Win Rate & Confidence Interval Calculator
Winning 7 of 10 is not a 70% win rate. See the range your record actually supports, using the Wilson interval rather than the one that breaks at the edges.
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How many games would settle it
How often a 95% interval is actually right
That is a claim, and it can be checked exactly rather than argued about. For a given number of games only so many results are possible, so every one is enumerated and weighted by how likely it is. No simulation, no sampling error — this is the true figure.
| Games | True rate | Wilson | Normal |
|---|---|---|---|
| 10 | 10% | 93.0% | 65.0% |
| 10 | 50% | 97.9% | 89.1% |
| 20 | 10% | 95.7% | 87.6% |
| 20 | 50% | 95.9% | 95.9% |
| 50 | 10% | 97.0% | 87.9% |
| 50 | 50% | 93.5% | 93.5% |
Both columns should read 95%. Wilson does, near enough, everywhere. The normal approximation drops to 65% — on ten games against a one-in-ten rate its "95% interval" misses the truth better than a third of the time. That is not a rounding difference, and it is why this page does not use it.
What a win rate can and cannot tell you
- Winning 7 of 10 is not a 70% win rate. It is one sample, and the honest answer is a range — which in that case runs from about 40% to 90% and still includes a coin flip.
- The normal approximation taught in most statistics courses breaks at the edges: on 10 wins from 10 games it gives 100% to 100%, which is certain and obviously wrong. The Wilson interval is used here instead, and both are shown so the difference is visible.
- A small edge takes an enormous number of games to demonstrate. Proving a 52% rate is genuinely above even needs several thousand, which is why arguments about slightly-better decks rarely get settled by playing.
- An even rate is the hardest case. A deck winning 50% needs more games to pin down than one winning 90%, because the variance is largest in the middle.
- None of this accounts for who you played, what you played against, or whether you were learning as you went. It is the arithmetic of the sample, not a verdict on the deck.
How to use
- Enter your wins and how many games you played.
- Read the range, not the percentage.
- Check how many more games would settle the question.
Frequently asked questions
Why does 7 wins from 10 games not mean a 70% win rate?
Because ten games is one small sample, and the honest answer is a range rather than a number. At 95% confidence that record supports anything from about 40% to 90% — a span that still includes a coin flip. The percentage is real; the conclusion people draw from it is not.
What is the Wilson interval and why use it?
It is a way of turning a record into a plausible range that behaves properly at the edges. The normal approximation taught in most courses says 10 wins from 10 games means 100% to 100% — certain, and obviously wrong — and it runs below zero on lopsided records. Wilson does neither, so it is what this uses. Both are shown so you can see the difference.
How many games does it take to prove something?
More than feels reasonable. Pinning an even rate down to within ten points takes several hundred games, and demonstrating that a 52% edge is genuinely above even takes several thousand. That is why arguments about slightly-better decks almost never get settled by playing them.
Why is a 50% rate the hardest to measure?
Because the variance of a proportion is largest in the middle. A deck winning 90% of the time announces itself quickly; one winning 52% hides inside its own noise, and the closer the true rate sits to even, the more games it takes to distinguish from even.
Does a wider range mean I played badly?
No — it means you played fewer games. The width comes almost entirely from sample size, not from how well you did. Two identical 70% records, one over 10 games and one over 50, produce very different ranges and very different conclusions.
Can I trust this as a verdict on my deck?
Only as arithmetic on the sample. It knows nothing about who you played, what you played against, or whether you were improving as you went. It tells you what your own record can and cannot support, which is a narrower and more useful claim than most win rates get.
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