---
title: "Issue #169 | The Aggregation Function Problem"
date_published: "2026-05-24"
date_modified: "2026-05-26"
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This week's issue began years ago as a passing thought I had, and (as things often do), evolved into one of the more useful frameworks I've stumbled into in a while. It's a different beast than the usual DD ̵1; there's more math, it's a bit less tactical & the implications stretch far beyond marketing to investing, hiring, brand-building, and the day-to-day decisions every exec makes.

As a fair warning, this one is longer and more complex than usual (I'm writing this as my kids are watching Shrek, so I'm tempted to say ̵1; this one is like an Ogre or an onion ̵1; it has layers). That being said, this framework has changed the way I make decisions across every part of the business, and I suspect it will do the same for you.

With that out of the way, let's get to it.

Most brands/investors/operators I talk to hold 2 beliefs about variance simultaneously, and almost none of them notice that the beliefs contradict each other.

Belief #1: the great investors almost never have blowout years. Buffett grew Berkshire at ~20% for 60 years. The single-largest growth year was 1976, when it posted a per-share book value increase of ~59.3%. Peter Lynch averaged 29% over 13 years and was famously boring on a single-year basis (best year, on a NAV/unit basis was ~70% in 1980). Simons at Medallion posted a ~40% net for 3 decades and is, by the math, the greatest investor in history...and he did it without a single legendary year (his best was 2000, when he returned ~98.5% ̵1; which seems incredible until you compare it to Leopold Aschenbrenner posting a ~22x return in ~6 months). The investors who do post 20x years ̵1; a/k/a the Leopolds, the Melvins, the 2021 crypto cohort, the blown-up hedge funds we've already forgotten ̵1; are mostly a story about survivorship bias and volatility drag. Over any sufficiently long time horizon, the quiet, boring investors win as the loud ones flame out. This belief is correct, and any reader who has run the math has internalized it.

Belief #2: in elite talent selection ̵1; professional sports drafts, founder evaluation, A-tier hiring ̵1; the optimal play is to bet on the prospect with a single, truly top-0.1% trait and obvious holes, NOT the prospect who's "above average" across the board. The well-rounded player who does nothing exceptionally well is the one most professional scouting departments fall in love with, falling into the "good at everything, elite at nothing" trap. Objectively, this belief has proven to be correct time and time again, simply because when it hits ̵1; when you find the 100x engineer or you draft the Cale Makar or you hire the 10x marketer ̵1; the returns more than cover the costs associated with patching the holes.

But there's a tension I keep thinking about: these 2 beliefs recommend opposite variance preferences. The belief #1 (the investing belief) says minimize variance, accept moderate means & win over time. Belief #2 (the drafting belief) says maximize variance on key traits, accept dramatic holes & win on peaks. Most people never notice the contradiction because ̵1; in their view/experience ̵1; those domains are completely unrelated: one relates to investing, the other to talent selection (which, let's be honest, the vast majority of people don't do). Logically, 1 of those 2 beliefs must be wrong, or there must be a deeper principle that resolves both.

The deeper principle exists, it's more useful than either belief alone, and once you have it, a surprising amount of strategic disagreement across unrelated domains turns out to be the same argument.

## Long-Term Investing

Let's talk about the investing math first, simply because it's the most familiar and the one all of us have heard about at some point.

A 20x return transforms $1 to $20. An investment that returns 30%/yr needs ~11 years to catch that single 20x and 12 to surpass that single year return. But ̵1; by year 15 ̵1; the 30%/yr return is at $51. By year 20, $190. By year 25, that single dollar is worth $705. Every additional year multiplies the gap by another 1.3x... all while the 20x investor sits frozen unless they can catch lightning in a proverbial bottle once again. The crossover happens earlier than people expect; the divergence after the crossover is faster than people expect; while both observations are important, the 2nd one is the more interesting.

The catch is that the 20x year is almost never the start of a Buffett- or Simons-like run; it's a flash in the pan. Returns of that magnitude come from concentrated, levered exposure to a specific thesis, usually a single sector, sometimes a single trade (i.e. the memory trade of the past few months, or the semiconductor boom from 2022-2025, the BTC boom before that). The same structural decisions that produce the 20x have the unintended consequence that the drawdowns are proportional. A 20x year followed by an 80% drawdown leaves you at 4x (which is still good!), not 19.2x. Volatility compounds destructively against terminal wealth. That destruction is asymmetric in a way that most people don't intuitively understand.

