Right or wrong?

The problem with binary thinking.

Right or wrong? Win or lose? We’re conditioned to think in a binary way: either-or. In most cases, this makes plenty of sense! After all, whether we’re talking about a baseball game or predicting the outcome of a coin flip, there are only two possibilities: right or wrong, win or lose.

But the world isn’t always that simple. Stick with me here: sometimes you can be right and get the wrong answer (or wrong and get the right answer)! The better team doesn’t always win.

If you don’t believe me, let’s look at everyone’s favorite example: gambling!

When you roll two dice, there are 11 possible outcomes for the total number: 2-12. Of course, not all outcomes are equally likely: there are more ways to make a 7 (6+1, 5+2, 4+3, 3+4, 2+5, 1+6) than there are to make a 12 (6+6). We can calculate the probability of each outcome as follows:

The most common outcome, a 7, happens 16.67% of the time (6/36, or 1/6). Put another way, the probability of rolling a 7 with two dice is exactly the same as predicting which number you’ll roll with one die - 1/6. In the case of one die, each number is equally likely - so no matter which number you guess, you’ll have the same chance of being “correct.”

It might seem redundant to use two different examples to say the same thing (1/6 chance) but I’m being rather intentional here, and I’ll explain why:

When we calculate probability we’re not making a prediction, we’re just evaluating the numbers. In the case of rolling two dice, the math is straightforward and its validity provable. The probability of rolling a 7 is 16.67%, that’s far from impossible, but still rather unlikely! That means you’re 83.34% to not roll a 7. If someone were to give you $100 and you had to bet, even money, (risk $100 to win $200) whether the next roll would be a “7” or “not 7,” which would you choose?

Of course, the “smart money” would be to bet “not 7,” right? That’s the far more likely outcome. You throw the dice.

It’s a 7! You lost.

Look at the chart again. 16.67%. 1/6. You had a 5/6 chance of being right, but you were wrong. Just typing it out, I feel my blood pressure rising. Not that I’ve ever lost $100 on a dice roll…

After this loss, would you go back and crunch the numbers and try to figure out where you messed up? Was it incorrect to say you had a 5/6 chance of winning? Since you lost, would you conclude the math must have been wrong? Of course not. In the real world, rarely can we calculate probabilities so precisely as the roll of a dice, but that’s the lesson to take from this example: even if the math is perfect, there’s still a chance that unlikely events will happen. Don’t confuse an evaluation of probability with a “right or wrong” prediction. To say one thing is more likely than the other, is not the same as saying that something definitely will or will not happen.

On election forecasters

Stepping out of the realm of concrete math and into an area a little more abstract: elections.

To get it out of the way, predicting human behavior is hard!