How sure is the answer? Robust, Sensitive or Fragile

Each calculator gives you an answer, such as "buying comes out ahead". Next to it is one of three labels: Robust, Sensitive or Fragile. The label says how easily the answer would change if things went differently from the numbers you entered. It is worked out the same way in every tool that shows it (Rent vs Buy first; the others are being updated one by one).

The rule

Each calculator already reruns your numbers under a handful of stress tests: prices that fall, a sale you didn't plan, lower returns, a big repair and so on. The label counts how many of them change the answer, and checks whether a small change to one of your main inputs would.

• Robust: the answer holds in every stress test, and no single main input changes it within 10% of what you entered.
• Sensitive: the answer changes in one or two of the stress tests.
• Fragile: the answer changes in most of the stress tests (or in more than two), or a change of 10% or less to one main input changes it on its own.

The label describes the answer, not the decision. A Fragile answer isn't a bad idea; it means the two choices come out close, so details you can't know yet (what prices do, how long you really stay) decide which one wins. A Robust answer is one you'd still get if several things went wrong.

What would change the answer

Below the answer, each calculator lists the inputs that would change it, nearest first, with the value where it happens: "Renting wins at a price of $408,000". To find them it moves one input at a time, keeping everything else as you entered it, until the answer changes. It searches in both directions, in small steps first so it finds the nearest change rather than a distant one, then narrows in on the exact value. The value shown is rounded so the answer really has changed at it; the test suite checks every one of these claims at the value shown.

"Nearest" means the smallest change compared with what you entered: a price 2% higher comes before a rate 4% higher (6.5% to 6.75%). The same measure feeds the 10% test in the rule above. Inputs you entered as zero are compared with a typical range instead.

What this leaves out

• Inputs are moved one at a time. Two things going wrong together, such as flat prices and a short stay, can change the answer when neither does alone; the stress tests cover some of these combinations, not all.
• The search stays within sensible bounds for each input (for example, half to double the price). A change outside them isn't listed.
• The label is not a probability. It doesn't say how likely each stress test is, only whether the answer survives it.

Each calculator's own methodology page lists its stress tests and the inputs it checks. See the methodology index.