Probability of success vs projected balance

A plan page that prints 89.6% and a plan page that prints $1,083,603 are not in disagreement. They are changing the subject. Probability of success asks whether the pot hit zero. Projected balance asks what is left if it did not, or even if you average in the zeros. You can maximise one and wound the other. This page is the same freeze as the 90%-versus-100% curve, read with both meters on.

Same specimen, same 1,000 shared paths, same rigid rates from 2% to 6%. The treatment is the statistic, not the household. That is the control: worlds do not move. Only the column you quote moves.

Probability of success is a binary

Each path either makes it to the horizon with money left, or it does not. The success rate is the share that do. At 2% that share is 99.4%. At 4% it is 89.6%. At 6% it is 63.0%. There is no prize for finishing with $12. There is no extra credit for finishing with $8 million. A path with $1 left counts the same as a path with $8 million. That is a feature if the question is ruin. It is a defect if the question is standard of living after year 20.

Ruin-mass at zero also contaminates the median if enough paths fail. On this grid, p5 is already $0 from 3.5% upward. The median is still positive at 6% ($307,594), which means more than half of lives still have money, and a thick left tail does not. Quoting only the median would hide that tail. Quoting only the success rate would hide that the typical surviving household is not broke, just thinner.

This is why probability of success versus projected balance is a real question and not a slogan. Software that only prints $X trains you to ignore ruin. Software that only prints 89.6% trains you to ignore how poor the survivors are. A serious page prints both, on the same worlds.

Projected balance is a level

Median terminal wealth at 2% is $1,887,349. At 4% it is $1,083,603. At 6% it is $307,594. The dashed line on the chart is that median, drawn in the same box as success so you can see both slopes. They both fall. They do not fall as the same object. Success is a fraction of lives. Wealth is a dollar. A 12.8 pp drop in success is not interchangeable with a $415,968 drop in the median. One is a count of failures. The other is a typical remainder.

p95 at 2% is $10,378,565 and at 6% is $6,170,740. The right tail stays rich even when the rate is high, because some sequences are kind and a 6% withdrawal from a doubling market still leaves a pile. Planning around p95 is how people go broke in the other 95% of lives. Planning around the median without the success rate is how people ignore the pile-up at zero.

If you want a single number, you are asking the wrong question. If you must pick, pick the one that matches the decision. "Can I keep this spending without a serious chance of hitting zero?" is success. "If things are typical, what do I leave, or what can I gift?" is a percentile of balance. Mixing them in one sentence is how a success rate of 89.6% and a $8,234,376 projection end up in the same pitch deck.

They rank this rigid grid the same way, and that is not general

On a rigid rule, spending more makes ruin more likely and leftovers smaller. Both series fall. The interesting case, which this roster does not include, is a flexible rule that cuts spending to survive. Survival can then go up while lifetime consumption goes down. Guardrails that print 100% last-or-not with a collapsed paycheck are the textbook version. We did not run that roster here. The title does not claim that success and balance always disagree. It claims they are different questions. On this freeze they happen to slope the same way and still should not be substituted.

A tautological 100% success with unbounded cuts would have been a forbidden primary. We stayed on rigid rates so that success means what a reader thinks it means: the spending did not stop because the rule chose to stop it. The spending stopped because the account did.

Scope

Q1 is this 1,000-path grid. Q2 was not re-run for the metric comparison (the sibling 90% page did shave mu on two rates). Q3 is not run: not a historical claim. Q4: 5 bps, tax off. Teaching identity. No recommended rate. The 90% interpolation on the sibling page is a survival cut, not a balance target.

What would falsify the tension: median terminal and success ranking every step identically in a way that made one meter redundant, or ruin-mass at zero leaving the median unmoved while success fell. The median did move. The meters are still not interchangeable.

A worked row from the freeze

Take 4%. Probability of success: 89.6%. Projected balance as median terminal: $1,083,603. p5: $0. p95: $8,234,376. Ruin mass: 10.4%. If you only quote 89.6%, you hide that the typical leftover is still about a million of today's dollars and that the fifth percentile is already zero. If you only quote $1,083,603, you hide that one in ten lives, roughly, have already failed. The row is one household. The columns are different questions.

