Baseball Musings
Baseball Musings
June 20, 2006
Risking Winning

Geoff Young at Ducksnorts uses the Padres situation at third base to explore why people are risk adverse when they are winning, more adventurous when they are losing. He's looking for help with the answers:

We need to find a way through this "mental tunnel." We need to challenge our own thought processes and continue to innovate despite the potential risk to current success or else we risk "losing" additional future success. I'm mostly talking about baseball here, but it could be anything.

How do we get to that point? How do we avoid the trap of mindless risk aversion when all is going well -- especially when millions of dollars are at stake?

I don't have an answer to these questions. Like I said, I'm not smart enough to figure it out on my own. But I'm sure folks have some good ideas.

Okay. So, what are they?

He wants to know why choices are different in this situation:

He houses his discussion in the context of wagers, submitting that we will choose a sure gain over a probable gain, but choose a probable loss over a sure loss, even when the amounts -- the "calculus of expected values" -- are identical. The example provided, from studies conducted by pioneering researchers Amos Tversky and Daniel Kahneman, is as follows:
  1. Sure gain of $75.
  2. 75% chance of winning $100, 25% chance of winning nothing.
  3. Sure loss of $75.
  4. 75% chance of losing $100, 25% chance of losing nothing.

Given the choice between A and B, more subjects chose A. However, given the choice between C and D, the majority chose D. This doesn't make sense because both A and C represent certainty, while B and D involve risk with no additional overall reward. Either A and C should be preferred, or B and D. There would be consistency of thought here. Preference for A and D violates any concept of rational decision-making.

Let me give this a try. The 75% scenario represents probability over a long time. In other words, if you play the 75% win game thousands of times instead of just taking the $75 dollars, you come out about the same. You might come out a little better, but you also might come out a little worse. Taking the $75 each time puts a floor on the minimum you can pick up. It cuts off half of the possible outcomes of playing the game, all more negative than taking the $75 dollars. The fewer games you play, the more you're decreasing your risk.

In the other situation, the exact opposite takes place. You're going to lose money. By playing the game, you're giving yourself a 50% shot of losing less. If you play a lot, you won't lose a lot more than $75 per time, but you might actually save some money. And if you play just a few times, you might get lucky and save a lot. It seems to me it's a perfectly rational decision in terms of the probabilities.


Posted by David Pinto at 11:52 AM | Management | TrackBack (0)
Comments

By playing the game, you're giving yourself a 50% shot of losing less.

Sounds like you might have mis-read the #'s. It's a 25% chance of losing less/nothing.

Posted by: Jason at June 20, 2006 02:14 PM

Oh yeah, and the draft...

The draft definately needs fixing, there should be some kind of bonus cap (no help from the union here). Otherwise the draft will turn into what the free agent market is now - best talent for the best teams, and all the other teams will have to hope for lucky diamond-in-the-rough types.

Posted by: Vic at June 20, 2006 02:37 PM

It really depends on what the amounts mean to me, and how often I get to play this particular game.

For example, anyone reading this post is likely to not worry over dropping 75 cents or 100 cents. I would guess that most people are really worried if the amounts go up to 750,000 and 1,000,000 dollars.

If I only get to play the game once, and losing $100 is proportionally more painful than $75, I'll take the sure things. If, on the other hand, I get to play a round, and after seeing the results decide whether to play again, I could certainly decide to take both risks, wait until I'm ahead and then stop.

Jason: He didn't misread the numbers, but 50% isn't right either - it depends on how many times you play. If you play the game four times, you have a 1/256 chance of losing nothing, 12/256 of -100, 54/256 of -200, 108/256 of -300 and 81/256 of -400. In other words, the chances of losing less than or equal to the "expected value" are ~68%.

Posted by: Subrata Sircar at June 20, 2006 06:01 PM
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