Failure probability: reading it, choosing it, and not letting it run you

Every retirement simulator boils its verdict down to a single number: the failure probability, or its mirror image, the success rate. It is the most watched number in the field, and the most misread. People treat it like a weather forecast ("5% risk, that's fine"), compare it across tools that are not measuring the same thing, ask it for a precision it does not have, and forget that it describes a world in which nobody ever reacts.

This page teaches you to read that number the way a professional does: what it measures exactly, how to pick a threshold you can live with, why 2% and 8% are often indistinguishable, and how simulated ruin differs from the real thing.

What the number measures, and what it does not§

Take the definition apart, phrase by phrase. Each phrase hides a trap.

"The fraction of simulated futures." The number is a frequency inside a population of scenarios that a model made up. The model changes everything. Draw the years independently and you understate the clusters of bad ones (Sequence of returns risk: the retiree's real enemy). Replay American history and you inherit its optimism (Bengen, the Trinity study, and the birth of the safe withdrawal rate, Simulator traps: independence, US bias, survivorship). Replay the world sample and you take in countries and eras that may be harsher than any future you plausibly face (Beyond the United States: Anarkulova, Cederburg and the world sample). None of them is "the true one". That is why serious simulators show the same plan under several models at once, and why the right reading is the range they draw, never one model standing alone.

"The portfolio hits zero." Simulated ruin is binary and terminal. It does not tell failure at 71 apart from failure at 94, and it scores a plan that touches zero in its final month as a failure while a plan that ends with $15,000 in hand is a success. Two plans at 5% can hide very different lives: one fails early and hard, the other runs out of breath at the very end with Social Security underneath it. So look at two more things. When the failures happen, and how much wealth is left at the median at the end of the horizon (Reading a fan chart without fooling yourself).

"With no human reaction at all." The least realistic assumption, and the most useful. Unrealistic: nobody keeps drawing $40,000 indexed while the portfolio slides from $1M to $150k; they would have cut their spending years earlier (When to worry, and when to let it ride). Useful: precisely because the simulated rule is blind, the number measures the plan's intrinsic robustness, with no credit taken for a flexibility you have yet to show. A flexible plan gets simulated with its own flexible rule (Floor and ceiling and the Vanguard rules: bounded flexibility, Modern guardrails (Morningstar): the state of the art). Failure then drops, and what you have to look at is the standard of living delivered. Flexibility does not remove the pain, it moves it into years of smaller spending.

And what it blithely ignores: your mortality (ruin at 97 concerns very few people, which is why it pays to read the number alongside mortality tables, Horizon, life expectancy, and 50-year retirements), the real lumpiness of spending, the fine print of taxes, and every safety net that sits outside the model (family, a house, a return to work).

Choosing your threshold: there is no universal right answer§

How much failure should you accept: 1%, 5%, 10%? The question looks technical. It is personal, and it turns on three things.

How good your safety nets are. Simulated ruin assumes you have nowhere to turn. Someone in their forties who is employable, owns a home, has a pension coming and a family that would help can rationally accept 10 to 15% simulated failure, because real ruin (ending your life destitute with nothing to fall back on) is far rarer than the number suggests. Someone at 60 with no meaningful pension, no property and no way back to work should read the number almost literally, and aim low.

What a year of margin costs. Going from 5% failure to 2% typically takes 10 to 20% more capital, which is two to four more years of work. Going from 5% to 10% hands them back. The threshold is the price of a trade between two risks (The one-more-year syndrome): put a number on what each point of failure costs you, or gives you back, in working years, and the discussion stops being abstract. The general frame for trades like this one (utility, certainty equivalent, regret) is laid out in Deciding under uncertainty: utility, Kelly, regret, and robust choices.

How your plan fails. Look at when the failing scenarios fail. An 8% built out of late failures (after 85, with a pension covering the floor) is more comfortable than a 4% built out of collapses at 70.

False precision: 2% and 8% are often the same number§

The simulator prints "4.7%" and the mind files away a jeweler's precision. There is none, for three reasons that stack.

Sampling noise is the smallest of them. With the 2,000 paths simulators commonly draw, a true 5% prints anywhere between 4 and 6% depending on the draw. Annoying, but bounded.

Parameter sensitivity is far worse. Shave 0.5 point off the expected real return, a refinement nobody can actually estimate (Forward-looking expected returns (Morningstar, Vanguard, the investment banks)), and failure can double. The thickness of the tails (the degrees of freedom of the Student-t, Fat tails, crises, and the Student-t) moves it again. Your parameters are uncertain, so your failure probability is at least as uncertain.

