The Shape of Strategy

Today we’re going to take a look at Robert Keidel’s book, The Geometry of Strategy (2010). Keidel is a Professor of Management, a consultant, and former senior fellow at the Wharton School of Business.

In his book, Keidel argues that we can improve the content of strategy by paying closer attention to its form. By “form” he is referring to different styles of thinking, which he represents as shapes.

Keidel calls this lens the “geometries of thought.” He argues that strategy can be parsed into four general categories, each reflecting its own geometry. Paying closer attention to the shape or form of strategy helps us to move to more appropriate styles of thinking when needed. The four category/form pairings are questions of:

Persona (who we are), addressed by point thinking (either-or dichotomies).

Performance (what we measure), addressed by linear thinking (continuums).

Puzzle (what perplexes us), addressed by angular thinking (n x m matrices).

Pattern (how we organize, compete, and grow), addressed by triangular thinking (patterns involving three variables).

Let’s take a look at each.

Point Thinking

This frames things as dichotomies. It’s this or that, black or white. Researcher Paul Nutt famously found that executives frame 70% of decisions in this either-or way, and then make the right call roughly 50% of the time (Nutt, 1999).

Point thinking reduces value by blinding us to options. Point thinkers reduce complex issues to binaries and tend to ignore conflicting evidence. This can be value-adding, however, when it comes to matters of strategic persona (identity).

Persona encompasses questions like:

Who are we? (e.g., CarMax as the “Walmart of used cars”)

What are our non-negotiables? (e.g., “Always benefitting the customer”)

What contrasts do we want to draw? (e.g., Southwest’s avoidance of the hub-and-spoke model)

What metaphors highlight who we are or offer counterpoint? (e.g., Apple as the “anti-business school”)

What rules of thumb do we want to emphasize? (e.g., Warren Buffet’s maxim, “Beware of geeks bearing formulas”)

What comparisons can generate value? (Here, Keidel gives the example of Taiichi Ohno coming to America to learn auto-assembly methods, only to end up learning more from American supermarkets.)

Failing to address issues of persona can result in strategic failure. This can take the form of having no clear identity, the wrong identity, or a conflicting identity.

Examples Keidel discusses include Volkswagen’s luxury car, the Phaeton, which conflicted with its identity as an auto manufacturer, Las Vegas’ (unsuccessful) attempt to market itself as family-friendly entertainment, and Kodak’s obsolete identity as a company that sells film.

Linear Thinking

This is shades-of-grey. It moves us from contrast to continuum. Keidel links linear thinking to performance, to questions around what should be measured, what should not be measured, and whom measures should be shared with. In discussing linear metrics, Keidel distinguishes between process, outcome, and legacy.

Process metrics include things like cycle time, R&D spending, and percent of sales attributable to new products.

Outcome metrics include things like sales, profitability, and market share (i.e., what I call “impact metrics”). Only a few should be prioritized at a time. (Keidel cites Texas Instruments’ dictum, “More than two objectives is no objectives.”)

Legacy metrics have to do with long-term reputation, matters of humanity, and, at the very least, how a company approaches the issue of people development (the company’s “bench strength”).

Strategic failure stems from having no criteria, the wrong criteria, or the wrong number of criteria. Discussing legacy failure, Keidel cites Collins’ (2001) finding in Good to Great: More than 75% of the time, executives either choose weak successors, set their successors up for failure, or both.

Process failure often comes from ignoring that whatever is measured will be gamed. Keidel gives the example of Dell rewarding call-center employees for minimizing time spent on the phone with frustrated customers. (Time per call was reduced by handing off calls more.)

Angular Thinking

This is both black and white. It’s the use of matrices, often to identify “best-of-both-world” solutions. Keidel argues this applies to puzzle.

The aim is to surface options from perplexing dilemmas and generate insight. Angular thinkers often have an advantage over habitual point and linear thinkers, but may end up ignoring important third (or fourth) variables. In discussing matrices, Keidel distinguishes between classic, triadic, Solomonic, linear, and Goldilocks.

A classic n x m calls out the four combinations of two levels of two variables. An example would be an Ansoff 2 x 2 (new and current markets by new and current products).

What Keidel calls a “Solomonic” matrix contrasts variables to surface an insight. (The name refers to the story of King Solomon and the two mothers, from 1 Kings 3.) An example would be Jane Golden’s anti-graffiti initiative, which ended up reframing graffiti as desirous public art.

In many 2 x 2s, one of the cells is not a viable or desirable option. This is what Keidel refers to as a “triadic.” Below is an example adapted from UX expert Pavel Samsonov.

A linear matrix aims to reveal best-of-both-world solutions. An example might be trying to find a way to be both risk-taking and efficient. (Orgs often say they value both, when in reality one will be subordinate to the other.)

A “Goldilocks” (or curvilinear) matrix shows a U-shaped relationship. (The name refers to Goldilocks and the Three Bears—a “just right” bed is not too soft and not too hard.) An example might be Barry Schwartz’s (2016) “paradox of choice,” where as the number of options increases, satisfaction with one’s choice goes up, plateaus, then starts going down.

