The curse of the Double Axis Chart

It all started with Bruce Henderson (*1915–?1992). Henderson can be regarded as the pioneer of the double axis chart in the business world: In 1970, the American devised the Growth Share Matrix, which would propel Boston Consulting Group (BCG), the company he founded, to international stardom. Henderson's chart would gone down in management history as the "BCG Matrix": To business people today, the concept is probably as familiar as the "Freudian mistake". For half a century now, the saying goes among consultants: "Give me an X-axis and a Y-axis - and I can explain the world to you!" In terms of popularity, double axis charts may even have overtaken conceptual representations in the form of layered pyramids.

The triumphant advance of double axis charts, or matrix charts, ran parallel to the explosive growth of the consulting industry. The visuals, usually divided into four fields, met the needs of consultants and their manager clients, to quickly identify strikingly clear answers to tricky commercial and business questions: With little effort, and without hair-raising detailed analysis or statistical methods. From the start, the notion of visualizing conceptual relationships through multi-dimensional graphics was married with advertising purposes, of course. Including at BCG. Primarily, double axis charts are visual marketing instruments, used by service providers to pitch consulting products like strategic advice or cost management, or to drive conceptual dogmas such as economies of scale, pressure to grow, disruptive innovation, or digitalization into the market.

Google search results for "BCG matrix" (excerpt)

Double axis charts can appear quite convincing, at first glance. No matter how feeble or questionable a concept may be, a matrix chart bestows that idea with an aura of scientific logic. Critics of matrix-shaped marketing concepts have long pointed out that a look behind the axes of any matrix representation is required in order to analyze such a chart's rationality or quality. In other words: When encountering any matrix visualization, we should first ask ourselves: Why were those particular two axes chosen - and what does the fields identified in the chart imply? Usually, the assumption of a relationship between the respective X and Y axes, or a lack thereof, is the problem of a four-field matrix. Already, at this point, most of the charts should raise eyebrows around matters such as the ubiquitous "causality or correlation" debate.

But two even more fundamental problems with such charts exist. It is the the general assumption of relationships within a double axis chart. Upon closer inspection, the choice of the matrix dimensions itself usually turns out to be un-scientific, or even misleading and manipulative. This was already the case with the mother of all matrices, the above-mentioned BCG Matrix. Ultimately, that matrix served little more purpose than that of promoting fear in the business world: Fear of too little growth and declining market shares. That agenda resonated only too well with its time, and such fear among managers would later be stirred further by Michael Porter, who was set to become the world's first strategy guru. A second form of deception by double axis charts is embedded in the space between the axes: When that space is divided into four quadrants or into vertically arranged fields, further connections are postulated, and those quadrants or fields can be linked to "if-then" prescriptions, tools, action plans, "strategies" and other recipes. Consider Henderson's BCG Matrix: it dishes out four different strategies for the four fields entitled dogs, stars, cash cows and question marks. The prescriptions offered by BCG will appear downright laughable to anyone familiar with the complexity of real-life business decisions. But the treacherous nature of such strategy formulas only becomes obvious when the chart's assumptions are critically examined.

In short: There is something propagandist about all double axis charts. It is all too easy to be seduced into believing that the assumptions, relationships and derivations alleged by a multi-field matrix diagram are sound. We are easily led astray into assuming that the corresponding illustrations are rooted in ratio, or in scientific insight of some sort. But that would be a mistake. Instead of making distinctions or tricky connections clear, tangible and intuitively comprehensible, matrix representations obfuscate the very distinctions and connections that might lead to insight. Usually, what matrix charts do is promoting marketing narratives, opinions, distortions of scientific knowledge, and even anti-social theories. In summary, one could say:

Never believe a matrix chart. Especially if someone wants to sell something with it.

