Part 1 · Steps 1 to 6

When every catch is sold on the spot

Meet the fish

Are all fish worth the same?

Picture 100 fish lined up from biggest to smallest. Together they weigh 1,000 lbs, so the average fish weighs 10 lbs. But not one of them weighs 10 lbs.

A net drops over a random spot in the line. Over the giants it brings up a few heavy fish. Over the little ones it brings up dozens of light ones. It's the same net on every throw, shaped like a bell curve, and only where it lands changes. Over time the throws average about 25 fish and 250 lbs, but a single throw can land a long way from that.

100 fish, lined up by size

1,000 lbs in all, 180 lbs down to 0.5 lb

The first net goes in shortly
The 100 fish on one line, smallest to biggest
0.5 lb21050180 lbsAverage: 10 lbs. Not one fish weighs it.84 fish below16 above59 fish weigh less than 2 lbsthe biggest: 180 lbs

Put every fish on one line and the average sits in a gap. 84 fish weigh less than it and 16 weigh more. The biggest weighs 180 lbs, and 59 weigh less than 2 lbs.

Share of the fish and share of the weight, group by group
Share of the fishShare of the weight
A · 5 giants 56 to 180 lbs
5% of the fish
59% of the weight
B · 11 big fish 10.5 to 50 lbs
11% of the fish
25% of the weight
C · 25 small fish 2 to 9.5 lbs
25% of the fish
11% of the weight
D · 59 tiny fish 0.5 to 1.85 lbs
59% of the fish
5% of the weight

Now look at the bars. The 5 biggest fish are 5% of the fish and 59% of the weight. The 59 smallest are 59% of the fish and 5% of the weight. A few fish carry most of the weight. That shape is called a power law, and you'll find it in customers, in sales and in revenue. You don't have an average business. You have a power law business.

Keep an eye on those 5 giants. Most of the money is in them, and the rest of the story is about whether you catch them.

The four tiers

The four groups come from Power Law Nested Means. 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. Steps 5 to 9 come back to these tiers.

GroupWeightFishShare of fishShare of weight
A56–180 lbs55.0%59.0%
B10.5–50 lbs1111.0%25.0%
C2–9.5 lbs2525.0%11.0%
D0.5–1.85 lbs5959.0%5.0%
Total100100.0%100.0%

Cast the net

What does one cast bring up?

Now the same 100 fish swim wherever they like in a cube of water. You can't see which fish are where, so you cast the net in the middle every time and take what comes up.

The same 100 fish, in a cube

The first net goes in shortly
SmallerBigger: the bigger the fish, the darker the blue

What each cast brings up

Every cast is counted here, live casts as they come up and any quick casts you add.

Fish per cast

Pounds per cast

Every cast

The same round net every time, cast in the middle of the cube. Live casts appear here as they come up.

CastWhereFishWeight

One cast is luck. Some casts bring up fewer than 20 fish and some more than 30. The weight swings even more, because one giant can make a cast. But cast after cast, the average settles at about 25 fish and 250 lbs.

That steady average is your baseline. It's what happens if everyone takes their hands off the wheel and keeps doing the job the same way. If nothing changes, it's what the casts keep landing. The fish count settles fast. The weight takes longer, because one big fish can still make a cast.

Extra: the same fish, lined up and mixed

In step 1 the fish were lined up by size, so where the net landed decided the catch. Mixed together, the fish count evens out, but one giant can still make a cast. In the cube, every cast is a fair draw. The quick casts above count in all three.

Lined up by size, what each throw brings up

Every throw is counted here.

Fish per throw

Pounds per throw

Every throw

The bell-shaped net is lowered at a random spot. Live throws appear here as they come up.

ThrowWhereFishWeight

The same 100 fish, mixed

The same water and the same bell net as step 1

The first net goes in shortly

Mixed, what each throw brings up

Every throw is counted here.

