A Proposed Mathematical Model for Wardley Maps — Part 2

Revised Wardley Map Model: “Map Evolution, Not Maturity”

Following on from Part 1, below is an updated mathematical model that reflects the insight from “Map Evolution, Not Maturity”.

In other words, Evolution isn’t merely “age” or “time in market,” but rather how competition (supply & demand) drives a component from a novel idea to a widely available commodity.

1. Original Setup (Recap)

We have a set of components:

along with dependencies forming a directed graph. An edge

means

depends on

We also define two mappings:

Visibility (vertical axis) — how obvious or “close” a component is to the user.

Evolution (horizontal axis) — how far along the path from novel/uncertain to commodity/standardised a component is.

Each component becomes a point:

2. Visibility (Vertical)

One way to measure visibility:

Let

be the shortest path distance from the User to

Normalise this distance to produce

If

is the user, then distance is 0 → visibility = 1.

If

is far from the user,

approaches 0.

Hence, the vertical coordinate is:

3. Evolution (Horizontal) — Updated

Per the article, Evolution shouldn’t be reduced to “maturity” or “time in market.” Instead, it’s driven by:

• Ubiquity (how widespread a component is, i.e. supply & demand competition)
• Certainty (how standardised or well-understood it is)

Let

and

both range in

0 = rare, unknown, no best practices 1 = commodity, ubiquitous, highly standardised

Then define:

Low ubiquity + low certainty → near 0 (leftmost = “Genesis / Custom”). High ubiquity + high certainty → near 1 (rightmost = “Commodity / Utility”).

Thus, the horizontal coordinate is:

4. Final Coordinates

Each component

sits at:

• Left → Right = Movement from novel, uncertain to widespread, standardised.
• Bottom → Top = Movement from invisible to user to highly visible.

5. Interpretation & Rationale

• Evolution tracks market‐driven changes in certainty & ubiquity, reflecting how competition shifts components over time.
• Visibility helps you see how these components relate to user needs and where each sits in the overall value chain.

Strategic Takeaway:

1. Innovate on the left (high uncertainty, potential for differentiation).
2. Leverage commodities on the right (high ubiquity, low risk, lower cost).
3. Watch how components move horizontally over time as the market evolves.

Conclusion

By incorporating ubiquity and certainty into the Evolution function, we align with the principle that “Evolution is driven by competitive forces, not just age.” This helps teams build Wardley Maps that better capture real‐world dynamics of how components shift from Genesis to Utility as they become ubiquitous and well understood.

What’s Next

Read Part 3