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. Here's the part that wasn't in the first two scenes: the fish Bob catches aren't worth anything yet. They're caught small. They go into a pool, slide from pool to pool, and only the ones that reach the last pool grow into their size and get sold. Only 1 in 4 make it, so Bob fishes a net four times the size: each $250 cast brings up about 100 fish, and the 25 that reach pool 5 are the same 25 fish, the same 250 pounds, a cast sold at the dock.
The first fish are still growing.
On average a cast brings up about 100 fish; 25 of them reach pool 5 and grow to about 250 pounds, which the merchant buys for $375. The cast costs $250 and handling the sale $25, and it leaves $100: the dock's cast, sold weeks later. Not every cast covers its costs, and one giant can carry a cast a long way.
The same things, whatever the business: what it costs to get the product in, what it costs to carry and sell, what it sells for, and how much of it makes it to the sale.
About $100 a cast, and $10 for each fish sold, the same as if every fish sold at the dock; a fish caught costs $2.50, but three in four never sell. The difference is that the money is out for weeks before the fish are sold, and nothing in pools 1 to 4 says what a catch is worth. In a business, pool 1 is a new lead and pool 5 is a customer who grows into what they're worth over time.
contribution after acquisition per cast = $1.50 × pounds sold from pool 5 − $250 − $1 × fish sold
cost per fish sold = $250 ÷ fish sold · invested = $250 + $1 × fish sold
Every slide has a grate: 71 in 100 fish make it and 29 slip through, so 1 in 4 of the catch reach pool 5. The net here is four times the dock's: the same $250 cast brings up about 100 fish, and the 25 that reach pool 5 are a fair draw from the ocean, the same 25 fish and 250 pounds a cast the dock sold, so with enough fish caught, every 100 that reach it hold the same mix as the 100 fish in scene 1: 1,000 lbs, 5 A-tier fish and 59 D-tier fish. Pool 5 shows the latest 100 fish to reach it, and as new fish come in, the merchant buys the oldest, at the dock's $1.50 a pound. Nothing is spent on a fish that doesn't make it, and the $1 to handle a sale is the only variable cost, so the money is Story 1's: the average cast takes $275 to bring back $375. 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.
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, with one eye on the calendar: the money goes in at the catch and comes back weeks later, when the fish are sold out of pool 5.
One cast on its own is a gamble. 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 sold out of pool 5
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 sold out of pool 5, of about 10,000 caught. On average it 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. Sold at the dock, the same casts return the same 1.36 (136%) per $1; what changes here is when the money comes back. 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, about 100 to 110 caught a cast and 25 to 27.5 sold, and once they've grown, 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. Once the fish are sold, each cast earns $125 instead of $100, and each fish sold costs $9.45 instead of $10. Nobody at the dock can see that yet; it shows up in pool 5, weeks later.
Back to the investors. Bob said a dollar comes back as 1.36 (136%). With the bait, once the fish are sold, it comes back as 1.43 (143%). 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 sold, call it 100 a cast out of pool 5, with the cost per fish sold coming down and every fish still earning its $4.55 once it's grown. 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 per fish sold = ($250 cast + $10 bait) ÷ fish sold
contribution after acquisition per cast, once sold = $1.50 × pounds sold from pool 5 − $250 − $10 − $1 × fish sold
investor baseline per cast = fish landed × $4.55, where fish landed = $260 ÷ cost of acquiring a fish
The bait adds about 10 fish of the average size to each cast, 2.5 of them sold out of pool 5, and once they're grown that's $25 more contribution a cast after 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. The bait takes the average cast from $275 invested and $375 back to $288 and $413: 1.36 (136%) to 1.43 (143%) per $1, the same as at the dock. $125 spread over 27.5 fish sold is $4.55 a fish, and that is what the investors expect every fish to keep earning as the team lands more of them.
Bring the bait back at $10 a cast, and hand the team the plan: more fish, the cost per fish coming down, every fish still earning its $4.55. Each test tries a small change against the bait in use, cast after cast, and the team keeps the winner. But nobody knows what a catch is worth until its fish grow, weeks later. So the team counts what it can see: the fish that reach a pool. Pick the pool.
Every fish makes each slide at the same 71 in 100, so whichever pool the team counts, the tests keep the bait that lands more fish. The dashboard prices every fish at the average, so more fish always looks like more money. After 20 tests the dashboard says $1,707 a cast. Once the fish grow, it's $542: $97 short of the $639 baseline, with the cheapest fish in the story, $0.46 a fish caught and $1.85 a fish sold. The catch is 562 fish a cast and 140.5 of them sell, at less than half the weight the plan priced them at. Counting at pool 5 instead of pool 1 doesn't fix it. Each test takes longer, so the bait drifts the same way, more slowly.
