(FORTUNE Magazine) – There is an arithmetic to innovation that seems inescapable--it is repeated again and again in both the business world and the natural world. It is the essence of Silicon Valley. Out of a thousand nascent business plans, maybe 100 have will have enough merit to justify a few hundred thousand dollars of angel investment. Out of these 100, perhaps ten will demonstrate enough promise to warrant a few million dollars of VC money. And out of these, only one or two will ever make it to the public market and achieve the success of an eBay or a Juniper Networks. The same math can be found in the drug industry: No more than one out of every 5,000 to 10,000 compounds makes it through the gauntlet of tests and trials to emerge as an approved drug. The odds are almost as long for sea turtles. For every 1,000 eggs laid, only one sea turtle will survive to adulthood. And in every act of human procreation, 59,999,999 sperm turn out to be surplus to requirements.

Call it Hamel's Law of Innovation: For every 1,000 ideas, only 100 will have enough commercial promise to merit a small-scale experiment, only ten of those will warrant a substantial financial commitment, and of those, only a couple will turn out to be unqualified successes. It's the inverse log scale behind innovation.

So what's the lesson for your company? Just this: If you want to find a few ideas with the power to enthrall customers, foil competitors, and thrill investors, you must first generate hundreds and potentially thousands of unconventional strategic ideas. Then you're going to have to take the best of these and turn them into low-cost, low-risk strategy experiments--a new distribution channel here, a new pricing approach there, a new service offering somewhere else. Out of these experiments will emerge a few ideas worth pursuing wholeheartedly. Put simply, you have to crush a lot of rock to find a diamond.

Let me return to my biological metaphor. The problem for many slow-growing companies is that they possess a very low corporate sperm count. Unlike those wacky investors out there in Silicon Valley, they aren't experimenting with enough new ideas to have any real hope of stumbling upon a few that prove to be truly transformational. Many CEOs seem to posses a vain hope that a handful of really smart senior execs, aided by a few even smarter consultants, can quickly land on the one really big idea with the power to revive corporate fortunes. They don't want millions of sperm--what a waste. They're looking for the one giant sperm that will do it all. Unfortunately, biology doesn't work this way, and neither does innovation.

While companies have long recognized the low odds of success in new product development, and have endeavored to build and fill new product pipelines in response, they haven't applied the same principle to strategy development. As a result, most companies have no process for generating a surfeit of fresh strategy ideas, or for starting and tracking dozens of strategy experiments, and then committing to those that prove most promising.

Instead of building an innovation pipeline filled with unconventional strategy options, many companies have created innovation ghettos--incubators, new-venture divisions, and venture funds that are largely divorced from innovation in the core business. The assumption seems to be that it's impossible to really innovate in the core business--that the fear of cannibalization is so overpowering and the constraints of orthodoxy so absolute that the only way to innovate is to create a separate organization filled with native-born entrepreneurs. While dedicated innovation units have a purpose, they are often little more than ornamentation and are no substitute for an innovation pipeline overflowing with ideas for revitalizing the core business.

Perhaps an anecdote will help here. A few years back a young woman selling sewing machines for Sears noticed a worrisome trend--more and more customers were returning recently purchased machines. Perplexed, she began calling her dissatisfied customers and quickly learned that many had been stymied by the sheer complexity of the feature-laden machines. Her solution was to invite these frustrated customers into the store for sewing classes. As the flood of returns began to recede, it occurred to this enterprising employee that hers might not be the only Sears store facing such a challenge. Yet to her frustration, she discovered that Sears, like most companies, had no systematic way of encouraging and propagating grass-roots innovation like her own.

In the absence of an explicit process for building and managing an innovation pipeline, local experiments--even when successful--are unlikely to become companywide programs. Just as bad: Small ideas, like teaching customers how to use a sewing machine, that don't get shared and discussed never get the chance to become big ideas, like developing an entire portfolio of training programs focused on everything from kitchen remodeling to assembling a home-entertainment system.

