The problem of the local maximum

Business and Curves Sketching

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The name of the article probably evokes more or less pleasant memories of school days for many of you. The infamous Curve Sketching in Analysis was for many students a part of mathematics they would rather have avoided.

However, we have learned something exciting I’d like to discuss in this article. Namely, that there can be several maxima for given functions and that a local maximum is not necessarily the maximum value of a function (global maximum). But what does curve sketching have in common with good decision making and business? How can we profitably apply the understanding of this theoretical mathematics to our career and maybe even to our whole life?

First of all, we need to understand that there are clear and observable parallels between this model and the corporate world. Especially in (online) marketing, ignoring these similarities often leads to wrong decisions, a wrong focus, and the loss of enormous potential.

To further elaborate these parallels, let's go ahead and apply the theoretical model on professional work methods. Simply consider every abstract scope of action and decisions in your work as a given functional section.

Our concrete action/decision is the parameter within our function, on which we have a direct influence (Examples: whether we hire person A or B, whether we implement strategy C or D). The resulting function value is the benefit of our company (or our career). Our scope of action is, in most cases, rigid and predefined. Limiting factors are usually experience, know-how, competencies, and our social and professional environment. These adjust our scope of action in such a way that we approach a maximum benefit by adapting our behavior based on the negative and positive results of our past actions.

A concrete example:

A consultant for digitization is unlikely to consider the use of carrier pigeons when working on his client project. Neither will a sales director consider that he could welcome his most valuable key account in the lobby without clothing.

At first glance, this is definitely a reasonable mechanism by our brains. We reduce the complexity of our decision making. Instead, we can focus on the essential decisions and weigh the pros and cons. The problem with this reduction of complexity, however, is the premise that the benefit-maximizing decision always lies within our given scope of action. After the rough choice of action, we begin to make small iterations and adjustments to approach the local (benefit) maximum.

We intrinsically and automatically assume that any scope of behavior, outside our own, will lead to lower utility values than the one we have predefined.

What happens, however, is a drastic reduction of our scope of action and an increasing arrogance regarding the acceptance of alternative actions outside our field of consideration. Competence and years of experience become the foundation of the conviction that one's own decisions and behavior have an exclusivity right.

And as a result, successful visionaries appear and disrupt markets by questioning standards, rules, and common knowledge in industries. They build up companies around their new global (probably rather a larger local) maximum. They know that even the most elaborated company just operates within a rigid pattern.

Amazon's success, for example, was not founded on the concentrated expertise of the world's most successful book publishers. While they spent their time fine-tuning their existing business models, under the outdated premise that the true value of a book lies in its feel – a small, hairless investment banker with an online distribution business has ushered a consumer revolution. (For more references see Netflix vs. Blockbuster or Spotify vs. music industry).

The unused potential of the given industry was recognized and successfully exploited:

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In those examples, a pattern is recognizable which is not only visible in these gigantic scales. Competence and experience are becoming increasingly a double-edged blade. On the one hand, they are of great value for improving and optimizing existing systems. On the other hand, they may tempt us to put blinkers on and ignore new scopes of action. This in turn leads to wasted potential.

To go one step further into the core competence of FutureNext, I prepared an even more specific example in the field of online marketing that I would like to discuss. The nature of the excessive use of A-B tests.

With enormous scientific progress and unlimited testing possibilities, stiffening to local maxima is common practice here. For example, conversion rates are being tested based on adjustments of geometric shapes in the footer of the checkout process. The word "favorite product" is replaced by "our favorite". Different distances between the payment options. The term "website nudges" (small "nudges" to stimulate desired behavior among customers) justifies these procedures - a big thanks to Cass Sunstein and Richard Thaler at this point.

The danger that can naturally arise, however, is the eternal approach to a local maximum. In no case does this mean that conversion optimization with mini iterations is generally counterproductive. Nevertheless, one would do well to sometimes take a step back and focus on the big picture again. How is the customer benefit communicated? Where is the company's own content most effectively placed? How do I lead the customer from any position within my sales funnel to the final purchase? Is there a way to deliver my customer a new outstanding experience?

Competences in a specific area should not put blinkers on us or make us ignorant of new scenarios and areas. Rather, we should use our competences within a scope of action in order to gain new and possibly more beneficial "functional sections" even more efficiently.

In online marketing. In our career. In our company. In our lives.