Fish per throw

Pounds per throw

Every throw

The same bell-shaped net, lowered at the same spot each time. Live throws appear here as they come up.

ThrowWhereFishWeight

Let's turn it into a business

Does this business make money?

So far you've been fishing. Now it's a business, one operation from the cast to the sale. Every catch goes into a pool, and a merchant buys the fish straight out of it at $1.50 a pound. Each fish here is caught at its full-grown size, so it's weighed and paid for on the spot.

Two costs come out of the sale. The cast costs $250 every time, for the boat, the crew and the fuel, whether the net lands 10 fish or 40. Handling costs $1 a fish, to get each one out of the net. The cast is the acquisition cost, and handling is a variable cost, because it rises with every fish. The sale is the net revenue. Less handling, it's the contribution, and less the cast 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.

Each catch goes into a pool, and the merchant pays by the pound

The next cast from the cube comes here

The receipt for this cast

Sale–$1.50 a pound
The cast–acquisition, $250 every cast
Handling–variable cost, $1 a fish
Contribution after acquisition–this cast, so far
The last 5 casts
Every cast so far

The first catch is on its way.

The average cast, from net revenue to what it leaves
Net revenue$375The cast−$250Handling−$25Contribution after acquisition$100
One cast is luck: about 1 in 3 casts don't cover their costs
10 of every 30 casts lose money20 make money

On average a cast brings in $375, pays $250 for the cast and $25 for handling, and leaves $100. But one cast is luck. About a third of them don't cover the $250, and one giant can carry a cast to several hundred dollars.

What one fish costs to catch: the cast split across the fish it brings up
No bait: $250 for 25 fish$10.00 a fishone fish

Split the $250 cast across the 25 fish it brings up, and each fish costs $10 to catch. That's your cost of acquiring a fish.

The math

contribution after acquisition per cast = $1.50 × pounds − $250 − $1 × fish caught

cost of acquiring a fish = $250 ÷ fish caught

The price is locked at $1.50 a pound, so every catch is worth exactly what it weighs. Over enough casts the swings cancel out and the average settles at about $100 a cast: 25 fish and 250 lbs, $375 from the merchant, less $250 for the cast and $25 to handle the fish. The operating expenses stay the same from cast to cast, so the contribution after acquisition per cast is the number to judge a catch by.

A business that works. Every cast earns about $100, and every fish costs about $10 to catch. The averages hold, so the business can plan on them, and every extra cast adds about $100 more toward the operating expenses. Before it grows, someone has to put money behind it. So ask the question every investor asks first.

Take the investor's chair

Would you put money into this business?

Every cast has to be paid for before the merchant pays for the fish. Say the money is yours. You put up $27,500 to fund 100 casts: $25,000 for the casts and about $2,500 to handle the 2,500 fish they bring up. That's what you've invested.

Two numbers tell an investor how it's going, both read per $1 invested, the way The Numbers, Defined reads every return on this site. The revenue return, R2M, is the net revenue that comes back for every $1. The contribution return is the contribution after acquisition for every $1, which is R2M minus 1. Invested counts the acquisition cost, the $250 cast, and the variable costs, $1 to handle each fish.

Your $27,500, one cast at a time

Cast 0 of 100
0.001.002.003.00Paid back: 1.00 (100%)1255075100Casts fundedOn average: 1.36 (136%)8 in 10 investors land in the shaded band
Casts funded0of 100
Invested$0$250 a cast + $1 a fish
Net revenue$0what the merchant paid
Revenue return–net revenue ÷ invested
Contribution return–revenue return − 1
The first cast goes in shortly.

One cast on its own is a gamble. The average cast brings $375 back on $275 invested, a revenue return of 1.36 (136%). But about 1 in 3 casts comes in under 1.00 and doesn't pay back, and a cast with a giant in it can come back as high as 4.00 (400%).

