The Maths Every Day Trader Should Know
Is this trading skill, or a good run?
Learn what a trading record can support by comparing results with a relevant baseline, accounting for sample size, and looking beyond selected winners.
By ContextChart Research · 5 min
Published
A good run has a distribution
Try it yourself
Sample 1: observed wins
46 / 80
57.5% observed. Approximate 95% Wilson interval: 46.6%–67.7%.
Dashed line: known toy probability 50%. Highlighted band and larger dot: sample 1. Use “Inspect sample” to move the highlight.
Read all sample estimates and intervals
| Sample | Observed win rate | Approximate 95% interval |
|---|---|---|
| 1 · selected | 57.5% | 46.6%–67.7% |
| 2 | 53.8% | 42.9%–64.3% |
| 3 | 57.5% | 46.6%–67.7% |
| 4 | 45.0% | 34.6%–55.9% |
| 5 | 63.7% | 52.8%–73.4% |
| 6 | 53.8% | 42.9%–64.3% |
| 7 | 61.3% | 50.3%–71.2% |
| 8 | 47.5% | 36.9%–58.3% |
| 9 | 52.5% | 41.7%–63.1% |
| 10 | 50.0% | 39.3%–60.7% |
| 11 | 55.0% | 44.1%–65.4% |
| 12 | 55.0% | 44.1%–65.4% |
| 13 | 48.8% | 38.1%–59.5% |
| 14 | 46.3% | 35.7%–57.1% |
| 15 | 52.5% | 41.7%–63.1% |
| 16 | 48.8% | 38.1%–59.5% |
| 17 | 57.5% | 46.6%–67.7% |
| 18 | 57.5% | 46.6%–67.7% |
| 19 | 42.5% | 32.3%–53.4% |
| 20 | 42.5% | 32.3%–53.4% |
| 21 | 52.5% | 41.7%–63.1% |
| 22 | 51.2% | 40.5%–61.9% |
| 23 | 51.2% | 40.5%–61.9% |
| 24 | 45.0% | 34.6%–55.9% |
Each dot is a separate sample, not the next step of one trading record. The vertical bar is its approximate 95% Wilson interval; the highlighted sample matches the controls. All 24 samples came from the same specified probability. Choosing the most impressive sample would make one model look like several different levels of skill.
Deterministic examples from a seeded independent Bernoulli model with a known, constant win probability. The Wilson interval describes a binomial proportion under those assumptions; it does not establish profitability or handle dependent trades.
The idea
A good run is real. The harder question is how much it tells you about the next run.
An outcome contains both the decisions that produced it and the variation those decisions can experience. A useful advantage can lose over a short period. An approach with no advantage can have a memorable winning streak.
Start by choosing a relevant comparison. A 70% win rate is impressive only in relation to the payouts, losses, costs, and trade rules that produced it. A nearby target and distant stop may win frequently without useful information. “Better than half” is not the correct test for every trade shape.
Then examine the sample. How many genuinely distinct decisions does it contain? Are several positions expressions of the same idea? Did the record cover different conditions? Were the rules chosen before these outcomes, or because they looked good afterward?
Confidence should reflect those answers. It can grow with new evidence and decline when the evidence changes. You do not need to pretend certainty to make progress.
A result earns confidence through its comparison, sample, and repeatability rather than the impressiveness of a short winning run.
How this experiment works
Compare illustrative samples produced by a stated win probability. Change the sample length and examine how much the observed result varies.
The true probability is known in this demonstration because it was supplied to the model. In a real record, that is one of the quantities being estimated. A reassuring-looking sample does not make estimation uncertainty disappear.
How we use this
Our studies compare a claim with its look-alikes and appropriate baselines. Some use shifted price levels as placebos. Others compare observed paths with shuffled changes or split results into earlier and later periods.
The audited target study found that attractive trade shapes largely matched their no-information geometry before spread. Several apparent findings were revised after correcting calculations. Keeping those revisions made the research more useful: a claim's history became inspectable.
That is a process result, not proof that every future ContextChart trade has an advantage. Each new claim still needs evidence that matches its own decision and horizon.
Show the maths
For independent binary outcomes with the same fixed win probability p, the standard deviation of the observed win fraction is:
Square root of [p × (1 − p) ÷ number of observations]
The uncertainty shrinks roughly with the square root of sample size under these assumptions. Correlated trades and changing probabilities violate that simple model. Profitability also depends on the values of wins and losses, not only the win fraction.
What this does not establish
No universal trade count proves a trading career is viable. Multiple testing, selected reporting, changing rules, and costs can all weaken an impressive record. The next skill is designing a comparison before seeing the answer.