One Average Became Four Peer Groups
Samuel Martin replaced a single book-of-business average with four statistically valid peer clusters, built with Gower’s distance and partitioning around medoids on mixed-type client attributes. A client that account management had been telling it was below average turned out to sit at the median of its own cluster. The average had been mixing four businesses that share almost nothing.
Published 2026-07-25. Last updated 2026-07-25. Roughly a seven minute read.
In one paragraph
Every client in a book of 750-plus enterprise accounts was being compared against one average activation rate. Samuel Martin built peer clusters instead, using Gower’s distance to handle mixed-type client attributes and partitioning around medoids to form the groups, with k = 4 chosen on silhouette width. The clusters sit between 24% and 42% on 90-day activation, so a single book-wide average of 33% was a number no client had a reason to be near. The client in the figure moved from below average to the median of its own peer group, and nothing about its performance changed.
- 4
- statistically valid peer clusters
- 33%
- the old book-wide average
- 30%
- this client’s 90-day activation
- 24–42%
- activation range across clusters
- 750+
- enterprise clients in the book
01 / The spine
Four steps, in order.
Account management ran quarterly reviews against a single book-of-business average, and the review script for a client below it was a remediation plan. Clients pushed back on the comparison and had no vocabulary to push back with. The decision on the table was whether a given account needed intervention, and the input to that decision was one number.
A book-wide average mixes businesses with different operating models, contract shapes, and buying cycles, and the resulting number describes none of them. A high-touch enterprise account and a seasonal account are not two points on one scale. Half the book was always going to be below the average, and being below it carried no information about whether anything was wrong.
Clustered the book on mixed-type client attributes, which rules out plain Euclidean distance. Gower’s distance handles the mix of categorical, ordinal, and continuous fields without pretending a dummy variable has a magnitude, and partitioning around medoids gives each cluster a real client at its center rather than an imaginary average one. k = 4 was chosen on silhouette width, with the neighbouring values reported.
Quarterly reviews compare a client against its own cluster. The figure’s client sits at the median of self-serve mid-market while remaining below the book-wide average, which is the whole argument in one panel. Account management stopped opening reviews with a remediation plan built on a comparison that did not hold.
02 / The result
Against its real peer cluster the client sits at the median, not below average.
90-day activation rate, eight clients per cluster, one shared scale across all four panels.
The client sits at the median of its own peer cluster while falling below the book-of-business average, which is why the average was the wrong comparison. Clusters were built on mixed-type client attributes with Gower's distance and partitioning around medoids, with k=4 chosen on silhouette width.
All four panels share one 0 to 60% scale, so heights are comparable across panels. Figures redrawn on synthetic data. No client named. Method and reasoning are exact.
The shared scale is the argument. Four panels on four separate scales would show four tidy distributions and hide the thing that matters, which is that the clusters sit at genuinely different levels. Because the axis is common, the reference line lands in a different place inside each panel, and the reader can see that one average cannot serve all four.
“Below average is not a finding. It is a sentence that survives because nobody asks average of what.”
03 / The method, in full
The depth is on this page, not behind a link.
Each heading states its own conclusion, so nothing below requires opening to be understood. Open one when you want the mechanics.
Gower’s distance was necessary because the attributes are mixed type, and Euclidean distance on dummy variables would have smuggled in an ordering.
Client attributes span continuous fields such as contract value and seat count, ordinal fields such as support tier, and unordered categorical fields such as industry and contract shape. Encoding industry as dummy variables and running Euclidean distance implicitly asserts that two industries are a fixed distance apart, which is not a claim anyone would defend out loud.
Gower’s distance computes a per-attribute dissimilarity appropriate to each attribute type and averages them, so a categorical mismatch contributes its own well-defined amount rather than an artifact of the encoding. The cost is that attribute weighting becomes an explicit choice, and Samuel Martin documented the weights alongside the clusters.
Partitioning around medoids rather than k-means for the same reason. k-means needs a mean, and the mean of a set of mixed-type clients is not a client. A medoid is an actual account, which also made the clusters easier to explain: every group has a real example at its center.
k = 4 was chosen on silhouette width, and the neighbouring values were reported rather than hidden.
Silhouette width was computed across a range of k and reported as a curve, not as a single winning number. Four was the best-supported value, and the honest framing is that it was the best of several defensible choices rather than a fact the data forced.
Three and five were both plausible. Five split the regulated cluster in a way that matched no operational distinction anyone in the business recognized, and three merged seasonal into mid-market and lost the effect the project existed to surface. Samuel Martin used business legibility to choose between statistically similar options and said so.
Cluster sizes in the real book are unequal. The figure draws eight clients per panel because equal panels make the shared scale readable; the underlying clusters are not the same size, and cluster membership counts were published with the clusters.
The clusters changed what account management said in the quarterly review, which is the only test that mattered.
A clustering that nobody uses is a slide. The output that got adopted was not the model, it was a per-client line in the review template: the client’s cluster, its position within that cluster, and the cluster’s own level relative to the book.
The reframing cuts both ways, which is what made it credible internally. Clients that had looked comfortably above average turned out to be at the bottom of a high-performing cluster, and those conversations got harder rather than easier.
Adoption required giving up precision in presentation. The review line says median of its cluster rather than reporting a percentile with a confidence interval, because a percentile on eight to fifty accounts implies precision the clustering does not have.
04 / Limits
What this does not show, and what I would do differently.
Limits
Clusters are a snapshot. The book changes as accounts are won, lost, and re-contracted, and a cluster assignment made a year ago may no longer describe the account. Nothing in this work establishes how fast that drift happens.
Silhouette width is a weak criterion. It ranks partitions, it does not establish that clustered structure exists, and a book with genuinely continuous variation would still return a best k.
What I would do differently
Re-cluster on a schedule and version the assignments, so a review can cite which vintage it used. The first version was treated as a deliverable rather than as a thing that expires.
Test the attribute weights against how account managers already group their accounts before publishing. The weights were a defensible analytical choice made alone, and the people who would use the output had a strong prior worth eliciting first.