The chance you haven't been paid back yet
After 1 cast35%, about 1 in 3After 5 casts12%, about 1 in 8After 10 casts4%, about 1 in 22After 20 castsunder 1%, about 1 in 135After 50 castsalmost never, under 1 in 20,000

Your money doesn't ride on one cast. It rides on all 100. The more casts you fund, the more the good ones cover the bad ones, and the closer your return gets to the average. After 1 cast, 8 in 10 investors land anywhere from 0.50 to 2.31. After 10 casts it's 1.09 to 1.65, and after 100 it's 1.27 to 1.45.

What $27,500 brings back over 100 casts
A slow 100 castsRevenue return 1.27 (127%)
$27,500 invested · $35,000 net revenue
Contribution after acquisition $7,500Contribution return 0.27 (27%)
The average 100 castsRevenue return 1.36 (136%)
$27,500 invested · $37,500 net revenue
Contribution after acquisition $10,000Contribution return 0.36 (36%)
A lucky 100 castsRevenue return 1.45 (145%)
$27,500 invested · $40,000 net revenue
Contribution after acquisition $12,500Contribution return 0.45 (45%)

Grey is what's invested. The bar runs on to net revenue, so the colored part past the grey is the contribution after acquisition.

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%). Even a slow 100 casts brings back more than you put in.

The math

invested = $250 × casts + $1 × fish caught

revenue return = net revenue ÷ invested

contribution return = contribution after acquisition ÷ invested = revenue return − 1

These follow The Numbers, Defined, the page every number on this site uses. Invested counts the acquisition cost and the variable costs. Count only the $250 cast as invested and the same average cast reads 1.50, $375 ÷ $250, the acquisition-only setting. That one pays back at 1 divided by the contribution margin, 1 ÷ 93% = 1.07, because handling still has to come out of the $375. 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.

One cast is a gamble. A hundred casts is a business. Any single cast can lose money, but your return settles at about 1.36 as the casts add up, so you'd put your money in. That's what makes the averages worth planning on: an investor doesn't need every cast to pay back, only enough of them. The next question every business asks is how to make every $1 work harder. That's where marketing comes in.

Add bait

Can marketing help?

Marketing is bait in the net. It brings more fish into every cast, and it costs $10 a cast on top of the $250 cast, so it's part of the acquisition cost.

The marketing team builds the bait around the average fish, 10 lbs, so it pulls in more of the middle-size fish, the ones from 2 to 50 lbs. The giants and the tiny fish come in the same as before. Those 36 fish, tiers B and C, average exactly 10 lbs, so the bait is aimed squarely at the business's average.

The same 100 fish, bait in the net

The first cast goes in shortly
What's in the net, on average: 4 casts with no bait and 4 casts with bait

No bait

4 casts bring up 100 fish

Giants 5
Big 11
Small 25
Tiny 59

With bait

4 casts bring up 110 fish

Giants 5
Big 14 +3
Small 32 +7
Tiny 59

And it works. Every 4 casts with no bait bring up 100 fish, the same mix as the water. With bait, 4 casts bring up 110: 3 more big fish and 7 more small ones.

No bait next to bait, on average
No baitWith baitFish per cast2527.5Contribution after acquisition$100$125Cost per fish$10.00$9.45
Every $10 of bait brings back $35
Bait, every cast$10More profit it brings in$35

Each cast earns $125 instead of $100, and each fish costs $9.45 to catch instead of $10. Every $10 of bait brings back $35, so the marketing pays for itself three and a half times over. It adds volume, 10% more fish, and more importantly it adds value, 25% more contribution after acquisition per cast.

That makes $125 your new baseline, about $4.55 for every fish the bait lands: $125 spread over 27.5 fish.

In step 2 the baseline was hands off the wheel: what you get if nothing changes. Paying for bait changes that. Whoever pays for it expects the team to keep improving it, test after test: a lower cost of acquiring a fish, so the same $260 lands more fish, and every fish still earning its $4.55. So the baseline rises as the cost of acquiring a fish falls. Cut it to $1.85 a fish and the $260 lands 140.5 fish, so the baseline is 140.5 × $4.55 = $639 a cast.

