The Maths Every Day Trader Should Know
Why did I lose when my direction was right?
Replay price paths to see why a correct forecast and a profitable trade are different outcomes—and why neither should be measured through the other alone.
By ContextChart Research · 4 min
Published
Same destination. What happened first?
Try it yourself
All three calls finish +0.6 price units after eight hours. Predict whether all, some, or none finished with a positive trade result.
+0.6
Every path’s final price movement.
The final number has hidden the route.
Constructed ordered paths, linked by straight segments. Target +1 price unit, exact barrier fills, no costs. Stops are distances, not suggested settings.
The idea
Imagine making a correct call: price will be above its current level by the end of the session. The session ends, and it is. Your trade still lost.
There is no contradiction. The call described a destination. The trade also depended on the route.
Price could have reached your stop before rising. It could have reached the target and then reversed. It could have finished slightly higher without touching either boundary before the trade expired. All three paths can share the same final direction.
An incorrect forecast can also produce a profitable trade. Price may touch a modest target before ending on the opposite side. The trading result and the forecast result answer different questions.
This distinction gives you a better way to diagnose performance. A strong market read may be expressed through unsuitable timing or exits. A profitable exit may flatter a weak read. Recording both lets you investigate where the result came from.
The direction at a future time does not tell you which stop or target price touched first.
How this experiment works
Look at the constructed paths before revealing their outcomes. Each begins at the same price and finishes above entry. Predict which trades reach their target, which stop out, and which expire.
Move the illustrative stop and replay the paths. The final directional score stays fixed while the trade outcome changes. The paths are teaching examples, not observations selected to identify a profitable stop.
How we use this
At ContextChart, our research scores a directional call at a declared future horizon and separately walks the resulting trade to its exit. The accuracy-ladder study measured both correct calls that lost and incorrect calls that won.
That replaced an oversimplified assumption: there is no universal percentage of correct calls that markets “take away.” Conversion depends on the paths, trade rules, instrument, horizon, and sample.
The study's ladder combines historical outcomes under specified assumptions. A real trader can be correct on a different subset of paths, so the ladder is not a promised conversion from their accuracy into returns.
Show the maths
Let C mean the directional call is correct and W mean the trade wins:
P(W) = P(C) × P(W given C) + P(not C) × P(W given not C)
The first contribution contains correct calls that become winning trades. The second contains wrong calls that still win. Both require a defined horizon and trade outcome.
What this does not establish
Wider stops can rescue some paths and increase losses or holding time elsewhere. This lesson establishes the difference between destination and route. Choosing better trade rules needs a comparison of complete, after-cost outcomes. Start with testing an edge, keeping the forecast and execution records separate.