The Stacey Matrix: a double axis diagram gets weaponized

Perhaps the most dramatic example of the falsifying, misleading effects of double axis charts on widely-held insight and collective consciousness is that of the chart commonly referred to as the "Stacey Matrix". In 1996, management professor and organizational theorist Ralph D. Stacey (*1942), otherwise known for his rather abstract, academic prose, was tempted to add an inconspicuous matrix representation to his book Organisational Complexity. The diagram entitled The Edge of Chaos (The Zone of Complexity) tried to summarize the effects of complexity on decision-making. More specifically, to illustrate the effectiveness of different decision-making mechanisms under certain conditions. An understandable attempt – which failed.

Google search results for "Stacey Matrix" (excerpt)

As with every multi-field matrix, Stacey chose two dimensions for the X- and Y-axes (uncertainty and disagreement) and divided his matrix into different fields, three to five, depending on which way you read the chart. The biggest problem with this chart is this:

With his matrix representation, Ralph Stacey (surely unintentionally) suggested that complexity is stepped up complicatedness.

A flawed idea of explosive suggestive power. To understand Stacey's "error in the matrix" better, it is useful to recall some of the scientific basics about the distinction between the complicated and the complex. Here is one that matters:

Complexity is not "increased complicatedness", but a different animal, entirely. The domains of the complicated and the complex are not mutually exclusive, though: In work-related situations that require human action or decision-making, the complicated and the complex usually "shake hands". Problems and work possess both complicated parts and complex parts.

In other words, when humans work and solve problems, the complicated and the complex more often than not appear in combinations or in intermingled forms: A project, for example, is not just complex: The complex parts of project work will naturally be dominant, but projects possess complicated parts, or portions, too. A process, on the other hand, hopefully will not contain any complex bits: Otherwise, such a process would be poorly encapsulated - and any attempt of automatization would cause it to swell and wreak havoc.

In short: The evil spirit of over-trivialization was already embedded in Stacey's original matrix. Which, by the way, is also the reason why Stacey himself removed the chart from his book. Instead of addressing the entanglement of complicated and complex parts in most of the problems we encounter in business and in life, the illustration wrongly postulated a hierarchy of domains. A kind of "escalation-level theory of complexity". And that notion is utterly false.

As is so often the case, the problem of reality-defying over-simplification did not end there. The mistake was further amplified when Stacey's representation was taken out of context and further simplified by derivatives of the chart. At the same time, the visual was stretched further and further beyond its very modest original island rationality. During the 2000s, the initial diagram for the visualization of different decision-making modalities was upgraded to become a "model" and a "framework". And it was stylized as a "tool for dealing with complexity". Throughout that development of the last 20 years, two modifications to the initial diagram are particularly noteworthy. First: The assignment of titles to the different fields of what now became The Stacey Matrix. The different fields were declared to identify separate contexts and the individual fields categorized as (usually) Simple – Complicated – Complex – Chaotic. The catchy field names made it possible to popularize the chart as an alleged "thinking model" and tool. These field designations subsequently allowed each field to be linked into a plethora of "standard strategies", conclusions, product recommendations, rules and recipes. With these two additions (field denominations and strategy derivations), the options for promotional use of the Stacey Matrix was turned nearly infinite. Thus, over time, the Stacey Matrix was outfitted to become a powerful all-purpose weapon for any sales pitch, and a "must-be" element of any convincing PowerPoint presentation.

The island rationality of the original concept has been overstretched into all kinds of directions, over the course of the successive reproductions. New conceptual distortions and ever cruder untruths emerged from the imitations. For example, most Stacey copycats postulate that the Simple is a separate context. It is not. In complexity theory, the simple is not a domain, but a subjective view of the complicated that is dependent on the knowledge that an individual holds: For those who possess knowledge, the complicated turns simple! Another lapse in all Stacey Matrix derivatives: The Chaotic is a mere sub-case of the complex domain - instead of a further increase or escalation of the complex, or a "separate context". Furthermore, the chaotic does not matter to work and decision-making at work: While we may encounter hard-to understand patterns in organizations, we simply do not encounter any patterns in organizations that deserve to be called chaotic, in a scientific sense.