In academic contexts, this is known as the geometric versus arithmetic mean problem, which is Buffett's "first rule is don't lose money" expressed mathematically. The geometric mean is always less than or equal to the arithmetic mean, and the gap widens with variance. 2 investors with identical average annual returns but different volatilities end up at radically different terminal wealth ̵1; not slightly different, radically different ̵1; because the volatility tax compounds in the opposite direction from the wealth. A 30% mean return with 10% volatility compounds at roughly 29.5% in continuous time. A 30% mean return with 80% volatility- the kind of variance you'd need to even attempt a 20x year ̵1; compounds at roughly 0. Wild, right?

Then there's survivorship bias, which is the most underrated force in modern investing because it's structurally invisible. The investors who post 20x years and then disappear are erased from the discourse & relegated to random references or footnotes. The visible "one-hit wonder" is not really one investor with one good year ̵1; it's a population of high-variance bettors where only the right-tail survivors are sampled. The base rate is hidden from view, which means the implied edge of the strategy is mostly an artifact of selection. You're not seeing the strategy's expected outcome. You're seeing the outcome conditional on the bettor still being publicly visible, which is a wildly different distribution.

Also ̵1; this doesn't just apply to money. It applies to brands, too - the brands that become household names don't do it on the back of a single, out-of-the-box campaign; they do it by delivering on a set of promises/values/emotional expectations, consistently, for a staggeringly long amount of time. One killer ad may make for a great campaign or a nice bonus for the CMO/agency, but it does not make a brand.

The underlying principle is this: when the aggregation function across periods is multiplicative ̵1; when terminal wealth equals the product of (1+r) across years ̵1; variance is structurally punished. Lower variance at acceptable mean dominates higher mean at any variance, and the dominance widens with the time horizon. The math doesn't care how impressive any single year looks ̵1; the only thing that matters is the product.

10x Engineers & Pro Sports Drafts

Now that we've established that, let's break the pattern.

Consider the NBA draft. There are 2 prospects on the board. Prospect #1 is a polished, well-rounded player (solid shooter, solid defender, solid passer, no real weaknesses but no real elite skill). Prospect #2 is the raw athlete with a top-1% physical trait ̵1; but comes with massive holes in his fundamentals, shooting, basketball IQ, even his effort. Most people, given the choice, would go Prospect #1, simply because doing so is safer. But the best teams in the league, year after year, draft Prospect #2. Not always, not unanimously, but at rates that have only increased as front offices have gotten more analytically sophisticated. The polished prospect with no elite skill is the one that falls.

From the investing standpoint, that makes no sense. Variance destroys terminal value. The goal of any draft (or hiring, or venture investment) is to maximize value. Yet...here are billion-dollar organizations doing the exact opposite time and time again. But, if you step back, you'll see it's actually the same question as above, with a different aggregation mechanism.

In a draft (or hiring, or venture investing), the value a player generates is not the sum or product of their traits. It's the maximum of those traits relative to replacement at that role. The rest of the roster patches the holes. A coach can hide a player's weaknesses with scheme; a coach cannot manufacture an elite trait that isn't there. A good manager or account executive or assistant can patch over a 10x engineer with no people skills, or an elite marketer who happens to have no organizational ability or a world-class salesperson who happens to be a world-class jerk to colleagues. In each case, the scarce capability gets paid because scarce capabilities are the only thing that can't be substituted across a sufficiently large talent pool. The "good at everything, great at nothing" generalist provides no scarce capability. There are thousands of B+ generalists available, so he generates no premium. The specialist with one top-0.1% trait provides value the organization can't otherwise create.

Here's where this gets interesting: mathematically, this is the same math as the investing case, run through a different aggregation function.

When the payoff function is f(max(X₁, X₂, ̷0;, Xₙ)) instead of f(∏Xᵢ), the variance preference inverts. Fat tails become an asset, because the maximum of a fat-tailed distribution beats the maximum of a thin-tailed one almost as the sample size grows. The same statistical property that destroys terminal wealth in a multiplicative system creates value in a max-order system. The system doesn't dictate the answer. The function does.

