Little's Law
This is a named principle rather than a measured effect. The logic is sound, and the documented cases keep bearing it out. Trust the direction, and treat the boundaries as open.
By the late 1950s, people working in operations research had noticed a relationship that seemed to hold in every queue they studied. The average number of customers in a system, call it L, appeared to equal the rate at which they arrived, multiplied by the average time each one stayed. A 1954 paper had already used the relationship without proving it. In 1958, Philip Morse of MIT put it in his textbook on queues and issued an open challenge: readers who doubted how slippery such fundamental results could be were invited to work out the circumstances under which this simple relationship between L and W does not hold.
The answer came in 1961 from John D. C. Little, then at the Case Institute of Technology and afterwards a longtime MIT professor. In a four-page paper in Operations Research he proved that no such circumstances exist. As long as the averages are taken over a long enough run and the system is stable, meaning work leaves at roughly the rate it arrives, the relationship holds exactly. It does not matter what the items are, how their arrivals are distributed, how many servers there are, or what order anything is handled in. That independence from every detail is what earned it the name Little's Law, and it is why the same equation now appears in the design of telephone networks, computer processors, supermarket checkouts, hospital emergency departments and factory floors. Later work extended the proof further: a 1974 result by Shaler Stidham showed the law holds along essentially any single history of a system, not just in probabilistic models.
The version most useful in business rearranges the same equation. If L is the number of things in progress and the completion rate is the throughput, then the average time to finish equals work in progress divided by throughput. This rearrangement is the mathematical foundation underneath lean manufacturing and the kanban boards that came out of Toyota's production system: limiting the number of jobs open at once is not a preference or a philosophy, it is the only way, at a given rate of finishing, to shorten how long each job takes. Hospitals have applied the same arithmetic to patient flow through emergency departments, and software teams to the number of features open at once.
The honest limits are the theorem's own conditions rather than any dispute, because nobody disputes a proof. The law relates long-run averages in a stable system. It says nothing about any individual item, so it cannot promise that a particular project will take five weeks, only what the average must be. And it requires that everything entering the system eventually leaves: a board where work is quietly abandoned, or a backlog that grows without limit, is not the stable system the theorem describes. Applied to a real project list, the theorem stays exact while the measurement becomes the approximation, since real counts and real completion rates wobble from week to week. The arithmetic is exact; the reading of your board is an estimate, and a good one.
Divide the number of things your team has open by the number it genuinely finishes in a week, and you have your average delivery time. Eleven open and two finishing per week is five and a half weeks, for everything, on average, regardless of talent, effort or urgency. Most managers have never done this division, and almost none of them manage the numerator.
That is the strange part, because the equation only has two levers. When delivery is slow, nearly all management effort goes into the denominator: work faster, hire, automate, reorganise. Each of those is expensive, slow to arrive and uncertain to work. The numerator, the count of open things, can be changed this afternoon by a decision, without anyone working faster. Finishing rates are hard to move. Deciding not to start a twelfth thing is free, and it is the one lever the equation guarantees will work, because it is arithmetic rather than motivation.
The reason the count never comes down is an incentive reading rather than anything Little proved, and it deserves stating plainly. Starting work is visible: it gets announced, it counts as action on the day it happens, and the person who proposed it is on record as having ideas. Finishing work is the quiet end of something announced months ago. So credit flows to launches at every level of a company, the number of open items ratchets upward, and the queue is where all those launches get financed. Nobody in that system is behaving foolishly. Each person is responding correctly to what gets rewarded, which is exactly why the pattern never fixes itself from inside, and why telling teams to focus harder changes nothing.
The practical move costs one minute of arithmetic. Before any meeting where new work gets proposed, count what is open, divide by what actually finishes per week, and say the number out loud. A team that hears "anything we start today lands in five and a half weeks on average" is having a different conversation from a team that hears "we're at capacity", because the first statement is a division anyone can check and the second is a feeling anyone can override. The count of open work is the honest budget, and starting something new spends it whether or not anyone says so.
The cost that adding people imposes on a late project is Brooks's law, which is what happens when the denominator gets attacked under deadline. The per-person version of too much open work is attention residue, since a person on three projects pays the same tax a board with thirty items pays. And the pull that keeps half-finished work open long after it should be closed or killed is the sunk cost fallacy.
Little's Law says the time to finish equals what is open divided by what gets finished, so there are only two levers: cut the count of open work, or raise the rate of finishing. Brooks says the most tempting way to raise the rate, adding people to a late project, lowers it instead, because new people consume the time of the people who have none. Put together they explain why late organisations stay late: the lever that works is the one that looks like giving up, and the lever that looks like action makes the division worse on both ends at once.
Source: John D. C. Little, A Proof for the Queuing Formula: L = λW, Operations Research, volume 9, number 3, 1961, pages 383 to 387. The 1958 challenge: Philip M. Morse, Queues, Inventories and Maintenance, Wiley, 1958. The fiftieth-anniversary review, with the history and the range of applications: Little, Little's Law as Viewed on Its 50th Anniversary, Operations Research, 2011. The sample-path extension is Shaler Stidham, A Last Word on L = λW, Operations Research, 1974. Little was at the Case Institute of Technology when the proof was published and joined MIT in 1962, per the INFORMS biography.
Eliyahu M. Goldratt and Jeff Cox, 1984
A novel about a plant manager with ninety days to save his factory, and the strange fact is that it works as a novel. What Alex Rogo learns, chapter by chapter, is the arithmetic this entry describes: that a plant full of busy people and piled-up inventory is slow because of the pile, that the bottleneck sets the pace of everything, and that releasing less work into the system makes everything come out faster. Goldratt built a whole method on it, the Theory of Constraints, but the reason to read the book is simpler: it makes you feel the equation, and once you have watched Rogo's factory drown in open work you recognise your own project board immediately.
Draw your own card. It does not take long, and it rewards taking your time.