Somewhere in your organisation is a diagram showing people allocated to projects in fractions. Somewhere else is a plan that assumes those fractions can be added together. Only one of those documents is true.
There is a teaching diagram of a matrix organisation that is more revealing than its authors probably intended. It shows a chief executive, four directorates, three project managers, and — in the cells where projects meet functions — numbers. Two here, three there, one and a half, one and a half again, one, a half, one and a half. The columns total 6.5, 6.0 and 3.0.
The figures are unsourced and illustrative, on an undated diagram, and nothing about them describes any real organisation. What they describe is a form, and the form is worth looking at closely, because most large enterprises run on it and very few have examined what it is asserting.
The assertion is this: that a person can be divided, that the divisions are additive, and that a project staffed with 6.5 people has six and a half people's worth of capacity available to it. Each of those three claims is false in a different way, and the aggregate error is one of the largest and least examined sources of delivery failure in matrix organisations.
The Strategic Context
The teaching material behind that diagram sets out three organisational forms with unusual candour about their trade-offs.
The traditional or functional structure has been, in its account, the dominant form of organisation for over a hundred years [FACT CHECK REQUIRED]. It groups people with similar skills under a similarly skilled manager. People become specialists and become very good at what they do. Its named weakness is that companies structured this way are not easily changed when market demands and new technologies enter their business areas.
The projectised structure gives the project manager total authority; all questions are directed to them as the ultimate authority, and they make all the decisions. The team's focus is clear, the goals are in sight, and the relationship with the client is direct.
The matrix came into being in the 1970s [FACT CHECK REQUIRED] as an attempt to put the best of the other two together. All employees report to a functional manager and are organised strictly by skill. The functional manager is responsible for staffing the project and the administrative work; the project managers direct the bulk of the work done by the employee. The notes are explicit about the instability this creates: there needs to be a balance between the project managers and the functional managers, otherwise one group will dominate the other. Where the balance holds, the arrangement is called a balanced matrix.
That balance question — who wins when a project manager and a functional manager disagree — is real, consequential, and the subject of [Related article: Accountability Without Authority: How Organisations Design Delivery Leadership to Fail]. It is not the subject of this article. The question here is arithmetic, not political: what capacity actually exists, and who is allowed to change it.
What Leaders Commonly Misread
The first misreading is that fractions are additive. Three people at one-third each are not one person. They are three people each carrying the coordination overhead of a fourth commitment, each holding context they must reload every time they return, and each subject to a queue at the other two commitments. The empirical shape of this is well known to anyone who has run delivery: the effective output of a person split three ways is well below a third each, and the shortfall grows sharply with the number of splits.
The organisation's planning systems, however, add the fractions. A resource plan showing 6.5 allocated will report 6.5 available. Nothing in the system knows that 6.5 assembled from thirteen half-people is a different quantity from 6.5 assembled from six people and one genuine part-timer.
The second misreading is that the fraction represents availability. It generally represents an intention. Someone agreed that this person would spend half their time on this project. What the person actually spends is determined by whoever escalates most effectively in any given week, and the fraction is a claim on their attention rather than a reservation of it.
The third misreading is that the residual is free. A person allocated 0.5 to a project is understood to have 0.5 available for something else. In practice a large part of the residual is consumed by the functional role — the administrative work the notes explicitly assign to the functional manager, the line responsibilities, the recruitment, the appraisals. The apparently unallocated half is frequently already spent, which is why adding "just a small allocation" to someone at 0.9 so reliably produces a person delivering nothing well.
A fourth misreading is that this is a scheduling problem. It presents as one — plans slip, people are overcommitted, resource managers negotiate. But the underlying issue is that nobody in the structure holds the authority to say no more. The functional manager controls supply and is rewarded for utilisation. The project manager controls demand and is rewarded for delivery. Neither is accountable for the total, and so the total is never governed.
Reframing the Issue
The reframing is to treat the matrix diagram as a capacity ledger and to ask the questions one would ask of any ledger: is it complete, is it denominated in a real unit, and who is authorised to post entries to it?
On the first question, most such ledgers are incomplete in one specific way: they record project allocations and omit functional load. The person shown at 0.5 to a project is not shown at 0.5 to their line role, because the line role has no project code. The ledger therefore records demand from one side of the matrix only.
On the second, fractional full-time equivalents are the wrong unit for the same reason that headcount is the wrong unit for output. A better denomination is uninterrupted blocks — how many days of substantially undivided attention does this person have available, and how many does the work require. This is harder to collect and enormously more informative.