This is extreme value theory in plain English.

The behavior of the maximum of a sample is governed by the tail of the underlying distribution, not by its center. If you want the maximum to be large, you want a fat tail, even at the cost of a lower mean and a worse floor, because the floor is irrelevant when only the peak gets counted. If you want the product to be large, you want a thin tail, even at the cost of a lower peak, because the floor is everything when bad outcomes (i.e. down years) multiply against you over subsequent time periods.

Same math. Opposite optimal path forward.

Most people spend an inordinate amount of time (unknowingly) asking the question, "should I prefer high variance or low variance?" Think about your own life. Most parents want their kids to be solid students (low variance), but they play the lottery (about as high variance as it gets). They want predictability in income (low variance), while investing $25k in a crazy startup idea (high variance). The irony is that the question has no universal answer. It's the wrong question. The right question, the one that resolves the contradiction from the opening, is this: what function aggregates my outcomes, and what variance does that function reward?

Once you start asking that question, you'll find (as I have) that it completely changes the way you approach your job, marketing questions, investment questions ̵1; you name it.

3 Aggregators Cover Most Decisions Worth Making:

Multiplicative aggregation: outcomes compound across periods and terminal value is the product of intermediate values. Lifetime (or retirement) wealth, durable institution-building, individual reputation over time, brand equity, organizational trust. In each of these cases, variance is punished. The optimum is low variance at an acceptable mean.

Maximum-order aggregation: outcomes are decided by the best realization out of many attempts and the rest get discarded. Drafts, venture portfolios, creative testing, A+/elite talent hiring, R&D, startup formation. For every one, variance is rewarded. The optimum is high variance at acceptable floor.

Additive aggregation: outcomes sum across decisions. Variance is roughly neutral because errors wash out. Most operational decisions, most run-rate optimization, most steady-state business activity. The optimum is whatever maximizes the mean.

3 aggregation methods, with 3 very different variance preferences. None of them are universally correct, yet all are locally correct. The entire question of "should I be aggressive or conservative" becomes legible only when the aggregator is named first. The apparent contradictions across domains ̵1; between Buffett's discipline & Howie Roseman's draft strategy, between index fund investing and seed-stage VC, between the slow-growth brand and the Gruns-style success story ̵1; all dissolve into the same underlying principle expressed through different aggregators.

The framework's payoff isn't intellectual (although I do think the math is fascinating). It has real-world applications for every person running an agency or leading marketing or pulling levers in an ad account.

Why?

Because the most expensive strategic errors I see come from importing a variance preference from one aspect of a system to an aspect with a different aggregator, without noticing that the function changed.

Over the last few months, we've started to consolidate our audit findings into a single database for use going forward. From that, I've pulled the 5 most common issues, each of which has as the common thread this exact failure mode.

The 5 Most Common Issues:

Creative testing. At the variant level, payoff is f(max(variants)). You scale the winner, you pause/kill the losers, and the only thing anyone cares about a few days later is how well that winner is performing. This is a draft, structurally identical to scouting talent or lottery ticket buying or venture capital. The more ads you create/launch, the higher the probability of finding a hit, the higher the expected maximum, which is the only number that matters. Audience/angle diversity expands the distribution from which the maximum is drawn, which further raises the expected peak. Fat tails are an asset.

The common error is running variant testing like a compounding portfolio. Agencies/marketers refuse to kill underperformers because they "haven't been given a fair chance." Brands demand statistical certainty before pausing low performers, which is exactly backwards: statistical certainty about a loser is information you've already paid too much for.

The end result? The brand inadvertently smooths the variance creative testing is designed to expose. Marketers treat a draft scenario as if it were a marriage. They fall in love with a creative they made or an ad they wrote or a design a competitor has used to scale. Every one of these moves destroys the max-order statistic the function depends on. The portfolio at the variant level should have wild variance, merciless culling of low performers and a small number of survivors that get the entire budget. Agencies/brands who refuse to run creative testing that way are leaving peak performance on the table ... all because they imported the wrong variance preference.