The baseline: CAC improves, every fish still earns $4.55
$0$200$400$600050$5.20100$2.60150$1.73FishCostFish landed per cast, and the cost per fish: $260 ÷ fishNow: $9.45 a fish27.5 fish × $4.55 = $125Cut to $1.85 a fish140.5 fish × $4.55 = $639
What every $1 brings back, with and without bait
No baitRevenue return 1.36 (136%)
$275 invested · $375 net revenue
Contribution after acquisition $100Contribution return 0.36 (36%)
With baitRevenue return 1.43 (143%)
$288 invested · $413 net revenue
Contribution after acquisition $125Contribution return 0.43 (43%)

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 bait lifts the revenue return from 1.36 (136%) to 1.43 (143%). Every $1 invested now brings back 7 cents more, and the contribution return rises from 0.36 to 0.43.

Fish per cast
Contribution after acquisition per cast

Replay the sales

The same merchant buys every baited cast at the same $1.50 a pound, with the same $1 to handle each fish. Single casts still swing, and some still lose money, but the average settles higher than before the bait.

The baited catch, sold at the same $1.50 a pound

The next cast from the cube comes here

The receipt for this cast

Sale–$1.50 a pound
The cast and the bait–acquisition, $250 + $10 bait
Handling–variable cost, $1 a fish
Contribution after acquisition–this cast, so far
The last 5 casts
Every baited cast so far

The first catch is on its way.

The math

cost of acquiring a fish = ($250 cast + $10 bait) ÷ fish caught

contribution after acquisition per cast = $1.50 × pounds − $250 − $10 − $1 × fish

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. 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.

How much more often the bait pulls in each fish, compared with no bait

Pick what to optimize

Which number do you tell the team to improve?

The view pulls back to 300 fish, three of every fish, so a cast still lands about 27.5 fish. Now the team gets one job: make the bait better. Each round they try a small change to the bait and test it against the bait in use, cast after cast. They keep whichever wins on the one number they were told to improve. No change is designed to favor small or big fish, but bait is finite, so making it more attractive to some fish makes it less attractive to others.

Every fish is still shown at its full-grown size, so each cast's contribution after acquisition is known the moment it lands. Pick the number the team optimizes on.

Bait chosen on cost of acquiring a fish, sizes in plain sight

Round 0 of 20
Drag to any round
Contribution after acquisition, round by round, for each way of testing the bait
$0$500$1,000$1,500$2,00005101520Round of testingTested on contributionafter acquisition$1,045Tested on CAC$28start $125

Each line is the average of 200 runs of the 20 rounds. The shading shows where 8 in 10 runs land, round by round.

Tested on the cost of acquiring a fish, the bait drifts toward the fish that are easiest to catch in numbers. By round 20 it lands about 94 fish a cast, almost all of them tiny, and each cast's contribution after acquisition falls from $125 to $28. Tested on contribution after acquisition, it lands fewer, bigger fish, about 24 a cast, and climbs to $1,045.

What one cast brings up after 20 rounds of testing

Step 5 bait

27.5 fish a cast

Giants 1
Big 4
Small 8
Tiny 15

Tested on CAC

93.7 fish a cast

Giants 1
Big 2
Small 13
Tiny 78

Tested on contribution after acquisition

23.95 fish a cast

Giants 6
Big 5
Small 6
Tiny 7

The team testing on contribution after acquisition pays more for each fish, $10.86 instead of $9.45, and still earns more than eight times what a cast made at the start. The cheapest fish are the smallest ones.

Those lines are averages over 200 runs of the 20 rounds, and runs vary. Tested on contribution after acquisition, 8 in 10 runs finish between $446 and $1,905 a cast. Tested on CAC, 8 in 10 finish 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 testing on contribution after acquisition comes out ahead 996 times in 1,000.