Grey is what's invested. The bar runs on to net revenue, so the colored part past the grey is the contribution after acquisition.
For an investor, the dashboard promises a revenue return of 5.26 (526%). Once the fish grow, it's 2.35 (235%), against the 2.59 (259%) the plan priced those fish at. More fish did bring more money, five times the fish sold for about four times the contribution, but every one of them was priced at a fish it isn't. Every number on the dashboard is green. The dashboard is 15% ahead of the business it describes, and growing.
contribution after acquisition that never shows up = fish sold × $1.50 × (10 lbs − the real average weight), where fish sold = fish caught ÷ 4
When every fish is sold the day it's caught at its full size, as in Point of Sale, tests on contribution after acquisition raise each cast from $125 to $1,045. Here, aimed at the fish caught, they sink it first and lift it only to $542 after 20 tests, against a baseline of $639, while the dashboard reports $1,707 and the cost per fish sold falls from $9.45 to $1.85. A test runs a week of casts, and its fish take another week for every slide they cross, so a test aimed at pool 5 takes five weeks: after 20 tests, 100 weeks in, it's $464 against a baseline of $565. Until the fish grow, every pool is a count of fish. 100% of the baits adopted pull in fish that grow up lighter. The real weights only show once the fish have reached pool 5 and grown, about 6 weeks after the catch.
What the bait is really pulling in (nobody can see this at the dock)
Look closer at the catch. Every fish is still the same size and still blue, but some have a green tail and some a pink one. The funnel treats every fish the same, and 71 in 100 of each make every slide. Pool 5 is where they split: as each fish grows, its tail's color spreads over the whole fish.
Run the business first. Before anyone tests a bait, run it as it is, with no bait, so every cast is a fair draw from the ocean. Nothing in pools 1 to 4 shows what the catch is worth. Pool 5 shows it, as the fish grow. Once the teams below pick a bait, this funnel follows it.
Run it long enough and pool 5 has the data: the tail at the dock says what a fish grows into. A green-tailed fish grows into a giant 1 time in 5. A blue fish or a pink-tailed one does it 1 time in 50. Once the fish grow, every green-tailed fish sold earns about $59, and every other one about $5.
Now hand the bait to two teams. The Lower CAC team does what most teams do: it counts fish, at pool 1 or further down, and keeps whichever bait lands the most. The Value/signal team counts green-tailed fish at pool 1 and prices each one at what green-tailed fish grow into, so it knows what a cast is worth the moment it lands. Pick an option below.
The Lower CAC team's catch is almost all blue and pink-tailed fish, the easiest to land in numbers. The Value/signal team's catch is about three quarters green-tailed.
Both teams spend the same $260 a cast on the net and the bait. By round 20 the Value/signal team makes 2.2 times the contribution after acquisition on 73% of the money: $294 a cast in, $1,188 out. The Lower CAC team puts $400 in, because it pays to handle the sale of a crowd of small fish, and makes $542: 1.9 times the baseline against 85% of it. Every $1 the Value/signal team puts in brings back 5.05 (505%); the Lower CAC team's $1 brings back 2.35 (235%).
Grey is what's invested. The bar runs on to net revenue, so the colored part past the grey is the contribution after acquisition.
Against the baseline, the Lower CAC team delivers the cheapest fish in the story, under $2 a fish sold, and still finishes $97 a cast short of the $639 baseline, because its fish don't keep their $4.55. The Value/signal team pays more for each fish at first, up to $10.83, then less as the green-tailed fish come in, and finishes at 1.9 times the baseline. Runs vary: 8 in 10 Value/signal runs finish between $345 and $2,570 a cast, and 8 in 10 Lower CAC runs between $172 and $1,042. Pair one run of each at random, and Value/signal comes out ahead 76 times in 100.
Optimize for the signal, not the thing. Same boat, same bait budget, same funnel. The only difference is what each team optimized for.
Find a signal you can see at the catch that tells you what shows up later. Price every fish by what its signal grows into, not by the average fish. Judge every test against the baseline in real contribution after acquisition and return on every $1, not in cost per fish.
contribution after acquisition per cast at the dock = $59.80 × green-tailed fish sold + $6.04 × every other fish sold − $260 − $1 × fish sold, where the fish sold are 1 in 4 of the catch
150 of the 900 fish have green tails: 30 of the 45 A-tier fish, all 99 B-tier fish and the 21 heaviest C-tier fish. The other 750 are 400 blue fish and 350 with pink tails, each with the same mix: 1 in 50 of them A-tier and the rest C and D-tier fish. At pool 5's $1.50 a pound, a green fish sells for about $60 and a blue or pink one for about $6. Both teams start from the scene 5 bait, about 110 fish caught and 27.5 sold a cast in the same mix as the ocean, and run the same tests. Some fish swim into any net whatever the bait, so even the Lower CAC bait keeps landing a few green-tailed ones, a little over 1 in 100 by round 20, and each cast sinks from $125 to about $111 before the sheer number of fish lifts it back to $542. Bait is finite, so drawing more green-tailed fish means drawing fewer of the rest: at first the Value/signal bait lands fewer fish, and each one costs more, up to $10.83 by round 8. Then the green-tailed fish come in numbers, the cost falls to $7.70, and each cast climbs to $1,188. Every fish with the same tail is alike at the dock, so the price the dock puts on a cast is right on average: the value seen in pool 5 is the value priced at pool 1. The signal here is perfect and never degrades; a real one is found by back-testing it against realized value and confirmed with a holdout.
