by Dr. Sam L. Savage
The Funnel
My colleagues Bridget Cash, Matthew Raphaelson, and I have recently been examining Chance-Informed marketing decisions. It is common to view the transition of a potential customer from first awareness of a product to purchase as a funnel. As a simplified example, consider an email list of 5,000,000 potential customers. Suppose you believe that 10% of these will visit your site. Of those that do, 50% will move on to your Products page, and 40% of those will move on the shopping cart and make the purchase.
But Are You Certain?
Typically, these probabilities are not known with certainty. They may be estimated with Beta distributions or other methods. Let’s assume that the percentages are the correct average of the funnel probabilities, but that they are uncertain with independent errors as shown. Then the funnel fallacy can be stated as follows.
The Fallacy
On Average the Conversion Rate will be the Product of the Probabilities
BUT
The Chance is Over 50% that the Conversion Rate will be Below Average
Why? When you multiply positive uncertainties together, they skew to the left. The most famous example of this is the normal distribution, which comes from adding independent variables together to make a symmetric distribution and the lognormal distribution which comes from multiplying independent variables together to make a skewed distribution. But skewed to the left implies that more of the distribution is to the left of the average than to the right.
This means that when you are estimating conversion rates based on average funnel probabilities, you will get the correct average, but (and this is the legal term of art) More Likely Than Not you won’t achieve your target. And because this is a universal mathematical fact, you (and here is another legal term of art) Know This or Should Know This.
If you are involved in marketing, hiring, product development, or any other funnel driven enterprise, keep the above in mind the next time you are setting expectations.
I will be discussing the Marketing Funnel Fallacy in my Welcome to the Chance Age webinar series, taking place on September 28 and 29. I hope to see you there.
© Copyright 2022, Sam L. Savage