Tuesday, November 04, 2008
Prospect Theory And Roster ChangesPosted by Marco Fujimoto at 12:01am
I want to start off by running a quick experiment where I present you with two scenarios.
In the first scenario, imagine I gave you $1,000, and then gave you two options to choose from. In option A, you will have a 50 percent chance of gaining $1,000 and a 50 percent chance of gaining nothing. In option B, you will have a sure gain of $500. Which option would you choose?
Now let’s imagine another scenario where this time I gave you $2,000 and presented you with the following two options. In option A, you will have a 50 percent chance of losing $1,000 and a 50 percent chance of losing nothing. In option B, you will have a sure loss of $500. Which option would you choose here?
In the first scenario, did you choose option B? And how about the second scenario? Did you select option A?
These are the exact scenarios psychologists Daniel Kahneman and Amos Tversky posed to a group of test subjects while developing their Prospect Theory. They found that a large majority (84%) chose option B, the sure gain of $500, in the first scenario while in the second scenario, the majority (69%) chose option A, the equal chance of losing $1000 and losing nothing.
The mathematical expectation is exactly the same between all options, and in the long run, you will end up with $1500 no matter what choice you make in either scenario. And in theory, if most people choose a sure gain of $500, they should also choose a sure loss of $500 since, in both scenarios, there is a guaranteed payout of $1500. Even though the outcome may be the same, people appear to feel and react differently to the ideas of losing and gaining.
Though it may not be obvious, I think this concept from the Prospect Theory has some application to fantasy baseball, especially with regards to trading, the waiver wire and team standings. You may have noticed this also, but in my experience, it is awfully difficult to make a trade in the middle or second half of the season with the first-place team. And the flip side of this is that I have always been reluctant (or overly demanding) in potential trades when I am the team in first place.
But this makes sense, doesn’t it? If someone is in first place, why would he want to make a change? After all, “if it isn’t broke, don’t fix it”, right? The flip side of this is if a team is losing, of course he wants to make a change! And the aforementioned portion of the Prospect Theory helps explain this; people are fairly loss-averse, and they are less likely to gamble when they are poised to lose something but more likely to gamble if the risky choice might allow them to avoid a loss.
So how is this information helpful? In general, I think a manager should always try to improve his team, no matter how the standings look. Obviously, some transactions carry more risk than others, but assessing the risks and benefits of a transaction comes down to proper analysis, which is a different story. What I’m talking about here is that if your analysis of a potential transaction shows a net gain in points in the overall standings, versus zero points if you decide not to pursue the transaction, then you should make the change whether you are in first or last place.
I was a victim of this type of irrational thinking a couple years ago in a H2H league during the semifinals of the playoffs. Heading into the week, my hitters were raking and my pitchers were dealing—I thought this was in the bag. Well, about two weeks earlier, Salomon Torres had taken over the closer role for Pittsburgh and he was available on the waiver wire. I had J.J. Putz, Chris Ray and Takashi Saito so I didn’t have an immediate need at closer. The addition of Torres would have provided depth and made my team better though, if only because it would have prevented my opponent from loading up on closers and gaining an edge in the saves category.
But my team had been winning, and I thought it was good enough that I didn’t particularly need to make any roster changes. I could have parted with one or two guys who spent most of the time on the bench, but I was reluctant because they had helped my team reach the semifinals. So I stood pat, and allowed my opponent to add the newly appointed Pittsburgh closer. Torres consequently racked up four saves during the week, and I lost the saves category by three and the overall match-up by two. Bye-bye championship and hello consolation match...
This is an example of risk aversion and the Prospect Theory, and though the consequence may lie on the extreme end, I think the moral of the story is very clear: I had the opportunity to improve my team, but because my team had already been doing well, I was reluctant to make any changes, and it ultimately cost me an opportunity to win the league. A lot of times, the result of avoiding a decision that carries a positive expectation may not be as blatant as my H2H blunder, especially since most decisions don’t carry such a large expectation. Even if you only gain a small edge, you shouldn’t be hesitant to make that change because these small edges, especially over the course of a long 162-game season, will add up and, anything, like Torres picking up four saves in one week, can happen.
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.