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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:

  1. Multiple players available that meet or exceed our expectation
  2. One player available that meets or exceeds our expectation
  3. Zero players available that meet or exceed our expectation

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
In the first scenario, where there are multiple investments that meet our criteria, we tend to make our decision based on losses. Here we tend to overweight low-probability, negative outcomes. This is the same reason why we buy phone insurance and buckle our seatbelts. If we can pay for the insurance (decrease the risk), while still acquiring value that meets our expectations, we are going to do so. To help me explain, I am going call on the developer of Prospect Theory, Daniel Kahneman (credentials: Nobel Prize winner in economics, Presidential Medal of Freedom recipient, spectacled, smart dude). Kahneman explains how we make decisions that involve risk from a loss standpoint through a monetary example similar to the one below:

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
In this scenario, we take the one player. Next.

Scenario 3: Zero players available that meet or exceed our expectation
In the third scenario, where there are no players that meet or exceed our expectations, we tend to make our decision based on gains. Here we tend to overweight low-probability, positive outcomes. This is why we play the lottery and why heavy underdogs run trick plays in football. If we think there is nothing to gain, we will take on long odds instead of choosing lower yielding (perceived as meaningless), higher probability investments. Below is a Kahneman-esque example for decision making through the lens of gains:

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
Because we are all beautiful, unique snowflakes our expectations will not always be the same. Owners who have lower expectations for certain picks will tend to choose less variable players (the owner taking Jay Bruce in the middle of the second round), whereas owners who have higher expectations for certain picks will choose more variable players (the owners taking Harper 1.6 in a redraft). Note that this is not simply risk appetite, as these very same owners will take on varying amounts of variability throughout the draft as their expectations change. When you see the above occurring, take the more (or less) variable player that has fallen to you. Do not start doubting your rankings and get caught up in the momentum of framing your pick through losses or gains, continue to look at your decision in terms of value.

Early-round and late-round trends
In the early rounds we expect high amounts of production, whereas we expect very little production in the later rounds. Consequently, in general, we tend to look at early rounds in terms of losses and later rounds in terms of gains (the same could be said for the most expensive and cheapest players in auctions, respectively). In the early rounds, do not be afraid to take the risky player who has inexplicably fallen too far and in the later rounds, conversely, do not be afraid of taking the boring, consistent player instead of taking the hot sleeper a round too early. It is also common place to take upside in the later rounds because of replacement level production available if the player does not work out. This can be a factor depending on league depth and bench, but too often this is used as an excuse to take on long odds.

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.

Kahneman, Daniel and Amos Tversky. “Prospect Theory: An Analysis of Decision under Risk.” Econometrica 47.2 (1979): 263-292. Print.

Thank you for reading

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Very nicely done.
I can see myself doing the exact same things at every draft I have ever participated in. I am taking my own three sentence adaptation of this article with me to my drafts.
I've read Kahneman's best seller, but I wasn't really thinking about it when I started my draft the other day. Andrew McCutchen would have been the safe bet with the second overall pick, but Troy Tulowitzki has the higher ceiling. He's got that injury risk, but "no guts, no glory" seems applicable here.
I really enjoyed this. But I think I need some help understanding what I'm supposed to have learned.

"The first takeaway here ... 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 ... we should be selecting the player that most exceeds our expectations..."

The two takeaways seem contradictory. 1. Risk delayed is value. 2. Risk not chosen is loss of value. What am I missing here?

The takeaway is to draft for expected value. The mistake people make is to let their decision get swayed AWAY from expected value because they're too focused on the upside or downside risks.
My take is that Risk is a variable in value while choosing the option with the least risk is, statistically speaking, more likely to result in an overall loss over time.

Example: Take a Dynasty league. You can own one of the following players for their entire career. At the end of both careers who will give you more production: "a player with a 50 percent chance of returning $20 and a 50 percent chance of returning $5 (valued at $12.50)or a player with a 100 percent chance of returning $12."

Hope I didn't confuse you more.
I like the framework implied by this article for _draft_ strategy.

First you need the expected value for each draft slot. Then you need expected values for each player along with ceiling and floor expectations.

Using the PFM for my 16 team league, Starling Marte has a higher expectation than Jay Bruce. The tiered OF rankings lump Bruce in the **** group while Marte heads up the *** group. The text makes it clear that Marte has the potential to be in the higher group, but there is concern about his floor. Bruce has a high floor.

I can (and do) use the PFM to set expected values while watching for real world events that can invalidate the PFM - aside from the pitfalls in any projection system. I can also use the PFM values to help compute draft slot expectations.

Pecota provides: breakout, improve, collapse, attrition values that can help with setting the range of expectations. I'd like to see a bit more guidance about using those values as opposed to having the expectations managed opaquely in the tiered rankings.

Is there any likelihood of followup work along these lines for the upcoming season?
(sorry for the length. Thanks for all the effort put into this site.)
Thanks. My advice is to strip out expectation and make your selections based on projected value. This is easier to do than say, but be cognizant when you feel the pull of expectations and find yourself framing through losses or gains.
I'd like to add to this with a request that future versions of the PFM have the option to report error bars for players. If it reported each separable prediction (perhaps playing time vs. averages, assuming that things like K%, BA, and SLG are not really separable) with its standard deviation, it would be easier to do analysis of risk.

The problem with applying the suggestions in this article is that humans make those "mistakes" with good reason - we know that we don't know everything, and that rare events are harder to predict. So if you tell me that I have a 5% chance of winning (or losing) $100k, it is hard to convince myself that you are estimating that chance properly (unless you specify a mechanism that makes it clear that the chance is precise, like rolling a d20). If you tell me that Risky Dude has a 50% chance of returning $50 and a 50% chance of returning $0, while Safe Dude has a 90% chance of returning $27, and a 10% chance of returning $7, then sure, mathematically these guys are the same, but do I really believe that Risky Dude's odds are well-understood? I'm going to assume that you are closer to correct in your prediction of Safe Dude than of Risky Dude.

Back to the PFM, though. If it is going to recommend a draft value, it seems like it would really be capable of running through the permutations of performance deviation, and assigning a %chance that so-and-so is one of the top-N players (where N is dictated by available slots in the league), instead of just relying on weighted means. This is a case where it really does matter, because the cut-off causes us to assign zero value to players whose expectation drops below the top N, but the reality is that a lot of the actual production across the season is generated by these zero-dollar players who get a lucky roll on their performance.

If you look at the top 10 1Bs, add up the homers they are projected to get, and then assign each of them a $/homer based on the overall percentage of homers projected at all positions, you are not making the right prediction, because, just as a simple example, if the #10 guy has a 25% chance of hitting 20 bombs, a 50% chance of hitting 15 bombs, and a 25% chance of hitting 10 bombs, you will factor him in as 15. If there are 10 guys just below him who have 15-24% chances of 20 bombs, 50% chances of 15 bombs, and 26-35% chance of 10 bombs, however, then the odds are extremely high that the #10 *slot* will produce 20 home runs, so all home run production is worth slightly less.
Is it too much information that I went from 6 to 12 reading this?