Why some channels reward breadth and others require commitment

Many fund allocation strategies presume that each transmission follows the aforesaid pattern: the first dollar is the astir productive, and each further dollar yields a somewhat little return.

The charts beneath show what that shape looks like.

The log style intends that the first dollar is the astir productive, and each consequent dollar is worthy a small less. When each transmission looks for illustration that, the crippled scheme is to dispersed the fund to arsenic galore channels arsenic imaginable and equalize the marginal CPAs to maximize profit.

But not each transmission looks for illustration that. Some person a warm-up region wherever the early walk is the slightest efficient, not the most. On those channels, the logic supra breaks, and truthful does the “test small, standard the winners” playbook that astir of the manufacture runs connected autopilot. 

The quality comes down to 1 mobility astir the channel: Is the consequence curve C-shaped aliases S-shaped?

The reply tin alteration really you attack transmission testing and transmission measurement, including immoderate MMM analysis. Moreover, Google has been incorporating much S-shaped run types, and aft its Google Marketing Live announcements, this inclination seems group to continue.

The 2 shapes — and the only portion that matters

The consequence curve land output (conversions, revenue) against input (spend). This mostly results successful 2 types of curves successful marketing.

• C-shaped (concave): Diminishing returns from the very first dollar. A log aliases powerfulness curve. Picture the top-left 4th of a circle: steep astatine the start, flattening arsenic you go.
• S-shaped (sigmoid): A slow, inefficient start, past an inflection constituent wherever it gets steep, followed by a flattening into saturation. A logistic curve.

The consequence curve itself isn’t what you allocate against. You allocate against the marginal curve, the derivative, which answers the question: “What did the adjacent dollar bargain me?” That’s wherever the shapes diverge successful a measurement that matters.

• For a C-curve, marginal return is highest astatine the first dollar and falls successful only 1 direction. Marginal CPA rises from the first dollar onward. If conversions are a*ln(s), marginal conversions per dollar are a/s, truthful marginal CPA is s/a, climbing successful a consecutive statement arsenic you scale. There’s nary warm-up. The cheapest conversion you’ll ever bargain is the first one.
• For an S-curve, marginal return starts low, rises to a highest astatine the inflection point, past falls. Marginal CPA is U-shaped. It’s costly astatine the start, bottoms retired astir the inflection point, past climbs into saturation.

That region of expanding marginal returns is the full story. It’s the quality betwixt a transmission wherever mini budgets are productive and 1 wherever they are wasted.

How this looks successful a trading campaign

Say your CPA extremity is $50. Here is an S-shaped channel, modeled arsenic Conversions = 1000 / (1 + e^(-0.25(s – 20))), pinch walk successful the thousands and the inflection astatine $20,000/month:

Run the $10,000 trial that a sane personification runs earlier committing existent budget. Average CPA comes backmost astatine $132, marginal astir $94. If those 2 metrics are each you look at, you reason that this transmission can’t deed $50, truthful let’s termination it.

That verdict is wrong. At $20,000 to $25,000, the transmission is moving astatine an mean of $32 to $40, and the marginal dollar successful the $15,000 to $25,000 set costs $18. That’s not “barely viable.” In that band, it’s the champion marginal bargain you have. The mini trial fell wrong the warm-up and reversed the conclusion.

In a C-shaped channel, the mini trial would person shown you the champion the transmission tin do. On an S-shaped channel, it shows you the worst.

This is the trap. The modular playbook is “test small, standard what works.” On S-curves, mini tests systematically condemn channels that would’ve worked astatine standard because the trial is structurally stuck successful the inefficient region.

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The allocation logic, restated

C-shaped channels, spell wide

The optimization is convex. There’s 1 world optimum, the equimarginal norm from the marginal-CPA station applies cleanly, and the solution is usually interior, meaning tons of channels get funded.

Even a mini allocation is productive because the first dollar is the champion dollar. Run galore channels lean, reallocate continuously astatine the margin, and propulsion backmost the instant marginal CPA crosses your goal.

S-shaped channels, spell heavy aliases skip

The optimization is non-convex. A mini allocation tin beryllium strictly worse than zero because beneath the inflection your marginal return sits nether your target, and you’ve sunk money to get nowhere.

The determination isn’t “how much.” It is binary: perpetrate past the threshold, aliases don’t money it astatine all. There’s a existent minimum viable budget, and it’s often supra normal trial budgets. You can’t sprinkle an S-curve and expect efficiency, and you can’t measure 1 connected an underfunded test.

Those 2 rules tin look for illustration they conflict each other, but that’s only existent to a definite point. Past the inflection, an S-curve is concave, truthful the equimarginal norm governs it precisely arsenic it governs a existent C. The S-specific instruction — perpetrate a artifact alternatively of sprinkling — is only astir the travel from zero to past the inflection.

Shape is truthful mostly a launch-and-evaluation problem. Getting a caller prospecting transmission into its businesslike scope requires a committed artifact and patience pinch disfigured early numbers. Once it clears the inflection, you negociate it astatine the separator for illustration everything else, correct up until you see cutting it hard, wherever style matters again because the downside is simply a cliff, not a ramp.

This is the portion that’s genuinely counterintuitive, and it echoes the original marginal-return point: The correct move isn’t ever the 1 that looks astir businesslike astatine a mini scale.

Which channels are which?

The humanities default was concave. Simon and Arndt reviewed much than 100 studies and concluded that advertizing follows the rule of diminishing returns, a concave response. 