Take 5%. Success 76.8%, median $667,635. You spent more, failed more often, and left less in the typical world. Nothing in that sentence requires a philosophy of risk. It requires two numbers. Tools that hide one of them are choosing the philosophy for you.

The 90% interpolation on the sibling page (3.95%) is a survival cut. It is not the rate that maximises median leftover. The 2% row maximises both on this rigid grid because spending less is safer and leaves more. That agreement is a property of rigid rates, not a law of planning. Do not export it to guardrails.

See both numbers

The can I retire calculator is built to show a success rate. The cone on the Monte Carlo retirement calculator is the balance distribution. Use them as a pair, the way this freeze is a pair. If a screen shows 89.6% and no leftover, ask for the leftover. If it shows $1,083,603 and no 89.6%, ask for the share that never hit zero. This freeze's 4% row is the example: 89.6% and $1,083,603 together, or not at all. A tool that will not print both is choosing the meter you are not allowed to see. That choice is a product decision, not a statistical one, and it is how probability of success versus projected balance became two cults instead of two columns.

What this page refuses to say

It refuses to pick a winner between probability of success and projected balance. It refuses to say you should plan around 90% because leftover at 2% is $1,887,349. It refuses to say you should plan around leftover because 6% still shows $307,594 in the middle. It refuses to treat p95 of $10,378,565 as a plan. It refuses to treat a zero p5 as a rounding footnote. The whole point of two meters is that a household can care about both, and software that hides one is making the preference in the dark.

It refuses to export the "both fall" pattern to flexible rules. Guardrails can raise survival by cutting the paycheck. Then the meters disagree on purpose. This roster cannot do that. If you want that disagreement, run the other roster and print spending percentiles next to survival. Do not quote this freeze as if it showed that.

It refuses a recommended rate. 4% is on the grid because it is the famous rate, not because the freeze crowned it. 89.6% and $1,083,603 are a description of 4% on this specimen. They are not a blessing.

Replication spec

This page does not have its own engine call. It reads the same WR grid as the 90% article. That is the control: worlds identical, statistic changes. Rows, in order of rate: 2% success 99.4% median $1,887,349 p95 $10,378,565; 2.5% 98.4% / $1,672,012; 3% 96.9% / $1,479,180; 3.5% 94.0% / $1,294,129; 4% 89.6% / $1,083,603; 4.5% 83.0% / $878,374; 5% 76.8% / $667,635; 5.5% 70.1% / $479,419; 6% 63.0% / $307,594.

p5 is positive at 2% ($269,935) and at 2.5% ($173,751) and at 3% ($86,453), then it is zero. That is the ruin mass arriving in the left tail. Median stays positive all the way to 6%. A page that only prints medians would have said 6% "still works" because $307,594 is not zero. A page that only prints success would have said 6% fails 37.0% of the time and would have ignored that more than half still hold $307,594. Print both.

CSV: /data/studies/probability-of-success-vs-projected-balance.csv. Same seed, same 1,000 paths, same household as the 90% page. If those two CSVs ever disagree on the 4% row, a freeze was edited by hand and both articles are void.

Last recap, in one breath: 2% lasts almost always and leaves $1,887,349; 4% lasts 89.6% and leaves $1,083,603; 6% lasts 63.0% and leaves $307,594. Probability of success versus projected balance is the versus, not the winner. Anyone who walks away with only one of those six numbers walked away with a slogan.

Notes. Same freeze as 90-percent-success-not-100. B4_RETIREE, seed 20260622, 1,000 paths, rigid 2.0%–6.0% step 0.5%. Primary: success rate and median terminal versus rate. Real terminals from the engine summary. Q1 run. Q2 not run for this metric card. Q3 not run. Q4: 5 bps, tax off. CSV: /data/studies/probability-of-success-vs-projected-balance.csv. Card dated 2026-08-28. This article is educational analysis, not investment advice, and does not recommend any security or strategy.