What every $1 brings back after 20 rounds of testing
Tested on CACRevenue return 1.08 (108%)
$354 invested · $382 net revenue
Contribution after acquisition $28Contribution return 0.08 (8%)
Tested on contribution after acquisitionRevenue return 4.68 (468%)
$284 invested · $1,328 net revenue
Contribution after acquisition $1,045Contribution return 3.68 (368%)
Before any testing: the step 5 bait1.43 (143%)

Grey is what's invested. The bar runs on to net revenue, so the colored part past the grey is the contribution after acquisition.

Read as an investor, tested on CAC, every $1 brings back 1.08 (108%), down from 1.43 (143%). Tested on contribution after acquisition, it's 4.68 (468%).

The math

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, which comes to 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. Counting the $1 handling as well changes nothing, because ($260 + $1 × fish) ÷ fish still falls with every extra fish. 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.

What the winning bait pulls in, compared with no bait

Every number starts at 100, on a log scale so that doubling and halving look the same size.

End of part 1

Part 1 settles one thing. When you can judge every cast right after the catch, by what the bait brought in, optimize for contribution after acquisition. Tested on a lower cost of acquiring a fish, each cast fell to $28 and every $1 brought back 1.08 (108%). Tested on contribution after acquisition, the bait took each cast from $125 to $1,045, and every $1 brought back 4.68 (468%).

Part 2 · Steps 7 to 9

When the fish aren't sold right away

Part 1 had a shortcut built in. Every fish was sold the moment it was caught, so you knew what each cast was worth from the size of the fish before the next one went in. Most businesses don't work that way.

What happens if you don't sell the fish right away, and not every fish makes it to the sale?

Part 2 follows that question. The view pulls back to the ocean, 900 fish, nine of every fish from step 1. The fish are caught small, they grow up in a funnel, and only some of them make it to the end. It ends with a way to sort the catch at the dock.

For an investor, it means the money goes in at the catch, and the return comes back weeks later, when the fish are sold.

The fish grow up later

What if you can't see a fish's value when you catch it?

In many businesses the catch isn't worth anything yet. The fish are caught small, and they only grow into their value later. Watch the ocean: every fish starts at its full-grown size, then shrinks to the size it's really caught at, all the same.

The ocean, 900 fish, no bait

Shown at the size each fish will grow to
Until now every fish showed the size it would grow to. From here they're caught the same size, and only pool 5 shows what they grow into.

The net drops each catch into pool 1. The fish slide from pool to pool, and every slide has a grate: 70 in 100 fish make it and 30 slip through. Out of every 100 fish caught, 24 reach pool 5.

Out of every 100 fish caught, 24 reach pool 5
Pool 1: 100 fish70 in 100 make the slidePool 2: 70 fish70 in 100 make the slidePool 3: 49 fish70 in 100 make the slidePool 4: 34 fish70 in 100 make the slidePool 5: 24 fish

Five pools, the conversion rate between each, and the merchant

The first drop is on its way

Each quick drop is 100 more fish caught, about 24 of them reaching pool 5. The totals settle as the fish add up.
What an average 10 lb fish caught is worth
Sale in pool 510 lbs at $7.75 a pound$77.50Less $15 to raise itper fish sold$62.50Per fish caught24 in 100 reach pool 5$15.00

Pool 5 is where the fish grow and get sold. The merchant pays $7.75 a pound, and raising each fish there costs $15. For an average 10 lb fish that's $62.50 once it's sold, and since only 24 in 100 get there, $15 for every fish caught, the same $15 it earned in part 1. With no bait, the business still makes about $100 a cast.

One cast with no bait, sold on the spot or raised first
Part 1: sold the day it's caughtRevenue return 1.36 (136%)
$275 invested · $375 net revenue
Contribution after acquisition $100Contribution return 0.36 (36%)
Part 2: raised in pool 5, then soldRevenue return 1.27 (127%)
$365 invested · $465 net revenue
Contribution after acquisition $100Contribution return 0.27 (27%)

Grey is what's invested. The bar runs on to net revenue, so the colored part past the grey is the contribution after acquisition.

