EV/NOPAT Calculator
The formula
What the ev/nopat tells you
Whether ev/nopat is worth playing at all: the expected value of one attempt, the break-even win rate, and the edge you hold over it.
Calculation: EV = p×gain − (1−p)×loss; break-even win rate = loss ÷ (gain + loss). Enter your inputs and every substitution is shown below the result.
Reading the result
A positive EV with ruinous variance is still a trap — the per-100-attempts line is the budget reality check.
Limitations and best practice
Probability estimates are where people fool themselves; anchor win % to observed frequency, not hope.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Is positive EV enough?
How many samples to trust the number?
Source & methodology
Expected value; foundational decision theory.
EV/NOPAT: what this tool answers
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Searchers land on an EV/NOPAT page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
Like most useful measures, EV/NOPAT is a summary, and summaries hide as much as they reveal. The companion outputs and the input table are here to reopen what the headline compressed.
Every investing metric in Investing & Markets is a bet about the future priced in today’s language. EV/NOPAT translates that bet: EV = p×gain − (1−p)×loss; break-even win rate = loss ÷ (gain + loss). The translation is mechanical and reliable; the judgement is deciding whether the inputs you feed it are honest forecasts or wishful numbers.
Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to expected value per attempt = $69.40 on the default inputs, and the sensitivity section ranks the inputs that move the result — Win probability first, at ≈17.3 % of the headline for a ten-percent error either way in that input. Work down the page and by the end you could re-derive the result in a spreadsheet from memory.
How EV/NOPAT is computed, line by line
One formula, published in full: EV = p×gain − (1−p)×loss; break-even win rate = loss ÷ (gain + loss). Anything you can read, you can reproduce in a spreadsheet, and that reproducibility is the whole point of printing it rather than hiding it behind a button.
Win probability (%) (example value 40) is a measured number in the unit named by the label; the formula does not convert for you. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
Gain per win ($) (example value 250) is a plain measured quantity — the unit shown in the label is the unit the formula expects. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
Loss per defeat ($) (example value 51) is a measured number in the unit named by the label; the formula does not convert for you. If you are unsure what belongs in this field, look at the printed steps: the substitution shows exactly how the engine uses it.
EV/NOPAT with real numbers, step by step
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Win probability (%), Gain per win ($), Loss per defeat ($). The endpoint of that chain is $69.40 of expected value per attempt, sitting in the “Positive but thin — costs and variance can erase the edge” band.
- EV = 0.40 × $250.00 − 0.60 × $51.00 = $69.40
- Break-even p = 51 ÷ (250 + 51) = 16.94 %
Break-even win rate — 16.94%. Read next to the headline, this is the figure that shows the shape of the trade-off.
Edge over break-even — 23.06 pts. Read next to the headline, this is the figure that shows the shape of the trade-off.
EV per 100 attempts — $6,940. Read next to the headline, this is the figure that shows the shape of the trade-off.
Re-running with your own figures is instant; re-running by hand once is the best way to know the tool is telling you the truth.
Scenario table: EV/NOPAT at ±10 % and ±20 % of the key input
The honest version of any estimate is a corridor, and this one is cheap to produce: EV/NOPAT was recomputed at 5 points along the dominant input, with every other field left untouched.
| Win probability setting | Expected value per attempt |
|---|---|
| 80 % of the example value | $45.32 |
| 90 % of the example value | $57.36 |
| example inputs | $69.40 |
| 110 % of the example value | $81.44 |
| 120 % of the example value | $93.48 |
Across 5 settings of Win probability, the result spans $45.32 to $93.48. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Win probability alone; the substitution steps will follow your figures exactly.
What actually moves your EV/NOPAT
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the expected value per attempt was recalculated from scratch. Read it as a map of where EV/NOPAT is fragile — drawn for the example inputs, which is the map you want when deciding what to measure carefully.