The choice of model dominates everything else. The same plan can print 2% on historical windows, 5% on the central model, 9% under sequence stress and 14% on the broad sample. None of them is wrong; they answer different questions ("what if the future looks like the history of my own holdings, or like a prudently calibrated i.i.d. world, or like that same world with sticky bears, or like a century across 16 developed countries").

THREE NOISES, ONE FIGUREWhat you read is the smallest of the threeOne plan, one failure probability on screen, and the three uncertainties around it, on one ruler05101520253035failure probability, in %the figure on screen: 3.6%Sampling noise2.7%4.4%2,000 paths, 95% binomial intervalParameter sensitivity2.2%5.9%the expected real return moved by half a pointThe choice of model0.0%35.1%the simulator's six columns, the same plan throughouthistorical windowslost decadeThe decimals are noise, the gaps between models are signal: read failure probability as a ranking, not a measurement.Reference plan: $1M, the book's type portfolio (60% world stocks, 25% long bonds, 7.5% gold, 7.5% trend following),a rigid 4% inflation-indexed withdrawal, 30-year horizon, 20,000 draws and a fixed seed for every measurement.Sampling noise: the 95% binomial interval around the true failure rate (3.56%, measured on 200,000 draws), for the 2,000paths a simulator commonly draws. Parameters: the same plan with the expected real return moved by half a pointup, then down. Model: the six columns of the FIRE page, from the most optimistic to the grimmest.The three noises add up, they do not cancel out. These figures are this plan's; the text's(2, 5, 9 and 14%) illustrate the same shape on another plan.
The three noises put on one scale, for a single reference plan: the figure on screen, the two points of uncertainty the draw leaves, the three and a half the parameters leave, and the thirty-five the choice of model leaves. The bar you stare at while believing you are reading a probability is the shortest of the three, by a wide margin.

One rule follows: read failure probability as a ranking, not as a measurement. It compares beautifully (plan A is more robust than plan B; this lever cuts risk more than that one; even the pessimistic model stays acceptable) and measures poorly ("my real risk is 4.7%"). The decimals are noise. The gaps between scenarios, and between models, are signal.

Real ruin looks nothing like simulated ruin§

One last correction, and the one that does the most for your sleep. In the simulator, ruin is a cliff: the balance crosses zero on a Tuesday and everything stops. In life, a retirement plan fails slowly, and visibly: the portfolio drifts off its planned path, the current withdrawal rate climbs year after year, the warning lights turn amber long before the drop. The historical paths that failed agree on the timing: between the moment a doomed plan becomes statistically recognizable and the day the money actually runs out, a decade goes by at the very least, and twenty years on the worst vintage on record. The 1966 vintage confirms its red light in 1974-75; the money does not run out until 1994. That is an enormous amount of notice for anyone who has written down thresholds for action (When to worry, and when to let it ride, The annual review: the retiree's checklist).

THE WARNING TIMEThe vintage that fails gives twenty years of noticeThe 1966 vintage, the worst on record: the capital above, the current withdrawal rate and its warning lights belowThe real capitalin thousands of constant dollars, capital at the start of the year02505007501,000The warning lightthe year's withdrawal divided by the capital of the daygreen: under 4.3%amber: 4.3 to 5.2%red: above 5.2%, confirmed4.3%5.2%09%first red, 1974$673krun dry1994confirmed in 1975, off the scale from 1979the light never turns green again1966197019741980198519901994notice: 20 yearsThe doomed plan gave 20 years of notice: first red in 1974, last line of the account in 1994.The 1966 vintage, a real US 60/40, $1M and a 4% withdrawal indexed to inflation, applied with no reaction at all. Everything is real.Thresholds quoted verbatim from "When to worry": green under 4.3%, amber from 4.3 to 5.2%, red above 5.2%,confirmed on two spaced readings. The notice runs from the first red (1974) to the year the money ran out (1994).
The 1966 vintage, the worst American history has produced, under a fixed 4% inflation-indexed withdrawal. On top, the capital drifting off its path and then running dry. Below, the same plan as the dashboard sees it (When to worry, and when to let it ride): amber as early as 1967, never green again from 1970, red in 1974 and confirmed in 1975. The account is not empty until 1994. On the day the light turns red there is still $673k in the account and twenty annual reviews left to act: that is what a real failure looks like.

That is the real reason failure probability, read properly, is an instrument of design and not a source of dread. It is there to compare plans and to size margins before you leave. Once you have left, it gives way to piloting: a few simple indicators, written thresholds, prepared answers. A plan at 8% failure with an attentive pilot is safer than a plan at 3% with a sleeping one.

The essentials§

Going further§