Meet Bob. Bob loves to fish.
After thousands of casts, Bob knows the average fish weighs about 10 pounds.
Everything Bob builds from here, he builds on that average. Watch where it comes from.
The same net, cast after cast
Live casts as they come up, and any you add.
Keep casting. The average settles and stays put. The bars behind it never do.
The bell-shaped net is lowered at a random spot. Live casts appear here as they come up.
| Cast | Where | Fish | Weight |
|---|
The groups come from Power Law Nested Means, the two-split test. Split the fish at the average weight, 10 lbs, then split each half at its own average. The 16 above-average fish, A and B, carry 84% of the weight. The biggest weighs 180 lbs, the smallest 0.5 lb. That shape is a power law: a few of something carry most of the total. You'll find it in customers, in sales and in revenue.
| Group | Weight | Fish | Share of fish | Share of weight |
|---|---|---|---|---|
| A | 56–180 lbs | 5 | 5.0% | 59.0% |
| B | 10.5–50 lbs | 11 | 11.0% | 25.0% |
| C | 2–9.5 lbs | 25 | 25.0% | 11.0% |
| D | 0.5–1.85 lbs | 59 | 59.0% | 5.0% |
| Total | 100 | 100.0% | 100.0% |
The net is a bell curve lowered over the line. Over the giants it brings up a few heavy fish; over the little ones, dozens of light ones. Cast after cast the throws average about 25 fish and 250 lbs. The averages settle because the water holds a fixed set of fish, the biggest 180 lbs; a true power law with a tail this heavy never settles, however many throws are added up.
There's a reason Bob never notices his average isn't really an average. He isn't fishing one side of the water, where the big ones are. He drops the net into a cube of water and pulls up a lot of fish.
Live casts as they come up, and any you add.
Same fish, same net. In the cube the average lands on 10 pounds and the casts bunch tighter. About 25 fish and 250 pounds a cast. That's something Bob can build on.
The same round net every time, cast at the middle of the cube. Live casts appear here as they come up.
| Cast | Where | Fish | Weight |
|---|
Between the line and the cube: the same 100 fish swimming mixed across one width, and the same bell net lowered at the same spot each time. The fish count evens out, but one giant can still make a cast.
Live casts appear here as they come up.
| Cast | Where | Fish | Weight |
|---|
Some casts bring up less and some more, but there's enough consistency to build around. Going to get it costs money every day, and so does selling it. Every business boils down to the same three things: a product, a sale and the margin between them.
The receipt for this cast
Each bar is one cast: what it left after the cast and the handling. Green above zero, pink below.
The first catch is on its way.
On average a cast brings in $375, pays $250 to get the catch in and $25 to sell it, and leaves $100. About 1 cast in 3 doesn't cover its costs, and one giant can carry a cast to several hundred dollars.
The same three things, whatever the business: what it costs to get the product in, what the sale costs, what it sells for.
About $100 a cast, and $10 to land each fish. One cast is a gamble. After enough casts, it's a business.
contribution after acquisition per cast = $1.50 × pounds − $250 − $1 × fish caught
cost of acquiring a fish = $250 ÷ fish caught
The $250 to get the catch in is the acquisition cost. The $1 a fish to sell it is a variable cost, because it rises with every fish. The sale is the net revenue. Less the variable cost it's the contribution, and less the acquisition cost as well it's the contribution after acquisition, what each cast leaves. Operating expenses, the dock, the boat payments and the rest of the overhead, don't change from one cast to the next, so they stay out of it and get paid out of it. Contribution margin is the contribution as a share of net revenue: $350 of $375 here, 93%.
Split the $250 across the 25 fish it brings up and each fish costs $10 to catch. That's the cost of acquiring a fish, what The Numbers, Defined calls the cost per acquisition.
Bob needs money to grow, so he takes the numbers to investors. For every dollar you put in, over the long haul, 36 cents comes back on top of it. They're excited: "You're telling us you take a dollar today and hand back $1.36 tomorrow?" The cycle is that fast. Pay for the cast, the boat goes out, the boat comes in, the fish sell, the money is back.
One cast on its own is a gamble: about 1 in 3 doesn't pay back. A hundred casts aren't. Over 100 casts, 8 in 10 investors land between 1.27 to 1.45 per $1. They put the money in.
Grey is what's invested. The bar runs on to net revenue, so the colored part past the grey is the contribution after acquisition.
But any investor group reads the numbers the same way. The boat is the big cost, and nothing is being done to support it. What if the boat had bait? What if the fish swam toward the net?
invested = $250 × casts + $1 × fish caught
revenue return (R2M) = net revenue ÷ invested · contribution return = revenue return − 1
$27,500 funds 100 casts: $25,000 for the casts and about $2,500 to handle the 2,500 fish they bring up. On average the $27,500 brings back $37,500 of net revenue, a revenue return of 1.36 (136%), and $10,000 of contribution after acquisition, a contribution return of 0.36 (36%). After 1 cast, 8 in 10 investors land anywhere from 0.50 to 2.31; after 10 casts 1.09 to 1.65; after 100, 1.27 to 1.45. Each investor here funds 100 casts drawn from 20,000 no-bait casts, and the band is where 8 in 10 of 4,000 investors land. These follow The Numbers, Defined, the page every number on this site uses.
"Bob, you've fished this water for years. You're the reason we're all here. You know these fish better than anyone. Who should the bait be built for?" The answer is the fish everyone has been planning around: the average one. Ten pounds, right in the middle of the bell.
They build it. Bait costs $10 a cast, on top of the $250, so it's part of the acquisition cost. And it works.
