Why not always look for the biggest swaps?

Each extra person is another yes you need, and another schedule that can change before the swap goes in. Bigger swaps help where smaller ones run short, as in kidney exchange.

Does the piece on this page match Capillary's numbers?

No. The piece checks only overlaps, 11 hours of rest and one kind of shift each colleague won't work. Capillary's simulation judged every hand-off with the model Find a swap uses to rank colleagues.

What kidney exchange teaches about shift swaps

Updated October 13, 2026 · with an example to try

Kidney exchange matches patients who have willing but mismatched donors. Economists found that three-way exchanges match many patients two-way swaps can't, and that long chains matter most where matches are scarce. Shift swaps follow the same logic: in a small group, a three-way or bigger swap is sometimes the only way out of a shift.

Try it: small groups and big ones

Example · runs in your browser; nothing you enter is sent

People in the group: 6Colleagues who won't work one kind of shift: 80%You take back

In 30 made-up months, you had 360 shifts. For 18 of them (5%), only a swap with three or more people got you out.

Swapping your shift: the smallest swap that works

One for one: 82% (294 of 360)
Three-way: 2% (8 of 360)
Four to six people: 3% (10 of 360)
No swap: 13% (48 of 360)

Giving it away: the shortest way

Taken outright: 57% (204 of 360)
Through one colleague: 21% (77 of 360)
Through two to four: 4% (13 of 360)
No one: 18% (66 of 360)

Each made-up month gives everyone 12 shifts in four weeks, 12-hour days and nights in turn, with at least 11 hours off between shifts. Your colleagues each refuse nights, weekends or days at the rate you set, and half pick up extra shifts. A swap passes when everyone in it gets a shift they work, with no overlap and 11 hours off on each side. Likelihood isn't modelled here, so these shares are not Capillary's; its own simulation is in the text below.

Move the group size. With 30 people, someone can almost always swap with you one for one. With 4 to 10, and colleagues who each refuse one kind of shift, some shifts move only in a swap of three or more people, and many giveaways need someone in between. Taking back only the same kind of shift, a night for a night, makes the bigger swaps matter more.

The kidney exchange idea

A person who needs a kidney often has a relative or friend willing to give one, whose kidney doesn't match. Two such pairs can swap donors when each donor matches the other's patient. Roth, Sönmez and Ünver showed that arranging three-way exchanges as well as two-way ones would substantially increase transplants, and that "larger than three-way exchanges have less impact on efficiency."

Alvin Roth shared the 2012 Prize in Economic Sciences with Lloyd Shapley, "for the theory of stable allocations and the practice of market design."

Chains: one person gives without getting

A chain starts with an altruistic donor, who gives a kidney without a patient of their own. In 2007, one such donor started a chain of 10 transplants, coordinated over 8 months by two registries across six centers in five states. Later work by Ashlagi, Gamarnik, Rees and Roth found that "large cycles of exchange or long chains can significantly increase efficiency when the opportunities for exchange are sparse."

The same ideas in a shift schedule

Kidney exchange and shift swaps, side by side
Kidney exchange	Shift swaps
A patient and a willing donor who don't match	You, and a colleague who can't swap with you directly
Blood and tissue match	No overlaps, enough rest, and shifts each person will work
Two-way exchange	One-for-one swap
Three-way exchange	Three-way swap
A chain started by an altruistic donor	A giveaway down a line of colleagues, ending with someone who picks up an extra shift

Capillary's simulation

We ran Find a swap's search on made-up groups, with every hand-off judged by the same model that ranks colleagues by how likely they are to say yes. In groups of 15 to 22 people, swaps bigger than three were never needed. In groups of 6 to 10, 28 of 591 shifts had no likely one-for-one or three-way swap; a swap of four to six people found a likely way out for 5 of them. Longer giveaway lines found a likely way out for 10 of the 33 giveaways that had none through one colleague. Most were weekend nights.

So Find a swap looks for bigger swaps only while the smaller ones give fewer than three likely ways out. Each extra person is one more yes you need.

Common questions

Why not always look for the biggest swaps?: Each extra person is another yes you need, and another schedule that can change before the swap goes in. Bigger swaps help where smaller ones run short, as in kidney exchange.
Does the piece on this page match Capillary's numbers?: No. The piece checks only overlaps, 11 hours of rest and one kind of shift each colleague won't work. Capillary's simulation judged every hand-off with the model Find a swap uses to rank colleagues.

Find swaps in your own group's schedule.

Find a swap is free for clinicians. Bring in your group's schedule from its calendar link, and Capillary checks every swap for overlaps and rest for both people, puts the colleagues most likely to say yes first, and finds three-way swaps, and bigger ones where smaller swaps run short. Your copy is yours: no one in your department or hospital sees it (who can see what).

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