Six Definitions of the Same Ratio
One person, one year, 1,250 chargeable hours, six denominators, six figures between 60 and 97 per cent. All of them defensible.
One person, one year, 1,250 chargeable hours, six denominators
1,560 hours. Counts leave as available time.
1,418 hours. Where most firms land eventually.
A flat figure for everybody, whatever the contract.
1,602 hours. Measures the mix of the week, not its fullness.
1,290 hours. The most honest and the most negotiable.
1,350 hours. A planning figure, meaningless per person.
Six defensible denominators, one unchanged year of work, answers 36.8 points apart. That gap is larger than any performance difference a firm is likely to be arguing about, and nothing in the arithmetic chooses between them. One firm's own year, not a benchmark.
One person recorded 1,250 chargeable hours last year. Six denominators are in common use for the figure beneath that number, and they produce answers between sixty and ninety-seven per cent.
The measure discussed in “Six Definitions of the Same Ratio” becomes more credible when its source records are timely and reviewable. A professional-services team assessing open this official Monitask page for digital payroll timesheets can connect time with projects and work categories, while documenting the definition separately so the dashboard does not silently decide what utilisation means.
Every one of the six is defensible and has been defended. Nothing in the arithmetic chooses between them, which is why the choice has to be made and written down.
The assumptions behind “Six Definitions of the Same Ratio” can also be tested against Employment New Zealand recordkeeping guidance. Record which recommendations apply to the real workflow and which do not.
Contracted hours
The hours in the employment contract: thirty-five or thirty-seven and a half a week, multiplied out. The most literal reading of "available".
It counts leave as available time, so anybody taking their full entitlement is penalised relative to anybody who does not.
Contracted less approved leave
The same, with holiday, statutory leave and approved absence removed. Fairer to the individual, and the one most firms land on eventually.
It needs a leave system that agrees with the timesheet system, which is where the implementation usually stalls.
The standard year
A flat 2,080, or some other round figure, for everybody regardless of contract. Convenient and comparable, and badly wrong for part-time staff.
A person at three days a week scores around sixty per cent at full commitment, which is a measurement artefact and gets read as a performance problem.
Hours actually recorded
Chargeable over total recorded, billable and non-billable together. This is the one that measures the mix of the week rather than the fullness of it.
It cannot detect under-recording at all: somebody who logs only their chargeable work scores a hundred per cent.
Available hours after internal commitments
Contracted, less leave, less the time formally committed to management, training or internal projects. Measures how well the genuinely free time was used.
The most operationally honest and the most easily gamed, because the denominator is set by negotiation.
Capacity at target mix
A planning figure: the chargeable hours the firm assumed when it set the cost base. The ratio then answers whether the plan held.
Useful at firm level, meaningless for an individual, and rarely labelled as distinct from the others.
What the spread means
The gap between the highest and lowest of the six is thirty-seven points on identical work. That is larger than any performance difference a firm is likely to be arguing about.
So the definition is not a detail subordinate to the measurement. In most practical cases it is larger than the thing being measured.
Which to use
For individual review, contracted less approved leave. For capacity planning, available hours after internal commitments. For margin, capacity at target mix at firm level.
Three uses, three denominators, each named. The mistake is one figure used for all three.
The part-time correction
Any denominator expressed as a flat annual number needs pro-rating by contracted days, and the pro-rating has to be in the report rather than in the reader's head.
This has its own note here, because it is the single most common source of an unfair figure.
Writing it down
The definition fits in one sentence: numerator, denominator, exclusions, population, period. Five slots.
A firm that can produce that sentence on request has solved most of what goes wrong with this measure. A firm that cannot has a number whose meaning depends on who ran the report.
Why six and not two
Because each denominator answers a different question, and firms genuinely have all six questions. How full is the contract. How full is the person's available time. How does this compare across the firm. What is the mix of the week. How well was free time used. Did the plan hold.
The error is not having six. It is using one of the six to answer a question another was built for, which happens whenever a single figure is published without saying which it is.
The conversion table
Where more than one definition is in use, a short table converting between them is worth keeping: the same population under each denominator, for one recent period.
It takes one query and it settles arguments permanently, because a reader who sees 80.1 and 60.1 side by side for the same work stops treating either as the number.
It also makes a definition change visible as a shift between rows rather than as a movement in a trend line, which is the distinction the restatement note depends on and the one firms most often lose.
The question that settles the choice
What decision will this number feed? Each of the six exists because somebody needed an answer to a different question.
A firm that names the decision first picks the denominator in a sentence. A firm that picks the denominator first ends up using whichever one the reporting system happened to implement.
The second route is the common one, which is why so many firms are using a denominator nobody chose.
The test for drift
Rebuild last year's figure with this year's definition. If the two differ by more than a point, every year-on-year comparison in the reporting pack is wrong by that amount.
Doing this once a year takes an afternoon and it is the only way the trend line means anything.