• Justin McBrayer

Possibility vs. Probability

To say something is possible is one thing. To say something is probable is quite another. The two are routinely confused in popular culture, especially the news.


Statements about what's possible tell you that something might happen or might not. Given this, finding out that something is possible doesn't tell you at all how likely this is to occur. For example, suppose you know that some people get sick after their second dose of the COVID vaccine. That only tells you that it's possible that you'll get sick after yours. It doesn't tell you how likely you are to get sick after yours.


Statements about probability tell you how likely it is that something will happen. Something is probable when it has a chance of occuring that is somewhere north of 50%. If you had to bet on it, the safe money would be to bet that it will happen. It's not guaranteed, of course, but that's where the odds lie. If you know that most people get sick after their second dose of the COVID vaccine, then you should think that it's probable that you will, too.


Anything that's probable is also possible. But most of what is possible is not probable. That's why claims about what's probable are stronger than claims about what's possible. The former give you more information than the latter.


In fact, for most cases, claims about what is possible give you no information at all. If I tell you that it's possible that my birthday is in March, you'll shrug. If I tell you that it's possible that it will rain next month, you'll shrug. If I tell you it's possible that a drug has a side effect, you'll shrug. That's because we ASSUME that things are possible unless we get positive reason to think otherwise. In other words, for most cases, possibility is the default position.


Given both the difference between possibility claims and probability claims AND the fact that we normally assume things are possible, our informational environment is confusing. Let me explain. Suppose you're driving along and see this sign:

Does it provide you with information you didn't already have? No. It tells you that the bridge may be icy. 'May' is an indicator of what's possible (though 'might' is actually more accurate). In other words, the sign tells you that it's possible for the bridge to be icy.


But of course it's possible. You assumed that already. No one gets on the road thinking that it's impossible that bridges are icy. We know full-well that this is possible. So signs telling us that it's possible aren't valuable from an information standpoint.


What WOULD be valuable is information about how likely it is that the bridge is icy. And here we have something to learn: it's more likely for a bridge to ice up than it is for a road to ice up. The first will happen before the second. To communicate this, we need a statement about what's probable. But all the highway department gives us is a signal about what's possible.


This isn't an isolated mistake. It happens every day in the news. I'll start with one from today's Washington Post, but there's no shortage of headlines on an informational par with the road sign:


"Anthony Fauci says wearing masks could become seasonal following the pandemic" Could = possible. Yup, it's possible that people start wearing masks. It's also possible that they not. So what? This headline is informationally vacuous.

"Boris Johnson says British coronavirus variant may be more deadly" May = possible. Well, of course, it's possible that the new variant is more deadly. It's also possible that it's less deadly. How does this headline tell us something new?

"Fast radio bursts could help solve the mystery of the universe’s expansion" Could = possible. Yup, it's possible that this new technology will help. Of course, you already assumed that. You also assumed that it's possible that the new tech won't help. Who knows?


"Biden will regulate gun device possibly used in Boulder shooting" Maybe the gun device in Biden's crosshairs was used in the Boulder shooting. Maybe it wasn't. Of course, you already assumed this, and the headline doesn't give you any new information about the Boulder shooting.


"The Big Number: Drinking 1 or more cups of caffeinated coffee could reduce your heart failure risk" Could = possible. Well, of course, it's possible that drinking coffee could reduce heart failure. It's also possible that it increases the risk of heart failure. We just don't know. So, how is this headline informative?

In fact, the only segment of the news ecosystem that I've found that does a reasonably good job of distinguishing claims about what's possible from claims about what's probable are those that focus explicitly on the quality of evidence and how evidence should alter our beliefs about the world. For example, news about the weather is often explicitly couched in probabilistic terms: there's a 30% chance of rain on Friday. Saying that it might rain or may rain or could rain is obviously too weak. We already assume that. So, weather sites give us probability instead.


There are news websites that function more like weather sites. I'm thinking of places like fivethirtyeight.com. These places weigh evidence carefully and rarely make claims about what is merely possible. Instead, they start with the assumption that a wide variety of outcomes are possible, and they gather evidence to determine which of the many possible outcomes are more likely. This means they skip headlines about what's possible and move right into the more difficult task of weighing evidence to determine what's more probable.


The take-away lesson for readers of the news is that we should be on our guard against hollow claims and headlines about what's merely possible. Reading that you can get a headache after a vaccine should make you no more likely to think that this will actually happen. Of course, it's possible that you get a headache. But that's a far cry from saying that getting a vaccine increases your chances of getting a headache.


So that's one way that we can be more careful consumers of the news. Don't accept claims about what's possible as deeply informative. They're not. We should resist drawing conclusions about what the world is like until we get evidence that shows us what's probable. When the news doesn't do this, we should remain unpersuaded.

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