Gambler’s Dilemma

asdWe hear it in baseball broadcast booths all summer long: “He’s a .333 hitter. He’s gone oh for two. He’s due.” But is this accurate? Should you bet on this? Or are you just wishing for an outcome that has no basis in the data, and setting yourself up to lose? The gambler’s dilemma can teach us a lot about all our interactions.

When you flip a coin, it can land in one of two states: heads or tails. The statistical probability that it will land in either of those positions is 50%.

So if I flip a coin six times and it comes up heads all six times, what’s the probability that the next toss will end up tails? It’s simply gotta come up tails this time, right?

The coin has no memory. (At least it’s got that over the baseball player!) On any given toss, it’s going to land either heads or tails. The odds are 50/50 on every toss, even if it’s been one way for 10 straight tosses. So betting your future on tails coming up after six consecutive heads is very risky. The coin is not “due.” Your chance of getting tails is 50/50. Period.

Yet we make this kind of bet all the time. The .333 hitter? He’s got a one in three chance of getting a hit. That stat is the result of hundreds of at bats (depending on how much of the season has passed). It’s what he gets paid for. He fails to get a hit two-thirds of the time (that’s another whole article) and gets paid for that one in three stat.

So he’s gone oh for two. What are the odds he’ll get a hit in his next at bat? 100%? Now, there’s the gambler’s dilemma. Simply put, his average is still one in three.

It is what it is. We develop expectations from our Knower/Judger (our favorite batter is “due”) and then freak out when our wishes (and that’s really all they are) don’t come to pass.

I’m reminded of the fable of the frog and the scorpion. Scorpions have batting averages; nearly 100% of the time, they’ll sting anything nearby. It is in their nature. When you clearly see the data, how could you possibly fantasize another outcome?

The data is always there

How many of your struggles (assuming you have one or two) can be attributed to expectations not supported by data? Really frustrated when your favorite batter doesn’t get a hit on his third attempt? He’s a .333 hitter. Period. Can’t believe the coin came up heads again? 50/50. Period. Tired of having to deal with that direct report who just tells you what you want to hear and then doesn’t act after the conversation? It’s in his nature. Period.

The interpersonal statistic can be useful two ways. You might witness a friend, employee, or family member performing outside his statistical norm—having a bad day. If you review the data and see he’s basically “on” 90% of the time, then you can rest assured he’ll be back on track, like a .333 hitter. But not necessarily today!

On the flip side, when you really need 99% performance out of someone who might be a .333 hitter (in your world) and you dare to expect it, you’re probably in for some frustration.

Our K/Js frequently assign wishes to outcomes that ignore data, and then we bet our emotions on those wishes. But ballplayers go through slumps. Coins fall the same way six, seven, eight, and more times in a row. People act according to their nature no matter how much we want them to act otherwise. Who’s responsible for your frustration? Look at the data that’s in front of you and you can end the frustration of losing on bad bets.

MLB: MAR 03 Spring Training - Nationals at Cardinals

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