Stretching

Two, Three And Four Hours Longer

Each additional hour buys exactly two more gaps, with no diminishing returns and no acceleration. Four hours buys eight gaps.

Lengthen one end's working day by one hour and two more gaps come into range. By two hours, four more. By three, six. By four, eight.

Lengthening	Gaps leaving at least an hour	Gained
none	15	—
1 hour	17	2
2 hours	19	4
3 hours	21	6
4 hours	23	8

Two gaps per hour, exactly, with no curve in either direction.

Why there is no curve

Each additional hour extends the working day by an hour at one end, which brings the gap of one hour further into range in that direction. Each hour of lengthening therefore buys precisely one additional workable gap on each side, which is two in total.

For work that changes shape during the week, managers can view the official product information and review task-level context rather than a single total. A useful external reference for the surrounding topic is MIT Sloan Management Review.

There is nothing to accumulate and nothing to exhaust. The relationship is linear because the underlying geometry is linear, which is the same reason the overlap falls at a flat rate in the first part of this record.

The absence of diminishing returns is not good news. It means there is no point at which lengthening starts paying better, and no threshold worth pushing through.

Which gaps get bought

They are always the next ones out: the eighth gap first, then the ninth, then the tenth, then the eleventh.

Those are the gaps at the far edge of the record, and the shared time they deliver is one hour each. A four-hour lengthening does not turn a bad arrangement into a good one; it turns eight impossible arrangements into eight arrangements with a single shared hour apiece.

Lengthening	Furthest workable gap
none	7
1 hour	8
2 hours	9
3 hours	10
4 hours	11

Where it stops being worth it

The record does not say, because the record cannot say. It can only put the two columns side by side.

On one side: a working day of twelve hours instead of eight, every day. On the other: the ability to share a single hour with somebody eleven hours away, rather than none.

Stated that way the trade answers itself for almost everybody, which is the reason this table exists. The lengthening lever is real, it is exactly measurable, and it runs out of usefulness long before it runs out of arithmetic.

What else a longer day does inside the range

The counts above measure reach. They say nothing about depth, and the depth effect is where most of the value actually sits.

A day lengthened by two hours adds two hours of shared time to every gap in range in the favourable direction, not only to the two newly reachable ones. A pair at a gap of three go from five shared hours to seven; a pair at a gap of six go from two to four.

Gap	both on eight hours	one end on ten hours
3	5	7
5	3	5
6	2	4
8	none	2

That is a substantial improvement, and it is the thing to weigh rather than the reach. Doubling the shared time of an arrangement at a gap of six is worth considering; adding a tenth gap that delivers one hour is not.

Why the two effects point different ways

Reach grows by two gaps per hour and each new gap delivers one hour. Depth grows by one hour per hour at every gap already working.

So the value of lengthening depends on where the arrangement already sits. Near the middle of the range, the depth effect dominates and lengthening is a real improvement. At the edge, the reach effect dominates and lengthening buys a single hour at a distance.

The lever is therefore most useful where it is least needed and least useful where it is most wanted, which is a pattern that recurs throughout this section and is worth expecting.

An arrangement that is working will get noticeably better. An arrangement that is failing will get one hour. The lever does not know which one you are and pulls the same way.

What a smaller lengthening is actually for

One hour is the only lengthening in this table that is widely plausible, and its effect is described on the previous page: one gap further, in one direction.

Everything past that is in the record for completeness and to establish the shape of the relationship. Anybody considering a four-hour extension of their working day to gain one shared hour has a problem that is not about overlap.