The $100 a cast holds, but more money goes in to earn it. About 6 fish a cast reach pool 5, and raising them costs about $90, so each cast takes $365 invested to bring back $465: a revenue return of 1.27 (127%), down from 1.36 (136%). And the money is out for weeks before the fish are sold.

In a business, pool 1 is a new lead and pool 5 is a customer who grows into what they're worth over time. Every lead moves through the stages at the same rate, so the conversion rates show nothing about which leads grow into the revenue. Every account costs something to serve, and its revenue grows with it.

The math

contribution after acquisition per cast = $7.75 × pounds sold from pool 5 − $15 × fish raised in pool 5 − $250 − $1 × fish caught

invested = $250 + $1 × fish caught + $15 × fish raised in pool 5

To keep the counts simple, each drop into pool 1 is a few catches mixed together, 100 fish. The fish that reach pool 5 are a fair draw from the ocean, so with enough fish caught, every 100 that reach it hold the same mix as the 100 fish in step 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. The losses through the grates were always in the price, so with no bait the contribution after acquisition still settles at about $100 a cast. Raising the fish is a variable cost, so it counts in what's invested.

What the dashboard can't see

So what does the team count?

Bring the bait back, at $10 a cast. The team still picks a winner after every test, 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 below.

Bait chosen on the fish caught, as the fisherman sees them

Test 0 of 20 · week 0
Optimize on the fish reaching
What the dashboard shows
What the catch grows into (known about 6 weeks later)

What the bait is really pulling in (nobody can see this at the dock)

Drag to any test
Contribution after acquisition per cast once the fish have grown, test by test, for each pool the tests can aim at
Cost per fish reaching each pool, test by test, what the cast and the bait cost for each one

The pool you picked · what the catch earns once it grows; the faint lines are the other pools Baseline · what the people paying for the bait expect: the cost of acquiring a fish the tests deliver, and every fish still earning the $4.55 it earned when bait came in, in step 5

Every fish makes each slide at the same 70 in 100, so whichever pool the team counts, the tests keep the bait that lands more fish. The dashboard prices every fish at the 10 lb average, so more fish always looks like more money. After 20 tests the dashboard says $1,707 a cast.

After 20 tests: what the dashboard says, the baseline, and what the fish grow into
Dashboard saysevery fish at 10 lbs$1,707Baselinecheaper fish, each at $4.55$639Once the fish grow$263

Once the fish grow, the catch earns $263. The tests deliver the cheaper fish the baseline expects, $1.85 each, but the fish don't keep their $4.55, so the catch finishes at less than half the $639 baseline. 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.

After 20 tests: what every $1 brings back
Dashboard saysRevenue return 2.88 (288%)
$906 invested · $2,613 net revenue
Contribution after acquisition $1,707Contribution return 1.88 (188%)
Once the fish growRevenue return 1.29 (129%)
$906 invested · $1,169 net revenue
Contribution after acquisition $263Contribution return 0.29 (29%)
Before any testing: the step 5 bait1.32 (132%)

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 2.88 (288%). Once the fish grow, it's 1.29 (129%), just under the 1.32 (132%) the bait brought back before any testing. Twenty tests cut the cost per fish to $1.85, and every $1 brings back a little less than when they started.

The math

contribution after acquisition that never shows up = fish caught × 24% × $7.75 × (10 lbs − the real average weight)

With sizes visible in step 6, the same tests raised each cast from $125 to $1,045. Here, aimed at the fish caught, they sink it first and lift it only to $263 after 20 tests, against a baseline of $639, while the dashboard reports $1,707 and the cost of acquiring a fish 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 $249 against a baseline of $610. 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.

The signal at the dock

Is there anything you can see when a fish is caught?

