The PMP communication-channels formula counts the wrong thing — and the channels that hurt you are the ones it can't see

The formula every PMP candidate memorises was invented as an argument, and the exam kept only the arithmetic. N(N−1)/2 is the group intercommunication formula from Fred Brooks's The Mythical Man-Month (1975), where it exists to support a conclusion — Brooks's Law: adding manpower to a late software project makes it later (SECONDARY; corroborated across multiple independent summaries naming the book, formula and law together). Brooks's point was never "count your channels." It was: the coordination cost of an extra person grows faster than the work they bring, so do not add them. Taught as a counting exercise — 17 people, 136 channels, next slide — the formula becomes exam trivia with no Monday-morning consequence. Taught as Brooks's argument, it is a veto on the most common move in project recovery.

But even Brooks's version quietly assumes something false: that all channels are the same. N(N−1)/2 counts potential pairwise links and weights them equally. Real collaboration load is savagely skewed. Cross, Rebele and Grant, studying more than 300 organisations, found 20% to 35% of value-added collaborations come from just 3% to 5% of employees, and that time spent in collaborative activities has grown by 50% or more, with people at many companies spending around 80% of their time in meetings or answering colleagues' requests (HBR, Jan–Feb 2016; SECONDARY). That reframes the whole exercise. Your project's coordination risk is not a channel count — it is a distribution, and the thing that will actually hurt you is one over-subscribed person, invisible to a formula that treats every link as identical. On a 17-person project the formula reports 136. The number that predicts your delay is closer to how many of those 136 route through your one senior BA.

The channels that damage projects are usually the ones that don't exist. Granovetter's "The Strength of Weak Ties" (American Journal of Sociology 78, 1360–1380, 1973) argued that bridges between otherwise-disconnected clusters are carried by weak ties, and that novel information arrives through them rather than through close contacts (SECONDARY). That held up under causal test: Rajkumar and colleagues used randomised experiments on LinkedIn's People You May Know across more than 20 million people over five years, 2 billion new ties and 600,000 new jobs, and found weaker ties drove more job mobility than strong ones — with an inverted-U: benefit rises as ties weaken, then falls off, so moderately weak ties outperform the very weakest (Science, Sept 2022; SECONDARY). The PM translation is not "network more." It is that a project rarely fails from channel overload; it fails because no channel exists between two clusters that needed one — and the formula, which counts only what could exist, is structurally incapable of flagging that absence.

Remote work is the cleanest natural experiment, and it broke the count-based model outright. Yang et al. studied 61,182 US Microsoft employees across the 2020 shift to firm-wide remote work and found collaboration networks became more static and more siloed: time spent with cross-group connections dropped by about 25% of the pre-pandemic level, employees added fewer new collaborators and shed fewer existing ones, total meeting and call hours fell about 5%, and communication shifted toward asynchronous, less rich media (Nature Human Behaviour 6, 43–54; published online Sept 2021; SECONDARY — figures read directly from Microsoft Research's own page for the paper, the one publisher-adjacent domain reachable this session). Note what this does to the formula: headcount N did not fall, so the counted channels were unchanged or higher — while the network's actual capacity to move information degraded sharply. The metric said nothing while the thing it claims to measure got materially worse.

And the structure you communicate through becomes the structure you ship. Conway's Law — from "How Do Committees Invent?", rejected by HBR and published in Datamation, April 1968 — states that any organisation designing a system will produce a design whose structure copies the organisation's communication structure; Conway's sharper corollary is that the act of organising a design team has already made certain design decisions (SECONDARY). For a PM this promotes the communications management plan out of the admin pile: it is an architecture decision made early, under a different name. Physical and temporal distance is the other governor — Allen's curve, from MIT research published in Managing the Flow of Technology (1977), found communication frequency falls off sharply with distance, near-vanishing past roughly 50 metres (SECONDARY) — which is why a hybrid team is not one team with the same channel count, but two clusters with a thin bridge.

The one move worth making this week: stop counting channels and start naming bridge owners. Take your stakeholder register, and instead of a channel total, mark (1) the two or three people every path routes through — that is your real coordination risk, and it is a capacity problem, not a communication problem; and (2) every pair of groups that must share information but have no named person connecting them — each of those is a missing bridge, and each gets an owner with a name against it. That converts the deck's N(N−1)/2 slide from exam trivia into a fifteen-minute audit you can run on a live project. The formula is not wrong; it is answering a question — how many links could exist? — that nobody's project has ever failed on.

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Evidence table

Claim	Source	Confidence
N(N−1)/2 is the group intercommunication formula; underpins Brooks's Law	Brooks, The Mythical Man-Month, 1975	SECONDARY
20–35% of value-added collaborations come from 3–5% of employees; collaborative time up 50%+	Cross, Rebele & Grant, HBR, Jan–Feb 2016 (300+ orgs)	SECONDARY
Bridges between clusters are carried by weak ties	Granovetter, AJS 78:1360–1380, 1973	SECONDARY
Weak ties causally increase job mobility, inverted-U in tie strength	Rajkumar et al., Science, Sept 2022 (20M+ people)	SECONDARY
Remote work: cross-group collaboration −25%, networks more static, −5% meeting hours, more async	Yang et al., Nature Human Behaviour 6:43–54	SECONDARY (figures from microsoft.com)
System design copies the organisation's communication structure	Conway, Datamation, April 1968	SECONDARY
Communication frequency decays with distance, ~50m threshold	Allen, Managing the Flow of Technology, 1977	SECONDARY

Verification note. No primary PDF was opened in this session — nature.com, hbr.org, science.org, pubmed and melconway.com were all blocked by the egress proxy. Every figure above appeared consistently across independent search-result summaries naming the same authors, journals, years and numbers; the Yang et al. figures came from Microsoft Research's own publication page. Anyone reusing these numbers publicly should open the primary sources first.

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Published page. The reader-facing version of this note is The Channel Count Fallacy (page.html in this folder), published as an artifact at https://claude.ai/code/artifact/d098b978-cb5a-4bde-bd95-ab98f5c28d77.