A Good Way To Think About Probability

I was a mathematics major in college, so it's a bit of a pet peeve when probability & statistics are presented in every day life as measures of confidence or – even worse – certainty.

The most common source of irritation is the dang weather app. Let's say that it predicts a 90% chance of rain today. And they add a little icon with a lightening bolt and change the background of the app to show some falling rain, so you know it's legit. What's an average person supposed to conclude? Probably that it's going to rain A LOT today. A 90% chance of rain must mean a lot of rain, right? Or maybe that it will rain for 90% of the day?

Not really. A 90% chance of rain means that it rained on about 9 out of 10 days in the past on days with similar conditions. That doesn't mean it rained a lot on those days; it still counts as rain if it sprinkled for 5 minutes. It's also completely possible that this happens to be that 1 day out of 10 where similar conditions produced no rain.

Now, I'll admit that you'd be smart not to plan a picnic on a day with a 90% chance of rain. It's useful to have some sense of what to expect. But probability is a measure of chance & randomness, not one of confidence & certainty.

Here's a framework that I like for adding context to probabilities & statistics: think about it in terms of a deck of cards – and how much you'd be willing to wager on pulling a card at random.

Let's look at that weather example from above. If you had a deck of cards and removed all the jacks, queens, and kings, your odds of pulling a card at random that is NOT an ace are 90%. That's probably a reasonable wager: there are a lot more non-aces than aces. But you can still imagine drawing an ace, right? Does it feel a little bit less certain in those terms than when you think of it as 90%?

Now let's say that you see an add that claims that 4 out of 5 dentists recommend blah blah toothpaste. Four out of five seems like a lot, right? That's nearly all of them! But let's imagine it in terms of a deck of cards. Four out of five is pretty much the same as pulling a card from a full deck and it NOT being a spade between ace and ten. Again, the odds are in your favor, but it sure doesn't feel like as much of a sure thing compared to the wording "4 out of 5".

Here's a final example to connect this back to money & personal finance. When it comes to investing, the odds that the U.S. stock market will be positive on any given day are just over 50% – barely any better than a coin flip. Now, that might appeal to some people, but I'd rather not wager my money on a coin toss. However, investing has a weird statistical tendency: the longer you stay invested, the better your odds get. The chances that the U.S. stock market has a positive return in any given year are around 73% – about the same likelihood of pulling a card from a full deck that is not a heart. Over five year periods, the odds of a positive return go to 88% – about the same as not drawing an ace through six of hearts. Over ten year periods, the odds of a positive return are about 94% – nearly the same as not drawing an ace, two, or three of hearts. And over 20+ year periods, the statistical odds of a positive stock market return is 100% – meaning there is no recorded rolling 20 year period with a negative return. That's like pick a card, any card, and you win.

Now those are odds I can get excited about!

(FYI – I pulled my investing stats from here and here.)

Thanks,

Timothy Iseler, CFP®

Founder & Lead Advisor

Iseler Financial, LLC | Durham NC | (919) 666-7604

Iseler Financial helps creative professionals remove stress while taking control of their financial lives. We'll help identify your current strengths and weaknesses, clarify and refine your long-term goals, and prioritize decisions to improve your financial well-being now and later. Reach out today to take the first step.