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 70 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.

What each tail color grows into in pool 5
Green tail: 1 in 5 grows into a giantBlue or pink tail: 1 in 50

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 you catch earns about $70, and every other one about $3.

What each color is worth, once the fish grow

Green-tailed fish

Grows to about 40 lbs

Sells for about $309

$70

contribution for every one caught

Blue or pink-tailed fish

Grows to about 4 lbs

Sells for about $31

$3

contribution for every one caught

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.

Same size at the dock, valued by tail color

Round 0 of 20
What lands in the net: the share of green-tailed fish
No bait25 fish a cast17% green-tailedLower CAC140.5 fish a cast1.2% green-tailedValue/signal35.06 fish a cast74% green-tailed

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.

Follow the catch through the funnel

The funnel follows the option picked above: no bait, or the bait each team settles on by round 20. Nothing in pools 1 to 4 shows what the catch is worth. Pool 5 shows it.

The bait chosen on margin by tail color, through the funnel

The first drop is on its way

Each quick drop is 100 more fish caught with this bait. The odds settle as the fish add up.

The result

Round by round, what each team earns once the fish have grown and what it pays for each fish, against the baseline from step 5: the cost of acquiring a fish the Lower CAC tests deliver, and every fish still earning $4.55. The shading shows where 8 in 10 runs land.

Drag to any round

The result: contribution after acquisition and cost per acquisition

Round 0 of 20
Contribution after acquisition per cast, once the fish have grown
Cost per acquisition: the cast and the bait for each fish caught
Value/signal · optimized on the green-tailed fish caught at pool 1 Lower CAC · optimized on the fish counted Baseline · set in step 5: the cost of acquiring a fish falls the way the Lower CAC tests cut it (right), and every fish keeps the $4.55 it earned when bait came in (left) Shading · where 8 in 10 of the 200 runs land, round by round
Round 20: 6 times the contribution after acquisition on less than half the money
Value/signalRevenue return 4.74 (474%)
$421 invested · $1,997 net revenue
Contribution after acquisition $1,576Contribution return 3.74 (374%)
Lower CACRevenue return 1.29 (129%)
$906 invested · $1,169 net revenue
Contribution after acquisition $263Contribution return 0.29 (29%)
Before any testing: the step 5 bait1.32 (132%)

Grey is what's invested. The bar runs on to net revenue, so the colored part past the grey is the contribution after acquisition.

Both teams spend the same $260 a cast on the net and the bait. By round 20, the Value/signal team makes 6 times the contribution after acquisition on less than half the money. It puts $421 a cast in and makes $1,576. The Lower CAC team puts $906 in, because it pays to handle and raise a crowd of tiny fish, and makes $263. Every $1 the Value/signal team puts in brings back 4.74 (474%). The Lower CAC team's $1 brings back 1.29 (129%), under the 1.32 (132%) the step 5 bait brought back before any testing.

Round 20 against the baseline: the average cast, and where 8 in 10 runs finish
$0$1,000$2,000$3,000Value/signal$1,576 a cast2½ times the baseline8 in 10 runs: $532 to $2,894Lower CAC$263 a castless than half the baseline8 in 10 runs: $68 to $536Baseline $639

Against the baseline, the Lower CAC team delivers the cheapest fish in the story, under $2 each, and still finishes at less than half 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 $11.02, then less as the green-tailed fish come in, and finishes at 2½ times the baseline.

Those are averages over 200 runs of the 20 rounds, and runs vary. 8 in 10 Value/signal runs finish between $532 and $2,894 a cast, and 8 in 10 Lower CAC runs between $68 and $536. The Value/signal team beats the baseline in 85 runs in 100, the Lower CAC team in 6. Pair one run of each at random, and Value/signal comes out ahead 97 times in 100.

Same boat, same bait budget, same funnel. The only difference is what each team optimized for. Optimize for the signal, not the thing.