The dissent came later: Vakratsas, Feinberg, Bass, and Kalyanaram recovered that period effects do beryllium and that consequence is not needfully globally concave. Their mentation for why thresholds were truthful difficult to find is the useful part. Mature accounts already run wrong the effective range, truthful the warm-up ne'er shows up successful the data, and astir studies fresh a concave exemplary (the double-log) that can’t cull an S-curve moreover erstwhile 1 is present.

The level displacement has made the period visible again. Here is simply a fuller map, ordered astir from C to S. The style file is an conclusion from really each strategy targets and learns, not a measured constant, and the correct style for your relationship still has to beryllium measured.

Two rows do astir of the work.

AI Max is the unrecorded illustration of a transmission migrating from C toward S. Swapping definitive keywords for wide and keywordless matching intends it needs conversion measurement to study which queries convert, truthful beneath a information period it explores severely (MCP, ‘AI Max for Search,’ 2025). The mixed independent results fresh that: Google reports astir 14% much conversions connected mean and up to 27% for exact-match-heavy campaigns, while independent testing reports 84% of advertisers seeing neutral aliases antagonistic results (ALM Corp, January 2026). Much of that dispersed is accounts that turned it connected without the conversion measurement to clear the learning region.

Performance Max is the trap, because its curve is simply a composite. It blends a harvesting furniture (branded, retargeting, Shopping against existing intent) pinch a prospecting furniture (keywordless description crossed surfaces). The harvesting furniture is simply a inexpensive C that pays disconnected connected the first dollar. The prospecting furniture is the S underneath.

Blended, the early ratio looks great, because you are mostly skimming request you already had, and the mean hides the prospecting warm-up entirely. That is besides why the level is gladsome to optimize it for you: the blend flatters the header number. You can’t publication PMax aliases tally the style study connected it until you divided the harvesting from the prospecting.

The throughline runs successful 2 layers. Rules-based auctions seizure the champion inventory first, which yields concavity; machine-learning systems must beryllium fed earlier they are efficient, which introduces a threshold. Underneath both, harvesting existing request is concave and mostly non-incremental, while creating caller request is the S-shaped portion wherever the existent maturation and the existent warm-up costs some sit.

Average versus marginal: full complete spend, aliases the slope wherever you stand.

What you allocate against is marginal incremental return, the slope of the incremental curve astatine your operating point. A holdout fixes the first axis only. Time-sliced marginal CPA connected attributed information fixes the 2nd only. A multi-cell scaling trial gets both, astatine a cost. 

MMM (method 1) estimates the full curve from aggregate information and sidesteps click attribution entirely, but pays successful identifiability and modeling assumptions instead. Most arguments astir ‘what is working’ are 2 group opinionated connected different axes.

There are 2 awesome cautions, and I would emblem some arsenic genuinely unsettled alternatively than settled facts. 

• Separating a existent S-curve from “concave pinch a precocious half-saturation point” is hard, because a concave exemplary will fresh S-shaped information good capable to hide the inflection (this is the Vakratsas point, and it applies to your ain dashboards arsenic overmuch arsenic to world studies). 
• The learning shape whitethorn beryllium a one-time fixed costs to train the exemplary alternatively than a imperishable characteristic of the steady-state curve. If it is transient, the transmission whitethorn behave concavely astatine the separator erstwhile it is trained, and the S you measured was a startup artifact. The truth is astir apt a mix: a one-time training cost, positive an ongoing minimum-volume request to enactment efficient. Treat each style telephone arsenic provisional and re-check it.

One much nonaccomplishment mode, and this 1 is not unsettled subject but a matter of wherever you are opinionated connected the curve. An S only looks for illustration an S if your information spans the inflection. 

Above the inflection, an S is concave, mathematically identical to a C. Look astatine only the $20,000-and-up rows of the array above: marginal CPA rises monotonically from $18, a textbook C-curve, and the convex warm-up is invisible because you are nary longer operating successful it. 

Established accounts usually beryllium past the inflection, which is precisely why Vakratsas recovered thresholds truthful difficult to detect, and why you tin tally an S-shaped transmission for years, correctly, while believing it is concave. The show arrives the time you trim difficult and autumn disconnected the inflection alternatively of easing down a slope.

When to spell wide and erstwhile to spell deep

The marginal-return station told you to equalize marginal CPAs crossed the program. That norm is still correct, but the style of the curve tells you really you’re allowed to get there. 

• On C-shaped channels, you tin get location by sprinkling, because each dollar is productive and breadth is the earthy answer. 
• On S-shaped channels, you person to perpetrate a artifact of fund past the inflection earlier the transmission earns its place, and past ore alternatively than spread.

Lay the harvest-versus-create trim connected top. Harvesting channels (branded, retargeting, non-brand search) are your C-curves: money the first dollars, past headdress them early, because they saturate accelerated and astir of the tail isn’t incremental, nary matter really beardown the attributed ROAS looks. 

Prospecting channels (Meta, YouTube, LinkedIn, the description half of PMax) are your S-curves and your only existent root of incremental growth: perpetrate past the warm-up aliases don’t start, and judge them connected incremental assistance alternatively than attributed CPA, aliases you’ll termination the point that was working.

Classic hunt rewards going wide. PMax, AI Max, and Meta prospecting reward going heavy connected less bets and giving each capable measurement to clear the warm-up. Run an S-curve for illustration a C-curve and you’ll starve it, publication the underfunded result, and termination a transmission that would’ve been 1 of your best.