In richly paneled conference rooms around the world, long-tenured executives are right now huddled in confidential strategy sessions where the goal is to outline "the store of the future" or "the bank of the future" or the "airline of the future"--pick your industry. One can just about bet that any plan that wins the support of such tradition-bound souls will be both orthodox--tightly constrained by industry "best practices"--and conservative, posing little risk to the careers of its senior sponsors. No wonder most strategy conclaves produce tepid ideas that are too little, too late.

Here's an alternative approach to generating strategy--one that is true to the arithmetic of innovation and has the potential to spawn powerful, mold-breaking ideas: Create an internal competition.

Why not offer every branch, region, or office a few hundred thousand dollars every quarter to fund a handful of "new rules" demonstration projects? Use a peer review panel to determine which projects should receive an initial dose of funding. Make it easy for volunteer teams to coalesce around nascent experiments by widely publicizing the list of such projects. Set up a series of 30- or 60-day hurdles where the goal is first to flesh out the basic idea, then build a mockup or prototype, and then conduct some sort of market experiment (even if the "market" consists of other employees) that can help refine and validate the idea. Projects that look viable after 90 days can be nominated for additional funding and broader corporate support. In my experience, this is a surer way to transform a hidebound company than incubators, megadeals, and top-down strategic planning.

Top managers who embrace such an approach to strategy development soon find that their job shifts from creating strategy to finding strategy in the rich pattern of ideas bubbling up from below.

Divisional managers play a critical role in ensuring that the pipeline has enough radical ideas coming in to yield an adequate number of successes at the back end. To build an innovation pipeline, senior management must set aside a small share of a company's capital and expense budgets (2% to 5%) to fund early strategy experiments. Moreover, employees must be taught how to explode conventional thinking, how to uncover the deep, unarticulated needs and frustrations of customers, and how to first imagine and then test unconventional strategic options.

How much work has your company put into building and managing an innovation pipeline? Would a significant percentage of the employees in your company say that strategy innovation is part of their job? Has your company taught employees the principles of strategy innovation in the same way it has taught Six Sigma or customer service? Does your company have a well-documented compendium of potentially valuable new strategy options? Do innovators in your company have access to a fast-track process for funding their ideas? If you can't answer yes to these questions, it's unlikely that your company will evolve fast enough to stay relevant in our topsy-turvy world.

Typically, corporate transformations stall once the relatively easy task of wringing out gross inefficiencies has been completed. In devoting themselves entirely to the pursuit of efficiency, top management inadvertently drives out the "waste" and "extravagance" that is the very fuel of innovation. This is why so many successful "turnarounds" are short-lived--yes, the company has been made more efficient, but it has also been left with a dearth of new wealth-creating strategies. Innovation is inherently an inefficient process. As top management strives for ever greater efficiency, it must learn to tolerate "stupid" ideas and "failed" experiments. Those are the byproducts of a well-functioning innovation pipeline. After all, when a man and woman celebrate conception, they seldom bemoan the 59 million little swimmers that never made it.

The arithmetic of innovation is the arithmetic of life itself: endless mutation, occasional progress. Through the millennia there have been uncounted mutations. Every once in a while one of these haphazard events improves the survival prospects of the species. Winning mutations become part of the genome. But unlike evolution, strategic innovation doesn't have to be a completely random process--we don't have to wait for mutations to appear. We can teach people to think unconventionally, we can put them into situations where they have the best chance to see the future, and we can help them quickly distinguish between ideas that are promising and those that are just plain stupid. But what we cannot do, in the absence of real trial and error, is predict exactly which of many apparently worthwhile ideas will make the greatest contribution to long-term competitive success. Just as no earthly being could have designed the genome, no single individual can design the perfect strategy or predict the next killer business model. As those much criticized venture capitalists have learned, there's no substitute for variety.

GARY HAMEL is the chairman of Strategos, a strategy consulting firm, and the author of Leading the Revolution. FEEDBACK: gh@strategos.com.