Thursday, March 19, 2009
Asymmetric dominance and trade proposals
Posted by Marco Fujimoto at 12:01amImagine that you own Kevin Youkilis. You’re a Yankees fan and you hate the Red Sox, so you want to get rid of him out of spite. So you toss him up on the trading block and list outfielders and starting pitchers as your needs. The next morning, one manager offers you one of the following players for Youkilis:
1) Matt Kemp
2) Roy Halladay
Which offer are you more inclined to accept?
It turns out that you’re not sure which you one you want, so you let the trade offers linger for a couple days until the other owner cancels them. A week later, you find that that manager has now offered you a choice of three players for Youk:
1) Matt Kemp
2) Roy Halladay
3) Alex Rios
Now which offer are you more inclined to accept? Did your answer change at all?
The point I am trying to illustrate is one that was raised by one of our readers, Ben, here in the comments section of my previous article. That idea is the asymmetrical dominance effect , also known as the decoy effect.
The asymmetrical dominance effect is the phenomenon in which people show a change in preference between two items when a third item, dominated by either of the first two items, is introduced as an option. There are multiple research studies in which this effect is manifested, and I’ll describe two of them, beginning with the one mentioned in the comments section of the article linked above.
The first study is one that was conducted by Dan Ariely, and in this experiment, students at the University of North Carolina and Duke University were presented with prospective dating partners and instructed to pick a single person to ask out on a date. Three different types of situations were presented:
1). Situation 1 consisted of dating options A and B, both of whom were attractive but had varying degrees of attractive characteristics.
2). Situation 2 consisted of dating options A, B and C(a), with C(a) being almost but not quite as appealing as A.
3). Situation 3 consisted of dating options A, B and C(b), with C(b) being almost but not quite as appealing as B.
So a graphical illustration might look something like this:
The effect manifests in situations outside of partner selection as well. The second study I want to describe is another study by Ariely. This time, subjects were divided into two groups. In group one, subjects decided between microwaves A and B, with microwave A being expensive and of high quality, and with microwave B being less expensive and of medium quality. Forty percent of the subjects in group one preferred microwave A and 60 percent preferred microwave B.
Subjects in group two had three microwaves to choose from: microwaves A and B, and then a third microwave, C(a), that was very similar in dimensions and quality to microwave A, but was more expensive. So in this scenario, it was very clear that microwave C(a) was dominated by microwave A.
A graphical illustration of this paradigm presented to group 2 might look something like this:
Microwaves A B C(a)
Group 1 40% 60% --
Group 2 56% 36% 8%Despite differing situations (people/dates vs. microwaves), the underlying theme in both of these studies is the same. That is, that the presence of a third option, one that has an asymmetric dominance relation with one of the two other alternatives, affects a person's preference of a given alternative over a second alternative. Let’s go back to my scenario at the top of the page. The construct, according to the studies mentioned earlier, would be as follows:
1) Player A
2) Player B: similar to A but has different attributes
3) Player C(a): dominated by A, meaning he has similar attributes but is slightly less appealing
Using Chone projections for 2009, and using the average draft positions (ADP) as sort of an anchoring point for market value, we’ll have this:
ADP Runs HR RBI BA SB W K ERA WHIP Matt Kemp 38 84 16 74 0.311 26 Roy Halladay 46 -- -- -- -- -- 13 152 3.56 1.22 Alex Rios 39 86 17 75 0.285 19In looking at these stat lines, I think it’s pretty clearly that Alex Rios serves as Matt Kemp's decoy. They both have similar attributes (R, HR, RBI), but Rios is slightly less appealing (lower BA and less SB). In other words, Rios is dominated by Kemp and would most likely never be chosen in this scenario given these numbers.
As Ben asked a couple weeks ago, the question then, is can this actually be applied to fantasy baseball?
My answer is yes, I do think that the asymmetric dominance effect can manifest itself within the realms of fantasy baseball. If we look at Ariely’s study, each potential dating option had varying degrees of attractive characteristics; some were funnier than others, some more intelligent, others a little more honest, and so on. Each option had different levels of attractive attributes that made it more (or less) appealing than the other options. We do the same thing with baseball players but instead of judging them by cost and quality like we did with the microwaves, we look at runs, home runs, batting average, etc.
Considering that these items are essentially the same, presenting our trade proposals in a similar format as with the dating options and microwaves should have some sort of effect since, what really matters, is the contextual configuration of the options. This doesn’t mean these types of trade proposals will always work, as there are many variables to consider. And, after all, the opposing manager can still decline all three proposals whereas the subjects in these studies were forced to pick. However, it does seem as if designing trade proposals in this way would have an effect in that it may increase the likelihood that a trade will happen in the first place or that the third, lesser player will really serve as a decoy.
Marco thanks everyone for reading, apologizes in advance for his tardiness and requests that readers be patient in awaiting replies. He welcomes all questions, comments and thoughts on any topic, baseball or otherwise, here.
Can the theory of relativity also be applied to fantasy trades?