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March 6, 2014
Prospect Theory on Draft Day
Prospect theory, a theory of behavioral economics, is actually unrelated to both our beloved and non-beloved prospects. Rather, prospect theory describes how we choose between probabilistic alternatives when risk (uncertainty) is involved. Hang with me here because this has a huge impact on the decisions we make during fantasy drafts. More specifically, prospect theory explains how we choose to take on uncertainty with each draft pick. In understanding how our league-mates and we make decisions during the draft, we will be able to find some arbitrage opportunities throughout the draft. Sometimes we take more static players and sometimes we take more dynamic players. It is easy to chalk this all up to an owner’s individual risk appetite, but that would be oversimplifying the situation. A fantasy owner’s expectation for each draft slot and the players available for selection will also be major factors in determining how much risk each owner chooses to take on with each selection.
For every pick in a draft we expect to obtain a certain amount of value. The issue is that with pick 1.6, we cannot simply draft $38 of value; we cannot draft a .303 batting average, 27 home runs, 20 stolen bases, 102 runs, and 108 runs batted in with “x” amount of positional scarcity. We have to draft actual players. So with pick 1.6, we will either be drafting Robinson Cano, Clayton Kershaw, Hanley Ramirez, or Chris Davis. Maybe we get lucky and one of Paul Goldschmidt, Andrew McCutchen, or Carlos Gonzalez falls to us. When it is time for our pick, there are three possible scenarios that we can encounter:
We will frame our decision for each of these scenarios differently. We do not simply choose the investment that is likely to return the most value; rather, “value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights.” Put differently for our purposes, by framing our decisions through losses or gains, we tend to overweight outcomes with small probabilities, which can have a profound impact on our decisions.
Scenario 1: Multiple players available that meet or exceed our expectation
You have $100,000. There are two options. Option 1: 100 percent chance of losing $5,000. Option 2: five percent chance of losing $100,000, 95 percent chance of losing nothing.
Without fail, humans will choose Option 1, even though the value of both options is the same at $95,000. The reason behind this is obvious: Why take on such severe risk when it can be avoided? For fantasy baseball sake, let’s say Option 1 is Robinson Cano and Option 2 is Ryan Braun. Cano is the safe play, while Braun contains the greater risk and the greater upside, but both will return the same value on average (remember this is not my forecasting, this is for the sake of the argument). More importantly, both will return a value that meets our expectations for the given pick. Consequently, Cano will be taken earlier. The first takeaway here is not that we are incorrectly choosing Cano over Braun; rather, the takeaway is that there is surplus value to be had in being able to select the “riskier” player later than the “safer” player earlier. The second takeaway is that while we should be selecting the player that most exceeds our expectations; we will tend to select the least risky player that meets our expectations.
How to combat prospect theory in Scenario 1: When there are multiple players that meet or exceed your expectation, take the player that most exceeds your expectation, not necessarily the safest player of the bunch.
Scenario 2: One player available that meets or exceeds our expectation
Scenario 3: Zero players available that meet or exceed our expectation
You have $100,000 dollars. There are two options. Option 1: 100 percent chance of winning $5,000. Option 2: five percent chance of winning $100,000, 95 percent chance of winning nothing.
In this case, more humans will choose Option 2, even though the value of both options is the same at $105,000. Again, the reason for taking the risk seems obvious; why not take on some risk when there is so little, relatively, to be gained by avoiding that said risk. I will spare your eyeballs and will not go through the entire Cano/Braun example here, but you could compare Chris Carter and Adam Lind or Brad Miller and Howie Kendrick and see how there is some profit to be had by taking the safer players (Lind and Kendrick) later or cheaper, even though they may lack the upside. We are tempted to take a player who has a long shot of exceeding our expectations instead of taking a player who has less upside, even if that player is as or more likely to return the same amount of value.
How to combat prospect theory in Scenario 3: When there are zero players that meet or exceed your expectation, take the player whose value comes closest to meeting your expectation, not necessarily the player whose upside exceeds your expectation. Note that “value” in this sense has nothing to do with variability; a player with a 50 percent chance of returning $20 and a 50 percent chance of returning $5 (valued at $12.50) is still more valuable than a player with a 100 percent chance of returning $12.
Lastly, below are some prospect theory takeaways that are not scenario specific:
Differing expectations among owners
Early-round and late-round trends
The critic in me is saying, “Are you not you just advocating that we take the best player available?” To that I would answer, “Yes, of course I am advocating that you take the best player available, and by that I mean the most valuable player according to your league structure.” What I am really trying to say is that choosing the most valuable player is always the goal, but one that we frequently fail to reach. Hopefully, in understanding the effects of prospect theory on our decisions we will be able to make the optimal decision more often. To quote Louis Pasteur, “opportunity favors the prepared mind.” Prospect theory will be in full attendance come draft day and auction day, so be prepared to capture those little surpluses as they pop up throughout the draft or auction.