Funnel Math: When Your Best Budget Move Isn’t Another Channel
Here’s a classic you’ve probably seen.
“A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?”
I’ve seen this quoted dozens of times, I know its wrong, but still my hardwired brain says “the bat is a $1.00, the ball is $0.10.” (Spoiler…no. Bat = $1.05, ball = $0.05).
This first shows up in a paper by Kahneman and Frederick, and an example of “System 1” thinking — our fast, intuitive, subconscious mode — and where it can get things wrong. The key is that the false assumptions seem both plausible and simple. It feels right that a ball would cost one-tenth of what a bat would cost. Also your brain likes easy math, and ($1.00 + $0.10 = $1.10) is quite easy.
When I talk with marketers about our service (for context — a tool to increase conversion on your existing traffic), a similar “quick math” error pops up that looks something like this:
“Your CAC is $200 through paid channels. You’re looking at a tool to convert more paid traffic that costs $100 per incremental customer — what is your new CAC?”
If your instinct was “$300”, you’re not alone. You would, however, be wrong. The reason is similar to the bat and ball — the two costs interact. If you convert more customers from your current traffic, your existing CAC goes down (because the denominator, customers, goes up).
For example, here’s what that math looks like with a 20% increase in customers (a conservative number from what we've seen):
| Baseline | New | |
|---|---|---|
| Spend | $200,000 | $220,000 |
| Customers | 1,000 | 1,200 |
| CAC | $200 | $183 |
You spend $20k more, but you get 200 more customers (i.e. that $100 CPA). Your overall CAC goes down by almost 10%, despite the spend increase, because you’re spreading it over more customers.
I think two cognitive quirks trip marketers up here:
(1) We like pumping acquisition budgets, especially in new channels, and
(2) we like to act as if each channel lives in its own silo
That’s why we swallow the CPAs ad platforms feed us, or lean on a simple click-attribution system that seems directionally correct, but better than wading into the multi-touch mess.
However, your existing on‑site traffic is a cleaner, cheaper sandbox for proving incremental gains. Even if you have to spend money to convert those incremental customers, as long as its less per customer than your current marginal CAC, its the right place to invest.
