The Math Behind Innovation

In a new Scientific American piece, Martin Reeves of the Boston Consulting Group and Thomas Fink of the London Institute of Mathematical Sciences show how mathematics can help us better understand how innovation works.

Their research also shows how a company can gain a strategic advantage in the innovation process relative to their competitors.

Imagine that you are a budding chef, and your objective is to create new culinary experiences. To do so, you add ingredients to your store cupboard in any order you choose such that you can construct as many recognized recipes (culinary innovations) as possible. But is it possible to have a strategy of innovation, given the quirkiness of what constitutes a valid recipe? And how would you factor in the seemingly imponderable serendipity of today’s ingredient choices paying off later in unexpected ways?

By modeling innovation as a search for valuable combinations of components (products), informed only by the knowledge of what has already worked for yourself and competitors, we aimed to get behind the important but murky topic of innovation strategy. Innovation is critical to sustained economic growth and has been variously explained as luck, special vision or, at the other extreme, just another business process to be optimized for efficiency. We looked both deductively at the recombinatorial math of innovation, and empirically at the performance of different strategies in real world innovation spaces where the innovation game has already played out, including language, gastronomy and technology.

They made an exciting discovery and found that it is indeed possible to have an information advantaged strategy of innovation.

Innovations can be characterized by their complexity—the number of unique components that they contain. Ingredients can also be characterized by the average complexity of the recipes they occur in. And innovation spaces have a characteristic distribution for the complexity of valid recipes, which determines how the innovation process unfolds. We found that impatient strategies—ones focused on simple ingredients and recipes with an immediate pay off were most successful early on. This echoes the “minimum viable product” strategies which are popular with tech start ups.

Later in the evolution of innovation spaces, patient strategies, which focus on more complex recipes and ingredients and have a postponed pay off, are more successful. These are more like the sustained research programs of large enterprises operating in mature spaces. Both strategies always beat random strategies for choosing ingredients. And by monitoring the average complexity of the recipes in an unfolding innovation space, one can spot the cross over point of these strategies, and thereby construct an adaptive strategy which optimally combines the attributes of patient and impatient strategies.

Innovation is critical to sustained economic growth. By understanding how it works and how you can gain a strategic advantage in the innovation process, you can increase your company’s chance of success.

For more on their research, see “Harnessing the Secret Structure of Innovation” in the MIT Sloan Management Review.