The Simple and the Chaotic are not separate domains – nor are they "contexts". And: In value creation, the Complicated and the Complex often shake hands. Two strong reasons why the meaningfulness of the Stacey Matrix for thinking & acting in work and organizations can be quantified as Zero. Zip. Nil. Nothing.

However, the Stacey Matrix in its countless variations appears to be well-suited for manipulation and deception - right up to that Stacey Matrix spin-off that is labelled as a framework and which manages to derive four quadrants, "BCG-style", from a single axis. With the consolidation of Stacey's diagram into tools with square or vertical fields, as well as the accompanying strategies for action, the Stacey matrix has become something of a successor to Henderson's BCG Matrix. That at least can be said some parts of today's business world. While these days hardly anyone seems to speak of strategy in presentations and at conferences, complexity is all the rage. Some variation of the Stacey Matrix will almost inevitably be displayed, warnings about complexity and chaos uttered, and maybe Stacey's name mentioned - before the presenter clicks through to his or her service offerings, which are, of course, "well-suited for those complex contexts."

Most problems are actually two-faced. So forget the Stacey Matrix

I already hear some of you raising objections to the above, at this point. You might say something around: "Yes, the above rings true to some point, but what I do is different! The way I use some variant of the Stacey Matrix is benevolent, in that I try to raise awareness for the topic of complexity, in order to encourage insight and reflection in my audiences. I mean well!" To this kind of objection, I can only respond the following: True invitation to reflection and discourse looks different than that! The reductionist framing, segmentation and prescriptions that all incarnations of the Stacey Matrix subject audiences to will no doubt inspire reductionist thinking only. Along with all kinds of misconceptions and erroneous actions. There is nothing inviting in over-trivialization. Or in distorting complexity sciences for the sake of pitching a sale. Oversimplification, as Einstein so aptly pointed out, inevitably leads to error, because it "makes things simpler than they really are".

Every double axis chart is an invitation to oversimplification. That, sadly, is also true for the Stacey Matrix. Which is ironic, given that the original chart aimed at addressing how complexity has its way of defying simplification! More generally speaking, however, any suggestion that real-world business problems can be grasped or tackled on the basis of two factors or "matrix dimensions", and their relationship to one another - regardless of whether that relationship is causal, mere correlation or just pretty to look at - that kind of notion is absurd, no less.

In addition, the strategies for action or rule--based recipes promoted through double axis charts provide an illusion of convention and regularity. In other words: They promise everything that does not exist in a complex, dynamic world! Which is precisely why, in my own work, I limit myself to the distinction between complicated and complex ("the Blue" and "the Red") – without talk of separate segments, without any kind of rule-based deduction, or silly claims of causality.

Working in, on and with organizations is about applying relevant distinctions that support intelligent people with their own thinking. So that they themselves can achieve insight and find solutions for problems they encounter.

The work of experts, consultants, coaches or advisors should never, ever encompass keeping intelligent people from doing the necessary, strenuous work of thinking and understanding themselves! All that we can achieve with pre-chewed, rule-based frameworks (along with oversimplifying strategies and recipes) is to drive thinking and enlightenment out of work and organizations. In a world of complexity, companies can no longer afford to over-trivialize, or have their people obeying rules and prescriptions.

As for our (flawed) understanding of complexity in a complex world: It will likely require many years and great collective effort to get rid of the evil spirits that Henderson and Stacey awoke.

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Niels Pflaeging is founder of the BetaCodex Network and co-founder of Red42, an innovation-centric start-up on the fringe of organizational development and Learning & Development (L&D). Niels is the author of ten books, three of which are available in English: The best-seller Organize for Complexity (2014), the OpenSpace Beta handbook (2018) and the recently published Essays on Beta, Vol. 1 (2020). Together with Silke Hermann, Niels is the creator of concepts such as Org Physics and Change-as-Flipping, and of social technologies OpenSpace Beta, Cell Structure Design and LearningCircles by Red42. As an advisor, speaker and author, Niels has earned a reputation as a highly progressive business thinker and innovator. You can reach him through [email protected]. He will usually respond to your comments here!