Mathematical Framework

The math behind the studies.

This page explains the probability and expectancy math behind each study. It is meant to bridge the result page and the implementation logic.

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Core Metrics

Conditional Probability

P(A|B) = P(A ∩ B) / P(B)

Probability of event A occurring given condition B is true.

Expectancy

E = p_w·W − p_l·L

Average outcome per trade or event over the long run.

Win Rate

p_w = Wins / Trades

Proportion of observed events that end favorably.

Average Win

W̄ = Σ Wins / #Wins

Mean profit of winning outcomes.

Average Loss

L̄ = Σ |Losses| / #Losses

Mean loss magnitude of losing outcomes.

Profit Factor

PF = Σ Wins / Σ |Losses|

Gross profit divided by gross loss.

MAE

MAE ≤ 0

Maximum adverse excursion, worst open excursion during the trade.

MFE

MFE ≥ 0

Maximum favorable excursion, best open excursion during the trade.

Confidence Interval

Ē ± t·s / √n

Range of values likely to contain the true mean expectancy.

Framework

Conditional Probability

P(A|B) = P(A ∩ B) / P(B)

Use this when a study asks a question like: probability the RTH breaks IB High, given Low Forms First.

Expectancy

E = p_w·W − p_l·L

A positive probability alone is not enough. The payoff profile matters.

R-Multiple Logic

R = Trade Result / Initial Risk

Normalizes outcomes into risk units so studies are comparable across instruments.

Confidence Interval

Ē ± t_α/2,n−1 · s / √n

Frames the uncertainty of the sample estimate rather than pretending the result is exact.

Worked Example

Sample Inputs

Trades (n): 1,000
Win Rate (p_w): 54.2%
Average Win (W̄): +1.36R
Average Loss (L̄): −1.00R
R-Multiple Std Dev (s): 1.98R

Step-by-Step Calculation

1) Convert win rate to probability
   p_w = 0.542
   p_l = 1 - 0.542 = 0.458

2) Expectancy
   E = (0.542 × 1.36) - (0.458 × 1.00)
   E = 0.73712 - 0.458 = +0.27912R

3) Profit Factor
   PF = 0.542 × 1.36 / 0.458 × 1.00 ≈ 1.61

4) Standard Error
   SE = s / √n = 1.98 / √1000 ≈ 0.0626

5) 95% Confidence Interval (approx.)
   CI = 0.279 ± 1.96 × 0.0626
   CI ≈ [0.156R, 0.402R]

Result Summary	Value
Expectancy (E)	+0.279R
95% Confidence Interval	[0.156R, 0.402R]
Profit Factor	1.61
Interpretation	Positive expectancy with statistical confidence

Interpretation

Focus on Expectancy

A setup can have a moderate win rate and still be superior if the win/loss profile is favorable.

Respect Variability

Large distributions and adverse excursions matter. Variability is part of the edge evaluation.

Avoid Overfitting

Robust edges should persist across time, context, and regime. Seek consistency, not perfection.