No bait
4 casts bring up 100 fish
With bait
4 casts bring up 110 fish
More fish, 25 to 27.5 a cast, and bigger fish, because the bait sits in the middle and the big volume of little fish is way over on the right. About 28% more B fish and 28% more C fish on every cast. Each cast earns $125 instead of $100, and each fish costs $9.45 to land instead of $10.
The receipt for this cast
The first catch is on its way.
Back to the investors. Bob said a dollar comes back as $1.36. With the bait it comes back as $1.43. Marketing looks like heroes, and the investors say what investors say: spend more on the bait. Get more fish in the net.
Grey is what's invested. The bar runs on to net revenue, so the colored part past the grey is the contribution after acquisition.
Scale it. Four times the fish, call it 100 a cast, with the cost per fish coming down and every fish still earning its $4.55. Drag the catch up to see their math.
That number is the investor baseline. The fish the team lands, each still earning its $4.55. Every test from here is judged against it.
cost of acquiring a fish = ($250 cast + $10 bait) ÷ fish caught
contribution after acquisition per cast = $1.50 × pounds − $250 − $10 − $1 × fish
investor baseline per cast = fish landed × $4.55, where fish landed = $260 ÷ cost of acquiring a fish
The bait adds 2.5 fish of the average size to each cast: 25 more pounds, $37.50 more from the merchant and $2.50 more in handling, so $35 more contribution before the bait's own $10. Every $10 of bait brings back $35. The fish it pulls in more often are the 36 fish from 2 to 50 lbs, groups B and C, which average exactly 10 lbs. $125 spread over 27.5 fish is $4.55 a fish, and that is what the investors expect every fish to keep earning as the team lands more of them.
Now the team has one job: make the bait better. Every round they test a small change against the bait in use, cast after cast, and keep whichever wins. Keep the winner on what? That one choice is the whole story.
Drive the cost per fish down
What most marketing teams are told to do. Count the fish, keep the bait that lands more of them for the same $260.
Grow the contribution on every cast
What the e-com world figured out. Connect what each cast actually leaves to the test, and let it optimize on that.
On path 1 every test wins, and every win is a loss. There are more small fish than big ones, so the bait that lands more fish is the bait that lands smaller fish, round after round. The team started in the right place and ends up in the wrong end of the ocean: $28 a cast, and the investor baseline they were chasing is $426.
On path 2 the cost per fish goes up first, $9.45 to $10.86. That's the point. The bait finds bigger and bigger fish, the misses get bigger than anyone expected, and it compounds: $1,045 a cast, eight times what the bait started at.
The bait, before testing
27.5 fish a cast
Tested on CAC
93.7 fish a cast
Tested on contribution after acquisition
23.95 fish a cast
Grey is what's invested. The bar runs on to net revenue, so the colored part past the grey is the contribution after acquisition.
Each bar is $1 of net revenue: light grey goes to handling, grey to the cast and the bait, and the colored part is what's left after acquisition.
Read as an investor, path 1 brings back 1.08 (108%) on every $1, down from 1.43 (143%). Path 2 brings back 4.68 (468%). Read as margins, the bait started at a 93% contribution margin and 30% after acquisition. Path 1 lands a crowd of tiny fish that each cost the same $1 to sell: 75% and 7%. Path 2: 98% and 79%.
Optimize for contribution margin, not for fish. When you can see what every cast is worth the moment it's sold, judge every test by what it leaves of every $1, not by the cost of acquiring a fish. Cost per lead going up only matters if you can hold margin. And if you have no way to tell how big a fish is when you catch it, you'll optimize in the wrong direction every time.
Most businesses can't see the size of the fish when they buy it. That's the next story.
Picking the bait that earns more is selection on how strongly each bait pulls each fish. The cast and the bait cost the same $260 whatever the bait, so whatever the fish, the result is
change in contribution after acquisition per cast = fish per cast × [Cov(pull, contribution per fish) + (average pull − 1) × average contribution per fish]
Pull is how many times as likely the new bait is to land each fish as the bait in use, and both averages are taken over the fish the bait in use lands. The first part is selection, more pull on the fish worth more. The second is volume, more pull on every fish. A fish's contribution is $1.50 for each pound it grows to, less $1 to handle it: about $176 for an A-tier fish, $33 for a B, $5.60 for a C and 27 cents for a D. Optimized on the cost of acquiring a fish, the tests keep whichever bait lands more fish, since the same $260 spread over more fish costs less per fish, and it drops to $2.77. Each test sets the bait in use against a new one, checks every 50 casts for up to 500, and keeps the new bait when it wins at p < 0.05. The lines are averages over 200 runs of the 20 rounds. Tested on contribution after acquisition, 8 in 10 runs finish between $446 and $1,905 a cast; tested on the cost of acquiring a fish, between −$78 and $166, and 48 runs in 100 end up losing money on the average cast. Pair one run of each at random and path 2 comes out ahead 996 times in 1,000.
What the winning bait pulls in, compared with no bait
About the numbers. Illustrative. 100 fish weighing 1,000 lbs, 180 lbs down to 0.5 lb, split into four groups by Power Law Nested Means. In scene 1 the net is a bell curve lowered at a random spot along the line; from scene 2 it is a round net cast at the middle of the cube, where every fish has the same 1 in 4 chance of being in it. Scenes 1 to 5 use the same 100 fish and scene 6 three copies of each. A cast costs $250, bait $10 a cast, handling $1 a fish, and the merchant pays $1.50 a pound. Every bait test sets the bait in use against a new one, checks every 50 casts for up to 500, and keeps the new bait when it wins at p < 0.05. The rounds in scene 6 are the average of 200 runs worked out in advance; the size of each change sets how fast the lines move, not which way. In scene 4 each investor funds 100 casts drawn from 20,000, and the band is where 8 in 10 of 4,000 investors land. Casts run in your browser, and caught fish go back in the water.