The Difference Between Probabilities and Confidence

Hi, this is Cameron Hight from Alpha Theory.  

What I am going to talk about today is the difference between probabilities and confidence.  

When our clients are performing their research and putting that information into Alpha Theory, one of the things they'll score will be the probabilities associated with different outcomes.

But they'll also come up with the confidence associated with those probabilities and price targets.

And, we get questions about what's the difference between a probability and a confidence?

Can I express my confidence in higher probabilities?  

Well, let me give you a thought experiment to help explain the difference.  

So let's imagine that I give you a bet.  

And in that bet, we're going to flip a coin.  

If it comes up heads, I give you $200.

If it comes up tails, you pay me $100, not $200.

You pay me $100.

So there's asymmetry.  

It's positive for you. The expected return of that bet is 50%.  

Most people would take that bet, especially if you get to do it over and over and over.  

So that's one bet. The second bet I'm going to offer you is there's a huge bag of poker chips.

Imagine it's just sitting on the floor.

It's like a Santa bag full of poker chips.  

And it's got, I tell you, it's just black and white poker chips.

And I tell you, you can draw out ten chips from that bag to try and figure out the distribution of black and white chips.  

You pull out ten chips. It just happens to be five black and five white.

And so your estimation of the distribution is 50% black and 50% white.  

And so then I give you the same basic bet where I say, you pull out a black chip, I pay you $200, you pull out a white chip, you pay me $100.  

So, same upside, same downside.

And right now, the same assumed probability of upside and downside of 50%.  

And so the same expected return of 50%.  

Here's the rub, though. Is that my confidence in my probability estimate for a coin flip versus the bag of poker chips is different because I really don't know the distribution inside of that bag.  

I have a Bayesian estimate of what that probability is, but it is not as concrete as a coin flip.  

And so therein lies the difference and the reason why it's important to have probabilities and confidence.  

You can imagine a scenario where you've done like the coin flip is a name where you've done lots of work, you know, the management team, you've built the financial model, you've had your expert network calls, and another is where you haven't done some of those things.  

Your confidence level and your probabilities are different. Thanks.

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