10 all things considered, then it neither constitutes a net win nor a net loss if you buy it.

Optimal Vickrey Strategy

As it turns out, Vickrey auctions provide an incentive for all rational players to bid exactly their ETV of the free agent player in question. Here’s why:

Let us temporarily assume that you only care about how much FAAB you spend yourself while being indifferent about how much the others have to pay for a player if they win the auction. When everyone has placed their bid precisely one of the three following scenarios will happen:

1. The highest bid by another owner than yourself is smaller than your ETV.
2. The highest bid by another owner than yourself is exactly equal to your ETV.
3. The highest bid by another owner than yourself is higher than your ETV.

In the first case it would have been best for you to bid more than the next-highest bid because you will be getting the player for less than your ETV, which is a net win for you. It is just as good to bid exactly your ETV as to bid any other amount of FAAB bigger than the next-highest bid.

In the second case all bidding strategies yield no net gain for you. If you bid less than the ETV, you don’t get the player. If you bid more than that, you get the player, but at the ETV, which is just as good for you as not getting the player (as discussed above). If you bid exactly the ETV, you will either get the player or you won’t (depending on the league’s tiebreaker rules), but in both of these cases there is not net win or loss for you.

In the third case you want to bid less than the highest bid, because otherwise you would get the player for more than your ETV, which is a net loss for you by definition. Since you won’t get the player anyway, bidding the ETV is just as good as any other amount of FAAB smaller than the highest bid.

The preceding argumentation may seem backwards to you. After all, you don’t know the other owners’ bids when you submit your own. This isn’t important, however, as it is clear that in each of the possible cases you can do no better than bidding the player’s ETV. So whether you know the others’ actions or not, the optimal strategy will always be to bid exactly the ETV. Therefore, Vickrey auctions may be described as “honest”.

Variation

Some leagues, such as Tout Wars, use a variation on Vickrey auctions, where the auction winner has to pay the next-highest bid plus $1. Going back to the arguments in the preceding section, it is clear that it is never a good idea to bid more than the ETV with these rules, either. That single dollar does mess up the logic a bit, though. If the highest bid by another owner than yourself is exactly equal to your ETV, it will actually be best for you to bid less than your ETV, because if you bid the ETV you risk (depending on the tiebreaker rules) getting the player for the ETV plus $1, which constitutes a net loss for you. One dollar is pretty insignificant, though, and since it is somewhat unlikely that many owners have determined exactly the same ETV for a player, this little complication shouldn’t change your strategy unless you are really sure that other owners will bid your ETV.

I don’t know why that one dollar is included in the rules since it only complicates matters. Maybe it is due to the fact that, according to the traditional Vickrey rules, when only one owner bids on a player, that owner gets the player for free. If this is a problem, I suggest using the traditional rules but with the addition that in the case of a single bidder that owner gets the player for $1.

Irrationality

All the arguments so far have been based on the assumption that each owner is trying to maximize his profits, i.e. his place in the standings. This may not be the case, though. For instance, if you’re mired in 8th place and you just want to thwart the attempts of your arch rival to win the league, maybe you would rather use every effort to hurt him than help yourself. This is where mathematics and game theory fold and psychology enters the picture. In some cases you may be able to adjust your ETV to these situations, but most of the time you will probably have to expand the logic in order to deal with these irrationalities.

It is true that fantasy baseball in some cases doesn’t seem very rational at all. People act on instinct, or they act out of spite, and inexperienced owners may make completely unpredictable moves. Yet, this shouldn’t change your approach towards the logic of the game. Since irrationality by definition isn’t measurable, it can be disregarded in the decision-making process. If some of these “irrationalities” were measurable, then you could incorporate their effect into your decision-making.

Exploitation

It is sometimes a secondary goal for a fantasy owner to make the other owners pay as much FAAB as possible, thereby rendering them less competitive in future auctions. Therefore, some might employ the tactic of bidding more than the ETV on a player just to make the winner of the auction pay more if you don’t win yourself. This is an extremely dicey tactic, however, because by engaging in the bidding you’re risking getting the player at a price which exceeds the expected proceeds from the player. As such, you need to have a pretty good idea about how the other owners will bid when using this trick in order to calculate how much of your own FAAB you want to risk giving up in return for hurting your opponents’ funds. Also, in most cases, owners will have similar evaluations about a player, and thus they will be bidding approximately the same amount as the highest bidder, so your “exploitation” strategy won’t do much of a difference.

Since there are a striking amount of people who think that you should bid “aggressively” in Vickrey auctions, it is possible to exploit their ignorance as explained above. Some people claim that rational owners should always bid all their FAAB on a player they want in Vickrey auctions. If you encounter such an owner, simply look up his amount of remaining FAAB and then bid that amount minus $1. Thereby he will get the player but have paid such a dear price that he won’t be able to bid on any other player.

Comparison with Regular Auctions

In a regular auction it is not always the best idea to bid the ETV of a player. For example, if you’re fairly sure that other owners don’t value a player quite as highly as you do, you can adjust your own bid a tad downwards in order to pay less. As all owners realize this and adjust their bids accordingly, the bidding process obviously gets quite complicated and might take some of the focus away from the baseball part of fantasy baseball.

This is the real advantage of Vickrey auctions: They allow owners to bid “honestly” and focus more on evaluating baseball players than evaluating other owners. On the other hand, it takes quite a bit of auction strategy away, as there really aren’t any “tactics” in Vickrey auctions: All rational owners should simply bid their ETV.

In real life, Vickrey auctions have the disadvantage that they don’t maximize revenue for the seller, because, in general, the price paid by the auction winner is smaller than his willingness to pay – as we have seen. This is not a problem in fantasy baseball, however, as the “seller” is actually the free agent pool.

Conclusions

The rules and optimal strategy for Vickrey auctions are quite simple for everyone to understand. Thus, implementing Vickrey auctions into your fantasy league is a way of shifting the focus away from FAAB speculation and back to the baseball world.

Many people haven’t yet understood the optimal strategy, and so it is possible to exploit their ignorance. However, if you show them the reasoning in this article, the auctions should most likely be quite ordered going forward.

Additional Reading

·        Wikipedia article on Vickrey auctions: http://en.wikipedia.org/wiki/Vickrey_auction

·        The Fantasy 411 blog discussion on Vickrey: http://fantasy411.mlblogs.com/mlbcoms_fantasy_411/2007/08/vickrey_bidding.html

·        “Intermediate Microeconomics” by Hal R. Varian, chapter 17 (7th edition)