What each color is worth over a lifetime
Point of Sale runs the same Lower CAC tests on fish sold the day they're caught, at their full size, and each cast falls from $125 to $28. Here, it climbs. Both teams keep whichever bait lands more fish. What differs is what the bait can tell apart, and so what each extra fish is worth.
| At the point of sale | Here, scene 8 | |
|---|---|---|
| What the bait can tell apart | Size | Only tail color |
| What landing more fish brings in | The tiniest fish: 78 of 93.7 a cast by round 20 | More blue and pink-tailed fish, in the same mix as always |
| Contribution after acquisition from each extra fish | 27 cents: 0.85 lbs × $1.50 − $1 handling | $5.04: the blue and pink average, after handling |
| Contribution after acquisition per cast | $125 → $28 | $125 → $111 by round 3 → $542 by round 20 |
At the point of sale the bait can pull some sizes harder than others, so the tests that reward more fish trade bigger fish for tiny ones worth almost nothing, round after round. Here the bait can only pick blue or pink-tailed fish. Those fish come in a fixed mix, 1 in 50 of them growing into a giant, so every extra one still carries their average, $5.04. For the first 3 rounds the bait gives up green-tailed fish faster than volume makes up for them: 0.8 green-tailed fish a cast at about $59 each, about $49, against 7 more blue or pink-tailed fish worth about $35, so each cast falls from $125 to $111. After that, green tails are nearly gone, 3.8 a cast down to 1.7, about $118 more, while the catch grows to 140.5 fish: 109 more blue or pink-tailed fish add about $549, and each cast climbs to $542. That makes this scene generous to the Lower CAC team. A bait that could pick small fish directly, as at the point of sale, would trade bigger fish for ones worth 27 cents each once they're sold, and each cast would fall the way it does there.
A signal can be applied from the moment a fish is about to be caught. Here the fish identifies itself before the net ever touches it: it swims at the green square, the blue circle or the pink triangle, and the one it picks is its tag. A fish-identified signal, and it stays with the fish all the way to pool 5, where its lifetime value shows. Track the two together long enough to see how tag and value line up, and the signal becomes the thing to optimize: land more of the fish that pick the shape that grows into value, and the value follows.
Optimize for the signal, not the thing. Once every fish carries its tag, the dashboard in scene 6 isn't blind any more: it can count green-tailed fish at pool 1 and price each one at what green-tailed fish grow into, the way the Value/signal team did.
contribution after acquisition per cast at the dock = $59.80 × green-tailed fish sold + $6.04 × every other fish sold − $260 − $1 × fish sold, where the fish sold are 1 in 4 of the catch
The tag is the signal read at the catch. Here it's perfect: every fish with the same tail is alike at the dock, so the price the dock puts on a cast is right on average, and the value seen in pool 5 is the value priced at pool 1. A real signal is found by back-testing it against realized value and confirmed with a holdout, and it can decay as the catch concentrates on it. The three walls are the three ways one book gets read on this site: revenue returned, investment made, and the funnel the account moved through.
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; in 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 and 2 use the same 100 fish and scenes 3 to 8 nine copies of each, the ocean. A cast costs $250, bait $10 a cast, and the merchant pays $1.50 a pound, at the dock or at pool 5. From scene 3 the net is four times the dock's: each cast lands about 100 fish, every one caught the same small size, and the fish drift from pool to pool at their own pace; about 29 in 100 slip through the grate on each slide, so 1 in 4 reach pool 5, grow into their lifetime size and are sold there, with $1 to handle each fish sold. Nothing is spent on a fish that doesn't make it, so the average cast sells the same 25 fish and 250 lbs as at the dock and the money is the same: $275 in, $375 back. In scene 6 a test runs a week of casts, and its fish take another week for each slide they cross. 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 scenes 6 and 7 are the average of 200 runs worked out in advance, and the shading in scene 7 shows where 8 in 10 of those runs land; 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. In scene 8 the three walls are the shadow room from Above Baseline Pro, redrawn here, and each fish picks a wall in the ocean's own mix of tails. Casts run in your browser, and caught fish go back in the water.