Account-portfolio management. At the account-across-time level, performance is multiplicative. A +30% month followed by a -80% month leaves you net negative. That sounds harsh, but it's reality. Channel concentration, product/offer fragility & platform dependence are all volatility contributors. As variance increases, the expected terminal value declines.

The common error here is the inverse of the creative-testing error.

Brands/agencies/marketers pile progressively more budget into the best-performing channel until something goes boom ̵1; a platform update, (yet another) Meta overspend error, the POTUS unilaterally starting a trade war, Apple deciding privacy means UTMs are PII, hyperinflation, whatever ̵1; and suddenly, all the gains they've accumulated through months or years of hard work go up in smoke. Anyone who works in DTC or travel or tourism or crypto or NFTs over the last ~6 years has had a front-row seat to the carnage that follows.

This is the exact opposite of the creative testing error above. In this case, brands/marketers have imported draft logic into a compounding problem. The right move at the account-portfolio level is diversification, durability, controlled drawdown, lower peak performance in exchange for floor protection. In about ~30% of the audits we've done, a single funnel or channel represents 80%+ of the business. I've been told ̵1; quite literally ̵1; that "our competitive advantage is that we rely exclusively on [platform] for leads ̵1; so we're better than anyone else at it." That is the exact wrong way to look at it ̵1; concentration is a ticking time bomb. My advice in those cases has always been the same: diversify, so that when (not if) that channel goes boom, your business isn't collateral damage.

And this is the paradox: the brand/marketer who (correctly) demands absurd variance in their creative pipeline should be running their channel mix like Buffett runs Berkshire: right sized bets into multiple acquisition funnels (audiences, angles, offers) and channels ̵1; so that when one fails, it isn't an existential threat to the business.

From our data, most agencies + brands have the variance preference backward on both!

Hiring. This is the application that produces the most counterintuitive answer....along with the most organizational damage when brands/teams get it wrong.

Specialist roles are drafts. Hire for the elite trait, accept the flaws + surround the specialist with supports that cover the floor. In my personal experience, when I've helped clients make hires + offer this advice, recruiters + HR people HATE it. Not dislike. Not disagree. Straight-up, Cruella De Vil-style loathe. Specialist hires are max-order extractions. You are buying access to a scarce capability that provides disproportionate value to the organization. The flaws ̵1; the aloof creative who couldn't manage a calendar if his life depended on it, the salesperson who closes more in 20 hours they barely work than the rest of the team could do in a month, the 100x engineer who is a complete asshat ̵1; are the cost of accessing that capability AND can be covered up with the right support system (which is MUCH cheaper to buy).

Now compare that to generalist roles ̵1; a COO, chief of staff, VP of marketing, head of operations, any role where the job is to make a long sequence of judgment calls across heterogeneous domains ̵1; are compounders. Performance is the product of decisions over a time. Variance in judgment is catastrophic because one bad call in a critical sequence destroys the geometric mean of the chain. You want consistency across a long horizon, not a peak in any single dimension. The "good at everything, elite at nothing" candidate that the draft framework rejects is exactly the right hire for the compounding role.

The expensive mistake ̵1; and the one I see all the time ̵1; is applying one variance preference across both role types.

Founders who hire every role like a draft pick end up with organizations full of brilliant specialists ̵1; which means when things go sideways, there's no one there who can stabilize + right the ship. Conversely, HR teams who hire every role like a compounder end up with smooth, reliable, deeply mediocre organizations that never produce a scarce capability. The same hiring philosophy applied across both role types is the source of an enormous amount of organizational damage in growth-stage companies, yet no one names the source as variance preference (even though, deep down, that's what it is).

Big-bet campaigns. A "tentpole" campaign ̵1; a SB spot, a brand film, a category-defining launch, whatever event that everything else in the marketing calendar revolves around ̵1; is structurally a draft. The portfolio of big bets a brand takes over its lifetime is a max-order extraction. Statistically, most of those tentpoles result in a temporary, mild lift....along with a deck full of charts going up-and-to-the-right that no one outside of marketing reads. But, a small number break through and generate cultural recognition that durably levers into brand equity for a generation. Think: Apple's ̶0;1984,̶1; Nike's ̶0;Just Do It,̶1; Dove's ̶0;Real Beauty,̶1; Old Spice's ̶0;Man Your Man Could Smell Like." Each one is a right-tail outcome from a population where the median is forgotten by the target audience after a few weeks. The math only works if the occasional hit covers dozens of wholly-unremarkable campaigns, which means the variance preference at the campaign-portfolio level should be high. You want fat tails. You want the big, home-run style swing. You want (ironically) manageable controversy.

