# Prospect theory

The other day I came across the behavioral theory known as Prospect Theory, where human behavior shows both risk-averse and risk-seeking qualities in similar situations. The theory was established by two psychologists, Daniel Kahneman and Amos Tversky. Their work was contrary to ideas that humans tend to weigh outcomes using expected utility (i.e. – What’s the expected payoff from a heads/tail bet of \$1?).

For example, in their work they asked the same audience a set of two problems on the lines of ‘would you rather have…’:

1) A: a payout of \$4,000 at an 80 percent probability OR B: a guaranteed \$3,000?

2) C: A payout of \$4,000 at a 20 percent probability OR D: a \$3,000 at a 25 percent probability?

They found 80 percent surveyed chose B over A in Problem 1, and 65 percent chose C over D in Problem 2. If you followed along and ran the expected utilities in your head, outcome A (\$3,200) has the better expected outcome over B (\$3,000), while outcome C (\$800) has a higher expectancy than outcome D (\$750). Problem 2 shows the use of expected utility theory, while the first goes against it.

Problem 1 shows how the guaranteed \$3,000 payout acted as a relative marker. The idea of losing \$3,000 was not worth risking to gain \$4,000. At the core of the theory, Kahneman and Tversky were trying to show how humans perceive a loss and a gain differently and they don’t always base decisions on the end outcome. The graph below shows the prime example of their work, that a loss has a more elastic effect on a person’s value function (similar to utility or happiness).

Now, to baseball we go. I wanted to discuss some thoughts I had while reading through Kahneman and Tversky’s breakthrough paper. My observations pertain to more of the economics side of baseball, but I am positive there are other applications of this theory within game strategy as well. As a disclaimer, I’m only trying to explain or find reasoning behind teams’ decision planning, rather than suggesting (in hindsight) teams should have executed their strategy differently.

### Safer waters: Free agency or the draft?

Through the MLB draft, teams try to balance potential with inherent risks. There have been plenty of studies showing how small a percentage of players drafted will actually have an impact in the majors. This is mainly due to injuries that can limit the prospect’s career, or the simple fact their skills would not develop into an asset for the organization beyond the minor leagues. Due to these risks, it’s not surprising how owners are unwilling to proportion a large sum of its finances into the draft. Prospects are risky investments who also ask for hefty signing bonuses.

I know its not an apples to apples comparison of a top 10 draftee to a potential free agent signee, but I think it applies in the realms of Prospect Theory. Relative to the “unwarranted” risk in prospects, why can’t I (as the owner of a team) spend my money elsewhere on an established player? The benefits of a free agent signing will be instant, while waiting for prospects is slow and many things could happen along the way to derail his development.

One prime example came to mind, especially with all the past year’s media coverage. Brian Sabean, GM of your 2010 World Series San Francisco Giants, hated draft picks. There have been many instances in his career where he would sign a free agent and more than willingly forfeit that year’s draft pick.

Granted, Sabean believed his team was one good piece away from the division title, but he spent without considering the ill effects of losing his draft picks. In this instance, Sabean viewed the relative marker or reference point of spending on established players through free agency was not worth risking on a first round draft pick, which would be considered a loss in his mind.

### Signing issues

Billionare Mark Cuban recently confessed he still gets aggravated by increasing gas prices and buys generic brand food products. In the same sense, teams are constantly thinking about signability issues and weighing if they really want to spend millions of dollars on unproven talent. This will push away teams who don’t have the budget to spend over their MLB-recommended draft slot signing bonus. This risk pushed San Diego to draft Matt Bush instead of someone like Jered Weaver with the first pick in 2004.

There are way too many players to list that were taken in previous drafts but didn’t feel the signing bonus was enticing enough. What if Cliff Lee signed with the Orioles? Tim Lincecum with the Indians? Barry Zito with the Rangers? Fans of these teams have and will continually criticize management for being too cheap.

These teams failed to sign these players because they weren’t willing to risk more sunk costs in a youngster. It’s essentially the issue brought up in Prospect Theory; take a chance on a prospect where he has an impact on the team say, 20 percent of the time, or save that money for future usage (the reference point)? I’m not saying these teams should have known to take these risks. More so, it’s an example of how teams believe they are weighing outcomes from Problem 1 using a reference point, but are more likely in Problem 2(from the example in the beginning).

### Injury Risk

In the 2006 MLB Draft, five collegiate pitchers were taken before Lincecum went to the Giants at the tenth spot. Despite being ranked as the top (if not, the second best) pitcher in the college ranks, most of those teams passed on him due to his size and their fear of injury. It was just too much to ask of them to make an investment in his 5’11″, 170 pound frame. I’m sure there are other examples where prospects are passed on not because of talent issues, but based on their conclusion the prospect is more injury-prone.

