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When was the last time you heard the story of a great innovation begin with, “I built a killer spreadsheet”?

More often you’ll hear stories like the one behind Airbnb’s early growth strategy. Founders Joe Gebbia and Brian Chesky’s had in their early days been advised by Y-Combinator’s Paul Graham to leave the confines of Silicon Valley and get face time with customers in their most concentrated market, New York City. By doing so, the duo quickly discovered three major problems inhibiting growth: hosts didn’t know how to photograph their apartments attractively, the website’s meticulously designed listing interface was actually a nightmare for hosts, and in-home cash transactions between guests and hosts were inherently awkward. Gebbia and Chesky’s focus on the ground level triggered an inflection at the high-level: top line growth doubled even as they just began implementing the raft of initial changes. And the growth never slowed down.

Or you’ll hear about Rent the Runway founders Jennifer Hyman and Jennifer Fleiss, who—with no money and no market analysis—maxed out their credit cards at Bloomingdale’s to buy 100 dresses. They had a ton of questions: Would women rent dresses through the mail? How much would they pay? Would merchandise come back in decent condition? Not only were Hyman and Fleiss able to resolve some of their initial questions, but they unexpectedly discovered that what early enthusiasts liked about Rent the Runway was that they could express their individuality and feel beautiful every single day. This emotional benefit was a much bigger insight than the functional focus of an online dress-sharing platform, and the founders knew they were onto something transformational. The insight carried business model implications as well: suggesting that a membership-based “unlimited rentals” model would resonate, and that this was a large market not just a luxury niche.

Airbnb and Rent the Runway are just two examples of entrepreneurs leveraging small data to make big decisions–and driving transformational outcomes. Essential insights resided in the rich, unexpected narratives of individual customers–not in the smooth predictability of averages or the snippets of surveys. Correlation does not reveal the one thing that matters most in innovation—the ‘why’ behind a customer’s decision to purchase and use a particular solution.

The power of big data to enable breakthroughs in many aspects of managerial and scientific endeavor is so staggering that it has generated a religious-like faith in its powers—if we can just get enough data, the truth will be revealed. But this faith is flawed.

Revealing innovation insights requires small, not big, data. All data is man-made—it’s a sanitized representation of the messiness of our lives. Successful innovators don’t walk away from the messiness. They immerse themselves in it to find rich meaning.

Useful data comes in the form of stories—not statistics

The innovator’s laboratory is full of real people struggling to make progress in their personal and professional lives. Each of us routinely encounters obstacles and opportunities, making choices about how best to deal with them. Real life experiences—whether they include finding a high-end dress for a special event or booking an affordable stay in a new city—are the ore containing innovators’ gold.

Intuit founder Scott Cook shared similar stories about the immersive customer experiences that reframed his thinking about their small business accounting software. “What we realized,” Cook told me, “is that accounting software was the last thing in the world these small business owners wanted.” In fact, the whole idea of accounting was unfamiliar and intimidating.

Entrepreneurs simply wanted to pursue their business-building dreams without fear of running out of cash, missing payments, or failing to collect an outstanding debt. They didn’t want better accounting tools—they wanted accounting to disappear. For Intuit, this insight revealed a much more powerful purpose: How do we design software so good that accounting disappears?

Outliers are more valuable than averages

In order to process mass amounts of data at scale, managers apply analytic software to transform the unwieldy narrative structure of real life into clean, fungible quantitative formats. They scoop up vast troves of information to populate spreadsheets, run analytics, and look for patterns. That path leads to the beige tones of the average, and no great innovation ever came from studying averages.

The danger resides in what gets lost: meaning. With the rough edges smoothed into averages and the outliers stripped as “mere noise,” there is no room for surprise discovery, and the prospects for innovation breakthrough dim.

Innovation is found on the fringes. Insights lurk in the anomalies and the unexpected. If Chesky and Gebbia had looked for the means and medians, they would have ended up offering only tract homes in suburban cities to middle class families with 2.3 kids. Thankfully, they followed Paul Graham’s advice and hit the streets—scooping up nuggets and changing the world. They went small to grow big and have sustained their success by never losing that granular focus on the experiences and the progress that Airbnb customers seek.

The beginner’s mind is far more helpful than the expert’s mind

Reporting layers only exacerbate the problem, as middle managers, following established processes and incentives, edit the information that gets passed up the organizational ladder. Ultimately, the combined effect of data cleansing and managerial filtering is that senior executives typically see a disembodied view of the market in which the lifeblood, quite literally, has been systematically removed and what remains is a synthetic veneer displaying the trappings—but not of the substance—of real life.

The implications for managers at large companies who are seeking to unlock new growth markets are clear. They need to return to their creative birth stories wherein the only data was the “real life” data of people in the world struggling to make progress. Startups are full of unwashed entrepreneurs, necessarily processing rich, narrative data with beginners’ minds. Unlike the expert’s mind, in which answers and constraints are already fixed, the beginner’s mind is open to endless possibility and surprise—challenging familiar habits and entrenched mindsets.

Insights have a narrative structure, and we need those stories if we are to develop successful new offerings. A story, not a statistic, is the shape that an innovation insight takes. As Airbnb, Rent the Runway, Intuit, and the extended annals of new business formation attest, the stimuli that prove most valuable are overwhelmingly small, not big, data.

Taddy Hall is senior partner at Lippincott, a creative consultancy.