The most common issue I've seen is evaluating these big-bet campaigns through the lens of multiplicative aggregation. Most CMOs ̵1; usually either out of fear of being fired or at the direction of a CFO, a board, or a committee process ̵1; demand de-risked creative for the biggest, most visible bet of the year. They run the Super Bowl spot through 11 rounds of focus groups, remove anything that scores controversial or polarizing, and end up spending millions to promote a "safe" piece of forgettable work. The problem is that you can't run a max-order extraction with a thin-tailed input. The campaign tests ̶0;well,̶1; it produces a modest lift in brand metrics, then fades from view/memory. It's a sandcastle on the beach.

Inevitably, the CMO and/or agency is blamed. The CEO/brand concludes big campaigns don't work and plows all those resources into something else. But the real irony is that the variance preference imported into the brief ̵1; ̶0;make sure this doesn't fail̶1; ̵1; made it structurally impossible for it to succeed.

Brand building. Here's where the framework produces its sharpest single inversion, because brand building is the structural opposite of the big bet campaign, even though most organizations file both under the same budget line.

As Kevin Plank famously said, "a brand is built in drops and lost in buckets."

Every customer touchpoint, every piece of packaging, every support interaction, every press hit, every product update, every repeat purchase, every recommendation to a friend ̵1; each is a small deposit into a brand equity account that compounds across years (and, in cases of iconic brands, across generations). The terminal value of a brand after 50 years is the product of trust accumulated across millions (or billions) of those moments, not the sum and certainly not the maximum.

One spectacular moment doesn't build the brand, but one catastrophic moment can break it ̵1; which is the asymmetric drawdown property of multiplicative systems showing up exactly the way Buffett warned about. Arthur Andersen going from the embodiment of trust to Enron's co-conspirator. United dragging a passenger off a plane. Bud Light's handling of the Mulvaney response. Boeing's safety culture revelations. Each one caused lasting brand damage that years + millions in marketing and clever campaigns could not un-do. When it comes to building a brand (or a reputation, for that matter), variance is punished. Consistency dominates the peak. The optimum is low variance at acceptable mean, sustained over decades.

The common error ̵1; and this is the most expensive marketing mistake I see at the senior level, full stop ̵1; is running brand-building like a tentpole portfolio. CMOs rebrand every 18 months because the new agency wants to make a mark. They reposition every time leadership changes. They chase whatever creative platform is trending at Cannes. A decade of inconsistent brand work doesn't compound into 10 years of brand equity ̵1; it compounds into roughly zero. Every time you re-brand, it restarts the clock back to zero, and zero compounds into zero no matter how long you run it. Meanwhile the brands that have become legendary ̵1; Patagonia, Hermès, Costco, In-N-Out, Rolex, Cisco, Microsoft ̵1; look boring at the campaign level on purpose, because they understand that the campaign level and the brand level have opposite variance preferences and you cannot optimize for both simultaneously.

Always-on lead generation. Always-on lead gen ̵1; the steady drumbeat of paid search, display, thought leadership, YouTube/Meta prospecting, nurturing, retargeting, lifecycle marketing, the unsexy workhorse channels that keep your sales pipeline full ̵1; is additive aggregation.

Your current pipeline is the sum of 100s or 1,000s of small individual conversions, no one of which matters and none of which compound multiplicatively against each other. A bad day in paid search doesn't destroy a good week in thought leadership content production. A brilliant webinar campaign doesn't multiply into demo bookings. The conversions sum, the variance washes out across the volume, and what ultimately matters is the mean efficiency per MQL/SQL/Demo/whatever. As such, your variance preference should be roughly neutral ̵1; you're not protecting a floor and you're not extracting a maximum. You're running an arithmetic average across a large sample.

The most common error is running always-on like a draft. CMOs and VPs of marketing chase the ̶0;breakthrough channel,̶1; reallocate budget to whatever generated the best individual results last week/month, turn off channels that didn't produce a standout outcome and hunt for the next growth lever as if pipeline were a max-order problem.

