An Overlap Of Three And A Quarter Hours

A gap of four and three quarters of an hour leaves three and a quarter hours of shared working time. That is the answer, exactly, and it is a slightly uncomfortable one to carry around.

The instinct is to call it three, or to call it three and a half, and both of those are worse than the number itself.

Readers adapting this model to real teams can read the feature summary and read every report beside outcomes instead of in isolation. A useful external reference for the surrounding topic is NIOSH.

What rounding down does

Rounding three and a quarter down to three discards fifteen minutes of shared time that genuinely exists.

Fifteen minutes is not nothing. It is the difference between a conversation that finishes and one that gets cut off, and across a working week it is over an hour. An arrangement planned as though it has three hours has a quarter of an hour of slack it does not know about and will not use.

That is the mild error. It makes the arrangement look slightly worse than it is and causes nothing to break.

What rounding up does

Rounding up to three and a half, or to four, is the dangerous direction.

An arrangement planned around three and a half hours when it has three and a quarter is planned around time that does not exist. The last fifteen minutes of every planned session falls outside one end's working day. The person at that end either stays late or leaves, and both of those are failures that get attributed to the person rather than to the plan.

Rounding down wastes time that exists. Rounding up spends time that does not. The second mistake is the one that gets somebody blamed.

Why the fraction is the right thing to carry

Three and a quarter hours is not a difficult quantity. It is three hours and fifteen minutes, which is a perfectly ordinary way to describe a duration and is how durations are described everywhere else.

The discomfort comes from the comparison with the whole-hour part of this record, where every answer is a round figure and the table is tidy. That tidiness is a property of asking the question in whole hours, not a property of the world, and importing the expectation into a part-hour arrangement produces exactly the two errors above.

Where the fractions actually land

Every value between a quarter of an hour and seven and three quarters, in quarter-hour steps, appears somewhere in this record. There are twenty-four distinct non-zero answers among the part-hour offsets, which is more distinct values than the whole-hour offsets produce.

The quarter hour in a working week

Fifteen minutes a day sounds like an amount nobody should think about. Over an ordinary working week it is an hour and a quarter, and over a year it is something like sixty hours.

That is not an argument for caring about fifteen minutes in any given day. It is an argument against the specific move of rounding it away permanently at the moment an arrangement is first described, because the rounding is not applied to one day — it is applied to every day for as long as the arrangement runs.

The asymmetry is what matters. A fifteen-minute error on Tuesday is nothing. A fifteen-minute error in the figure everybody uses is a standing misdescription, and it has the same size every day without ever being large enough to notice.

Which direction the error runs

Rounding is not neutral in practice, because the two directions are not equally likely.

People round towards the convenient number, and the convenient number is the one that makes the arrangement look workable. A pair with three and a quarter shared hours are more likely to say three and a half than three, because three and a half is a tidier figure and because it is the more encouraging one.

So the systematic drift is upwards, which is the direction that causes failures rather than waste. An arrangement planned against more time than it has produces somebody absent at the end of every session, and the absence is attributed to the person.

The harmless rounding is the one nobody is tempted to make. The tempting one puts somebody in the position of always being the one who goes.

The practical form

Write the shared stretch as a start time and an end time rather than as a duration, and the problem disappears entirely. "From a quarter past ten to half past one" cannot be rounded by accident, and it carries the information that a duration throws away: where the shared time actually is.

Next along

• The Forty-Eight That Leave Something
  Forty-eight of the seventy-two part-hour offsets leave shared time: thirty-two at quarter marks and sixteen at
• Why A Part-Hour Gap Is Harder To Schedule
  The shared stretch no longer starts on the hour, and everything built on hourly slots loses a slot. The loss e
• The Law Does Not Care About Fractions
  The one-hour-per-hour rule is exact for any offset, whole or not, while both working days are the same length.
• Why These Get Left Out
  Part-hour offsets are omitted from almost every discussion of these arrangements. The reason is not a good one