As Keidel puts it, “Every organization faces a small number of puzzles—paradoxes, dilemmas, conundrums, imbroglios—whose solutions are critical to its future. The challenge is twofold: to identify the relevant puzzles and then to frame them correctly” (p. 52). Angular thinking, he argues, is a key tool to navigating these waters.

The risk of strategic failure here sometimes lies in neglecting an important additional variable, such as in the classic “prisoner’s dilemma.” It may also lie in seeking a best-of-both-worlds solution while failing on both fronts, such as failing to effectively plan for both the short- and the long-term or remaining poor at exploration as well as exploitation.

Triangular Thinking

This brings three variables into play, exploring a larger pattern. In Keidel’s hands, triangular considerations often have to do with how the company itself is designed: How does it address its competitive strategy, its growth strategy, and its organizational strategy?

These three key questions, for Keidel, map to the variables of cooperation (competition), autonomy (growth), and control (organization). As he puts it, “To think triangularly is to make sense of problematic situations by extracting parallels with individual autonomy, hierarchical control, and spontaneous cooperation” (p. 62, italics in original).

Keidel represents these concepts as Venn diagrams, noting there are only a few such relationships possible (which he also maps to triangles).

Whether contrasting the trifecta of strategic, technical, and organizational, or identifying a balance between decentralization, centralization, and collaboration, Keidel maintains that a great many triangles can be used to think strategically that all (loosely) fall under his general triangular rubric of “autonomy, control, and cooperation.”

We can map our competitors in such a triangle, as in the image below-right, in attempt to surface a “blue ocean” strategy. Or we can consider the space within such a triangle to guard against strategic failure.

Consider the triangle below-left. Are we: 1) overdoing top priorities; 2) underdoing bottom priorities; or, 3) operating as though we don’t actually have any priorities? This form, what Keidel calls the “triangular donut,” speaks to his point that the “value of triangular thinking extends beyond linking similar concepts, to articulating structure within them” (p. 106, italics added).

With angular and triangular thinking, one may fairly wonder why only two or three variables? Why not “rectangular thinking?” To be fair, that’s also a viable option. Here Keidel references Peter Schwartz’s (1991) work on scenario planning: One variable may mislead. Two may leave something out. Three or at most four typically captures reality.

Anything more is a “hopeless muddle.” Consider also multiple regression: It’s often only a few variables that account for most of the variance. Things still get complex enough. As Keidel shows, the crucial questions of how we compete, grow, and organize can also be depicted as triangles, making the issue more a “triangle of triangles.”


It’s important to keep in mind this is meant only as a rough heuristic. As Keidel stresses, it’s hard to get people to even agree on what “strategy” means. It’s often vaguely defined by analogy, such as turning a destroyer (tactics) vs. turning an aircraft carrier (strategy). In general though, strategy tends to be synonymous with what is bigger-picture, more value-driven, higher-risk, org-wide, or harder to undo.

The main value Keidel brings to the table here is twofold: First is encouraging explicit consideration of how we address aspects of our persona, performance management, puzzles (dilemmas), and larger patterns. Second is moving from debating content to consideration of the underlying form of our arguments and how many variables are (and should) be at play.  

This encourages interplay between these styles of thinking. What 2 x 2 matrices would be more value-adding as a triangle? What point questions can be illuminated by contrasting them with linear?

As an example, Keidel discusses the point question of whether teams are treated more like assembly lines or SWAT teams. He contrasts this with the linear question of how much time they spend preventing fires vs. fighting them.

An insight emerges, he says: If teams are expected to function like factories while spending much of their time fighting fires, something is confused. SWAT teams fight fires. Teams that are like assembly lines should spend more time preventing them.

To take one more example, while writing this post I saw the comment below, from Agile expert Dan North. I read Dan’s reply and started thinking about it in terms of underlying form. (You know how you buy a certain type of car and then start seeing that kind of car everywhere? Keidel’s geometry is a bit like that.)  

If discussing resource efficiency (or traditional “productivity”) and the importance of improving it, we might realize we’re engaged in linear thinking (“A” below). This should lead to questions about what we are measuring, why, how it will be gamed, what we are not measuring and why not.

What might be better to measure? Some orgs have had the epiphany that flow efficiency is more important than resource efficiency and may experiment with looking at both (“B” below). They may come to the realization that resource efficiency is a red herring and seek better alternatives. Also, how do they know it’s actually “value” flowing through their “value streams?” They don’t, hence “C” below is even better.  

So, what are your strategic issues, and how might you diagram them as point, line, matrix, and triangle? How might this change your thinking?


Collins, J. (2001). Good to great: Why some companies make the leap and others don’t. New York: HarperBusiness.

Keidel, R. W. (2010). The geometry of strategy: Concepts for strategic management. New York: Routledge.

Mezick, D. & Sheffield, M. (2018). Inviting leadership: Invitation-based change in the new world of work. Mezick and Sheffield.

Nutt, P. C. (1999). Surprising but true: Half the decisions in organizations fail. Academy of Management Executive, 13, 75-90.

Schwartz, B. (2016). The paradox of choice: How the culture of abundance robs us of satisfaction. New York: HarperCollins Publishers Inc.

Schwartz, P. (1991). The art of the long view. New York: Doubleday Currency.

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