The math

contribution after acquisition per cast at the dock = $70.58 × green-tailed fish + $3.89 × every other fish − $260 − $1 × fish

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 $7.75 a pound, a green fish sells for about $309 and a blue or pink one for about $31, and each costs $15 to raise there. Both teams start from the step 5 bait, 27.5 fish 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 $71 before the sheer number of fish lifts it back to $263. 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 $11.02 by round 8. Then the green-tailed fish come in numbers, the cost falls to $7.42, and each cast climbs to $1,576. 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.

What each color is worth over a lifetime

What to change

  • Find a signal you can see at the catch that tells you what shows up later, like the color of a fish's tail.
  • 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.

The takeaway. A few fish carry most of the weight (step 1), and the same net lands the same average cast after cast (step 2). Selling the catch puts a contribution after acquisition on every cast, about $100 with no bait (step 3), and over enough casts an investor's revenue return settles at 1.36 (step 4). Bait aimed at the average adds 10% more volume and 25% more value, and sets the baseline: a cost of acquiring a fish that improves as the team tests, with every fish still earning $4.55 (step 5). When every fish's size shows at the catch, optimizing on contribution after acquisition works best, and optimizing on the cost of acquiring a fish makes it evaporate (step 6). When the fish only grow into their value at the end of a funnel (step 7), optimizing on what the dashboard can count delivers the cheaper fish the baseline expects, while the real contribution after acquisition falls to less than half of it (step 8). A signal you can see at the catch, priced at what it grows into, points the same optimizing back at the fish that grow into the value: 6 times the contribution after acquisition on less than half the money, and every $1 invested brings back more (step 9).

Addendum

Why the Lower CAC team falls in step 6 but climbs in step 9

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.

Step 6Step 9
What the bait can tell apartSizeOnly tail color
What landing more fish brings inThe tiniest fish: 78 of 93.7 a cast by round 20More blue and pink-tailed fish, in the same mix as always
Contribution after acquisition from each extra fish27 cents: 0.85 lbs × $1.50 − $1 handling$2.89: the blue and pink average, after raising and handling
Contribution after acquisition per cast$125 → $28$125 → $71 by round 7 → $263 by round 20

In step 6 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.

In step 9 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, $2.89. For the first 7 rounds the bait gives up green-tailed fish faster than volume makes up for them: 1.6 green-tailed fish a cast at about $70 each, about $113, against 20 more blue or pink-tailed fish worth about $59, so each cast falls from $125 to $71. After that, green tails are nearly gone, 3.0 a cast down to 1.7, about $84 more, while the catch grows to 140.5 fish: 95 more blue or pink-tailed fish add about $276, and each cast climbs to $263.

That makes step 9 generous to the Lower CAC team. A bait that could pick small fish directly, as in step 6, would land fish that lose $3.03 each once the $15 to raise them is counted: the more of them it landed, the more each cast would lose.

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 step 1 the net is a bell curve whose mouth spans about 54% of the water, and in step 2 it's a round net cast at the middle of the cube. On average the line lands about 26 fish and 246 lbs a throw, the mixed water about 25 fish and 265 lbs, and the cube about 25 fish and 250 lbs. Quick casts skip the swimming: each fish has the same 1 in 4 chance of being in the net, the same rule as steps 5 to 9. Steps 3 to 5 use the same 100 fish, step 6 three copies of each and steps 7 to 9 nine copies, the ocean. Bait costs $10 a cast. In step 7 each drop into the pools is a few catches mixed together, 100 fish, and about 30 in 100 fish slip through the grate on each slide, so about 24 in 100 reach pool 5, where they grow. In step 8 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 shown are the average of 200 runs worked out in advance, and the shading in steps 6 and 9 shows where 8 in 10 of those runs land. In step 4 each investor funds 100 casts drawn from 20,000 no-bait casts, and the band is where 8 in 10 of 4,000 investors land. Throws and casts run in your browser, and caught fish go back in the water.