On the third question, the honest answer in most organisations is that nobody is authorised, and allocations accumulate through a series of individually reasonable local agreements. The structural choice — functional, matrix, projectised — is at bottom a choice about where that authority sits, and it is worth restating in those terms:
- Functional: capacity authority sits with the functional manager. Projects request; functions decide. Delivery is slow and specialist quality is high.
- Projectised: capacity authority sits with the project. People are committed whole for a period. Delivery is fast, utilisation is poor, and specialist depth erodes.
- Matrix: capacity authority is contested by design, and the arrangement works only if somebody is explicitly accountable for adjudicating it.
Stated that way, the matrix is not a compromise between two structures. It is a structure with a deliberate gap in it, which functions only if the gap is filled by a named adjudicator.
The gap has a moment as well as an owner. Capacity is pledged to an initiative when its plan is signed, by functional heads attesting that people will be available — and how those pledges are collected determines whether they exist at all, which is the subject of [Related article: Most of Your Plan Is Somebody Else's Promise].
A prior question concerns standing. A responsibility that is genuinely part of somebody's job is resourced; one that is filed as a component of somebody else's job is performed by whoever has capacity. What separates the two, and what it costs to move something from one to the other, is set out in [Related article: When a Sub-Process Becomes a Domain].
Strategic Analysis
The arithmetic of the split, and why it is worse than it looks
Take a professional services firm with a specialist practice of ten senior people. Demand arrives as eight concurrent client engagements plus three internal initiatives, and the resourcing model spreads the ten across all eleven commitments in fractions.
On paper, capacity balances. In practice three things happen simultaneously and compound.
The first is switching cost. A person moving between four commitments in a week loses time at every transition, and the loss is not proportional to the number of commitments — it grows with them, because each additional context makes every reload harder.
The second is queueing. A commitment that holds 0.25 of a person waits for that person. When they are late on another commitment, the wait extends. Because every commitment is waiting on multiple part-time people, the delays interact, and the aggregate delay is far larger than any individual's lateness suggests.
The third is the disappearance of slack. A fully allocated system has no capacity to absorb variation, and variation is certain. The first unplanned event consumes the notional residual of several people at once, and every commitment slips together.
None of this is visible in a resource plan that sums fractions. It becomes visible only in delivery, at which point it is attributed to estimation, scope or supplier performance.
What the totals in the diagram are really saying
Return to the illustrative figures: three project managers drawing 6.5, 6.0 and 3.0 staff across the directorates. Read as a ledger rather than as a chart, the interesting entries are not the totals but the halves. A 0.5 and a 1.5 appear repeatedly. Those entries record that individuals are split, and each split is a place where the arithmetic above applies.
An organisation that wanted to reduce its exposure to this would not change its structure. It would change its allocation granularity — a policy that no person is allocated to more than two commitments, or that allocations below 0.5 are not permitted, or that a nominated proportion of each specialist's time is unallocated by rule. These are cheap policies with large effects, and they are rarely adopted because each individual violation of them looks harmless.
Where the interfaces argument stops and this one starts
A related failure is easy to confuse with this one. When work crosses a boundary between two functions, value is lost at the boundary because nobody is accountable for what happens there — a distinct problem examined in [Related article: The Work Happens Inside Functions. The Value Is Lost Between Them.].
The distinction is worth holding. That article concerns the handoff: what is lost when work passes between groups. This one concerns the person: what is lost when a single individual is committed to several places at once. An organisation can fix its interfaces completely and still fail on capacity, because the interface is a coordination problem and this is an arithmetic one.
What a maturity assessment will not tell you
Organisations frequently look for this problem in a capability assessment and do not find it, because maturity instruments examine process, method and competence rather than the allocation ledger. What such an assessment is measuring, and who it is produced for, is examined in [Related article: Who Is Your Maturity Rating For?]. A highly rated organisation can be running at four commitments per specialist, and the rating will not say so.
The structural choice is a strategy choice
Which form an enterprise adopts is usually treated as an organisational design question and settled by precedent or by whichever executive is reorganising. Treated as a capacity question it becomes a strategy question, because it determines what kind of work the organisation can do.
An enterprise whose value depends on deep specialist quality and whose change agenda is modest should sit closer to functional and accept slow delivery. An enterprise whose competitive position depends on speed of change should move toward projectised and accept the cost of underutilised specialists between assignments. The matrix is the right answer where both matter — which is often — but only if the enterprise is willing to fund the adjudication that makes it work.
Refusing to choose, and running a matrix with no adjudicator, produces the worst of the three: functional managers optimising utilisation, project managers optimising delivery, and an organisation whose real capacity is unknown to everyone.