- Win probability: ten percent up gives $81.44, ten percent down gives $57.36 — ≈17.3 % of the expected value per attempt either way
- Gain per win: ten percent up gives $79.40, ten percent down gives $59.40 — ≈14.4 % of the expected value per attempt either way
- Nudge Loss per defeat by ±10 % and EV/NOPAT lands between $66.34 and $72.46 (sensitivity ≈4.4 %)
Win probability is the dominant lever here: ten percent either way moves the result by about 17.3 %, from $57.36 to $81.44. That is where a careless figure does the most damage, so check it against a source, and treat Gain per win as the second priority (≈14.4 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
Is your EV/NOPAT good — reading the result bands
The value above only becomes useful the moment you know what it is being measured against. On the example inputs the band reads “Positive but thin — costs and variance can erase the edge”; your own figures place you on a different rung of the same ladder. How much of that band is luck? On Win probability alone ten percent either way covers $57.36 to $81.44. The practical reading rules: compare against your own history before comparing against other people; treat band boundaries as zones, not walls — one point on the wrong side of a threshold rarely changes a real outcome; and when a companion output contradicts the headline, believe the pair.
Where EV/NOPAT sits next to similar measures: this tool answers “how much is the EV/NOPAT”, while the related calculators answer “what do I do about it”. Reading the result alone tends to over-weight a single snapshot; pairing it with the companion tools above turns the number into a decision.
How people get EV/NOPAT wrong
Probability estimates are where people fool themselves; anchor win % to observed frequency, not hope. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Treating the example inputs as a recommendation. They are a demonstration of the mechanism — a decision-grade EV/NOPAT begins the moment your own figures replace them.
This model has its own particular trap: Win probability carries ≈17.3 % of the response per ten percent of error, so effort spent elsewhere is largely decorative.
The subtlest error is answering the wrong question precisely. Confirm that expected value per attempt is actually the quantity your decision needs — the arithmetic is flawless either way, which is what makes the mistake invisible.
Six things to confirm before acting on EV/NOPAT
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Re-verify Win probability against a source document — ten percent of error there moves the headline by ≈17.3 %.
- Verify each input against its original source document, not memory.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Confirm the answer against one independent method or published benchmark for EV/NOPAT.
A routine for decision-grade EV/NOPAT
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — start from evidence. The inputs behind EV/NOPAT are win probability (%), gain per win ($), loss per defeat ($). Write them down with their source next to each one; if you cannot name where a figure came from, that is the input most likely to be wrong. The test of a good estimate is not that it feels right but that it changes what you do.
Step 2 — compute the version you would not be embarrassed by. If a stranger audited your inputs, which set would you hand over? Enter that set, read the result, and treat everything else as upside. Half of a good calculation is knowing which input you would hate to be wrong about.
Step 3 — play with the inputs on purpose. Ten percent up, ten percent down, one field at a time. Within a few minutes you will know this calculation better than most people who quote its results. A figure nobody can reproduce is a figure nobody will act on twice.
Step 4 — compute a corridor, not a point. Three runs — worst, likely, best — turn EV/NOPAT from a snapshot into a range. Plan against the pessimistic end and treat the optimistic end as the upside story. If a result feels obviously right, that is the moment to check the inputs hardest.
Step 5 — write the one-line memo. “Expected value per attempt = $69.40 on this date, from these inputs.” That line is the entire deliverable; everything else on this page is how you earned the right to write it. If a result feels obviously right, that is the moment to check the inputs hardest.
Who actually uses EV/NOPAT — and when
Most Stocks & Equities disagreements are arithmetic disagreements in disguise. When Expected value per attempt of $69.40 sits on the table with its working shown, the conversation stops being about who sounds more confident and starts being about which input is wrong. Note the assumption you are least sure about; that is where the real risk lives.
Used properly this is a five-minute filter that saves weeks. Compute EV/NOPAT, reject what fails, and only then bring in the expensive analysis for the survivors. One decimal place more than your data supports is one decimal place of fiction.
Treat EV/NOPAT like a smoke alarm rather than a painting — its value is in being tested periodically, not in being admired once. Most surprises in numbers are surprises about inputs, not about formulas.
Quick answers: what searchers ask about EV/NOPAT
What affects EV/NOPAT the most?