But when you import draft logic into an additive aggregation problem, the result is whipsawed budget allocation, channels that never accumulate sufficient data to optimize, agencies churned every 18 months because none delivered a breakthrough that was never structurally available, and a marketing efficiency curve that bounces around its long-run mean without ever durably improving it. The right move at this layer is to ruthlessly optimize for mean efficiency, accept that variance is noise, and let the law of large numbers do its work. Boring program management, executed well, beats heroic reallocation almost every time ̵1; which is why most B2B marketing orgs underperform: they're applying the variance preferences from the 2 more glamorous aggregation methods to the unglamorous one that actually generates the majority of their pipeline.

## The Big Picture + The Common Thread

The common thread that weaves throughout each of the above examples: the most expensive strategic mistake isn't choosing the wrong variance preference; it's importing a variance preference from one domain to another without noticing that the aggregation method changed.

This is the failure mode the framework exists to surface.

Almost every brand/operator/executive I've worked with has the right variance preference somewhere ̵1; they understand at least one aspect of their business correctly. The error is that they generalize that preference (where it has almost always served them well!) to domains where it doesn't apply. The CMO who correctly demands brutal variance in creative testing then runs their brand work the same way and wonders why positioning never solidifies into awareness/preference. The agency that correctly runs concentrated, fat-tailed creative bets ̵1; but concentrates 100% of their budget into a single channel, only to be wiped out when Meta breaks (again). The founder who correctly hires specialists for specialist roles applies the same framework to their COO search and ends up with an organization full of peaks and valleys that eventually crashes + burns.

The solution isn't to memorize the right answer for each function (that's both impossible and a staggering waste of time/resources). It's to make the question itself routine, so that every meaningful decision about uncertainty starts with a moment of asking which aggregator am I operating under right now, before any variance preference gets selected.

The marketers and executives who can name the aggregator before they argue about variance reach better answers, faster. They also produce fewer of the strategic disagreements that look intractable but are actually 2 people implicitly assuming different aggregators and arguing past each other about variance preference (something that describes a startling percentage of the strategy debates I've been part of over the years). The CFO who wants the tentpole spot de-risked and the agency that wants to take the swing aren't actually disagreeing about creative philosophy; they're disagreeing about which aggregator applies. The CMO who wants to rebrand and the founder who wants to hold positioning aren't disagreeing about taste. They're disagreeing about whether a brand is compounding or max-order, and neither of them knows it. Once the aggregator gets named, the disagreement usually resolves itself in minutes.

The diagnostic is portable across more decisions than this newsletter has space to cover. Whenever the outcome involves uncertainty across multiple realizations, ask: what function aggregates my outcomes here?

If the answer is multiplicative across time, minimize variance at acceptable mean. Channel your inner Buffett or Simons or Lynch. Build a steadily-growing business, don't chase rocket-ship growth. Run the brand work like it's an account that compounds for 30 years, because it is. Be intentionally boring.

If the answer is the maximum across attempts, maximize variance and accept the floor. Draft for the elite trait. Run the creative test with staggering variety and be merciless in your culling of the losers. Take the swing on the big campaign. Experiment with wildly different offers. You want fat tails because fat tails are the only place the peak you're hunting for actually exists.

If the answer is additive across many small bets, optimize for mean efficiency and stop hunting for breakthroughs/golden bullets. Run the always-on pipeline like a manufacturing line, not a casino. Resist the temptation to pile budget to whichever channel had the best week. Resist the temptation to kill programs that didn't produce a standout outcome ̵1; because "standout" is the wrong selection criterion. The law of large numbers is doing the work; your job is to raise the average, not to chase the maximum or protect the floor. Boring program management, executed brilliantly well, beats heroic reallocation almost every time....which just so happens to be the underrated truth in B2B/high-volume B2C marketing.

If you can't answer the question about what aggregation method governs your outcomes, then you can't answer any of the downstream questions. Most strategic disagreement in the marketing industry ̵1; and most of the unforced errors we've found in 100s of audits ̵1; is really just people applying the wrong aggregator. Fix that, and you're better off than 80% of marketers.

Until next week,

Cheers,

Sam

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