Decision Framework
Six steps, and the first three can be completed in a week.
1. Build the complete ledger. For each specialist group, list every person and every commitment including line and functional load. The completeness is the point; a ledger with only project entries understates demand systematically.
2. Count the splits, not the totals. For each person, record how many commitments they hold. The distribution of that count is the diagnostic. A group where the median person holds four commitments has a capacity problem regardless of what the fractions sum to.
3. Re-denominate. Convert from fractional full-time equivalents to uninterrupted blocks — days per fortnight of substantially undivided attention, available and required. The gap between the two is the real shortfall.
4. Set an allocation floor and a split ceiling. No allocation below a stated fraction; no person on more than a stated number of commitments. Both numbers are judgement calls and both work better than no policy.
5. Name the adjudicator. One person, for each specialist group, with authority to refuse a commitment. Without this the matrix has no mechanism for saying no, and every local agreement will be reasonable while the aggregate is impossible.
5a. Expect resistance, and locate it. An adjudicator with authority to refuse takes something specific and immediate from managers who currently allocate freely, while the benefit is diffuse and later — the standard asymmetry examined in [Related article: Why the Old Order Fights Harder]. Plan for it at design time rather than treating it as obstruction.
6. Reserve slack explicitly. A stated proportion of each group's capacity held unallocated by rule. This is the hardest step to sustain, because unallocated capacity is visibly idle and its value is only ever visible counterfactually.
From Strategy to Execution
Immediate. Run steps one and two on the specialist group that is most frequently blamed for delays. The count of commitments per person is usually higher than any executive expects, and the finding is difficult to argue with because it is a count rather than an estimate.
Medium term. Adopt the allocation floor and split ceiling as policy, and name the adjudicator for each critical group. The adjudicator role is the change that matters; the policies without it become guidance that erodes within two quarters. Expect the first month of adjudication to be uncomfortable, because it makes visible a level of over-commitment the organisation has been carrying invisibly.
Long term. Decide the structural question deliberately, with the capacity consequences understood. If the enterprise wants matrix speed and functional depth, it must fund the adjudication and accept the reserved slack. If it will not fund those, it should move toward one of the pure forms and take the corresponding cost knowingly rather than run a matrix that only works on paper. The measurement question that sits behind all of this — what the organisation is actually optimising at delivery level — is treated in [Related article: From Margin to Milestones: What Happens to Strategy on Its Way Down].
Signals to Monitor
- Median commitments per specialist. The single most useful number in this article, and almost never collected. Track it quarterly by group.
- Allocations below a quarter. Count them. Each one represents a claim on attention too small to produce work and large enough to fragment a week.
- Plans that balance exactly at 100%. A resource plan with no headroom is a plan that has assumed zero variation, which no organisation experiences.
- Delays attributed to estimation across many unrelated initiatives. When the same explanation appears everywhere, it is usually a systemic capacity problem wearing an estimation costume.
- Escalations resolved by senior intervention. Where allocation conflicts are settled by whoever escalates highest, there is no adjudicator and the loudest programme wins.
- Reserved slack quietly consumed. Where a deliberate reserve exists, watch how long it survives. Its erosion is usually the leading indicator of the next delivery failure.
Questions for the Leadership Team
- In our most constrained specialist group, how many commitments does the median person hold — and do we know?
- Who is authorised to refuse a commitment on behalf of that group, and when did they last do so?
- Does our resource planning distinguish between capacity assembled from whole people and capacity assembled from fractions?
- What proportion of our specialists' time is unallocated by design, and if the answer is none, what absorbs variation?
- Have we chosen our organisational form deliberately for the kind of work we do, or inherited it?
- When delivery slips, do we examine the capacity ledger before we examine the estimate?
Closing Perspective
The matrix is a good structure and this is not an argument against it. It is an argument that the structure comes with an obligation most organisations have not met.
A matrix contests capacity by design. That contest can be resolved by adjudication or by attrition. Adjudication requires a named person with authority to refuse, a ledger that records all demand rather than half of it, and a policy that limits how finely a person may be divided. Attrition requires none of those, costs nothing to set up, and resolves every conflict in favour of whoever escalates hardest — which is why so many organisations run it without noticing they have chosen it.
The diagram that started this article is twenty years old and describes nobody. But the halves in it are still there, in every resource plan in every matrix organisation, being added together as though a person could be divided without loss. They cannot, and the difference between the plan and the arithmetic is the capacity your enterprise thinks it has and does not.
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