EV/NOPAT is driven above all by Win probability. Perturbing only that field by ten percent either way produced $81.44 against the $69.40 baseline — a ≈17.3 % response, while Gain per win manages ≈14.4 %.
Which matters more: gain per win or win probability?
Win probability, by a factor of about 1.2. Concretely: ten percent on Win probability is worth ≈17.3 % of EV/NOPAT, the same nudge on Gain per win only ≈14.4 %. That ranking is re-computed for each page from that page’s own defaults.
What is a typical EV/NOPAT?
There is no honest universal average for EV/NOPAT, but there is a reference point: the defaults on this page produce $69.40 (Positive but thin — costs and variance can erase the edge). Replace the inputs with your own and compare — that comparison is the useful meaning of “typical”.
How do I calculate EV/NOPAT by hand?
EV = p×gain − (1−p)×loss; break-even win rate = loss ÷ (gain + loss) is the entire method. Work the inputs in that order — EV = 0.40 × $250.00 − 0.60 × $51.00 = $69.40 — and you will reach $69.40 on the default figures, the same number this tool prints.
What happens to EV/NOPAT if win probability changes by 10 %?
On these inputs a ±10 % change in win probability takes EV/NOPAT to $81.44 against the $69.40 example — around 17.3 % of the headline. The same test on every other field is in the sensitivity section.
Is the EV/NOPAT result of $69.40 good or bad?
Neither, on its own — the label “Positive but thin — costs and variance can erase the edge” is the band this figure falls in for the example inputs, and your own inputs will place you elsewhere on the same ladder. Judge the number against your history and your alternatives, and remember that a ten-percent error in Win probability alone moves it by ≈17.3 %.
Is EV/NOPAT accurate?
The arithmetic is exact: EV = p×gain − (1−p)×loss; break-even win rate = loss ÷ (gain + loss) is evaluated with full floating-point precision and every substitution is printed in the worked example. What limits accuracy is input quality and the model’s assumptions, so treat the $69.40 result as the correct answer to the question you typed — and check the assumptions section before acting on it.
What affects EV/NOPAT the most?
Sensitivity depends on where you start, but the inputs Win probability (%) and Gain per win ($) typically move EV/NOPAT further than the rest because they enter the formula multiplicatively. If you can only measure two things well, measure those and hold the others at conservative defaults.
Is positive EV enough?
It is necessary but not sufficient — bankroll sizing (Kelly criterion) exists precisely because variance can kill a positive-EV player before the edge pays.
How many samples to trust the number?
Rule of thumb: hundreds, not dozens — the standard error of a 40 % estimate needs ~600 trials to shrink under 2 points.
Is my data private on this page?
Yes — computation happens locally in your browser, with no account, no tracking of your inputs and nothing sent to a server. The printed formula is the whole story of what happens to your figures.
Key terms on this page
- Break-even win rate
- 16.94% on the example inputs — a companion figure printed beside the headline of EV/NOPAT so that no result is read in isolation.
- Edge over break-even
- 23.06 pts for the EV/NOPAT worked case; it sits next to the main result because it carries context the headline leaves out.
- EV per 100 attempts
- $6,940 in the default EV/NOPAT calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Expected value per attempt
- The primary output of this tool: $69.40 for the default inputs, computed exactly from EV = p×gain − (1−p)×loss; break-even win rate = loss ÷ (gain + loss).
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- A named zone on the range of plausible results; the example inputs land in “Positive but thin — costs and variance can erase the edge”, and your inputs may not.
- Sensitivity (±10 %)
- How far the EV/NOPAT moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Methodology, sources and limits
The model is published arithmetic implemented exactly as written: EV = p×gain − (1−p)×loss; break-even win rate = loss ÷ (gain + loss). Source of record: Expected value; foundational decision theory. Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
This page is an estimation aid, not professional advice. The design rule is simple: two people entering identical figures must get identical answers. The design constraint was set by usefulness rather than by comfort: an estimate you can interrogate beats an answer you have to trust.
After the number: what to do with it
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
This page was written for people who need one trustworthy number before their next decision, and the promise is that nothing above required trust. Bookmark the tool, re-run it whenever an input moves by more than a few percent, and keep the date with the number.