My point from all this mumbo jumbo is that I’m not convinced there is ever a “safer” pick. If teams were worried of injury, I would argue (but not being a genius on pitching mechanics) pitchers at that age are equally susceptible of getting injured in their career. This is speculative, but risk of injury from overuse (and freak injuries) seems more like an inherent risk that affects all prospects.

From a pure probability standpoint (however foolish and naive this may be), if the overall probability of injury from one pitch is 0.0001, and a pitcher throws 10,000 pitches (and assuming a binomial distribution), the probability of a pitcher never becoming injured is 36 percent (could be higher if we assume a pitcher getting injured over 20 times in a career is very close to zero). We could change the 10,000 pitches to innings, or 100 starts, or whatnot, but I hope you understand my point. An every day life example of this is the risk of getting into a car accident is very small, but the constant repetition of driving every day makes it very unimaginable someone will not get into an accident over the course of their life.

The loss of a reference point (in this case, a “safe” bet on Luke Hochevar becoming at least a number four starter) was not worth risking when assessing the value gained from drafting a Lincecum. Holding all these collegiate player’s talent constant, why would a team risk more by selecting the one who doesn’t seem to have safe mechanics? A flaw in this type of reasoning is that the “safer” selection is still very risky (and seems to go line with the ideas brought up in the paper).

### Wrapping it up

All in all, I find teams to be quite risk-seeking in the free agency market. They are more than willing to bid up the prices of players, despite the risk that the player will not live up to their contract (especially at the back end of the deal for aging players). We of course see this more often from teams with higher payrolls. But at the same time, teams have risk-averse tendencies in the draft by trying to talk themselves into “safer” picks, from both an investment risk and injury risk perspective. Some also devalue the event as Sabean has shown (although he obviously owes a lot of the Giants’ 2010 success to his three lottery picks of 2006-2008).

References & Resources
Here’s a link to the paper from Kahneman and Tversky I have been referring to. Read it or take a glance at it if you’d like.

Also, a quick search on THT came up with this article by Marco Fujimoto pertaining to Prospect Theory applications in Fantasy Baseball and roster moves published a few years ago that’s worth reading.

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1. Jason said...

I think a more relevant example from risk theory with respect to free agency is auction bidding behavior and the winner’s curse.

Free agency seems like a clear example of a common value auction – Kagel and Levin 1986 and Cox and Isaac 2007 (google scholar winner’s curse to thin it down) might be worth taking a look at.

You can argue that different teams might have different values for a player, but—especially if you’re using something like WAR to value a player, you can model it pretty well as an asset with a common (but uncertain) value.

The rough result: in an auction with an uncertain value, different bidders have different noisy beliefs about an asset’s value. Typical bidding behavior means that the ones who win the auction will be those who had weirdly high draws on their estimated value, so auction winners will generally over-bid.

2. John Winters said...

Where else are you going to get serious academic papers on psychology (and really important ones, too) as a jumping off point for a discussion on baseball?  I love the Hardball Times.

3. DrBGiantsfan said...

In Brian Sabean’s 13 year tenure as GM of the Giants, there have been just 2 years, 2004 and 2005 when they did not have a first round draft choice.  Barry Bonds’ career was clearly coming to an end and there was pressure to try to win immediately while he was still playing.  Before those two seasons, Sabean drafted and developed Aisworth/Foppert/Williams and was monumentally unlucky with them.  He also drafted Matt Cain in 2002.  2004 and 2005 are the outliers of Brian Sabean’s career as a GM.

Otherwise good article.

4. Kevin Lai said...

Jonathan Halket mentioned that my explanation of the violation of expected utility theory was a bit confusing. Another way to think about the violation of the theory is not due to the majority of people choosing B and C, but the fact that outcomes B-C and A-D from the two problems are linked to one another. In this realm, people are choosing the options inconsistently with that of expected utility theory.

@DrBGiantsfan, thanks for the clarification on Sabean’s drafting past. I probably should have looked into it further beyond a couple of articles. I also couldn’t remember of too many early 2000 draftees beyond Cain. I was wondering though, do you think there’s some grounds for suggesting Sabean does tend to use the free agent markets to improve his teams (excluding the success he had with Lincy-Bum-Posey)?

@Jason, I completely agree with you about common value auctions and how team’s contrasting valuations and beliefs leads to over-bidding (and signings like Jason Werth, or Zito). What I was trying to get at using ideas from Prospect Theory is how the risk-averse and risk-seeking behavior of humans does manage to shift team’s use of finances in the two markets (so more money is allocated to free agency).