Financial Disclaimer: Mathematical probability models discussed herein are for quantitative educational purposes.

The Mathematical Expectancy Equation

The performance of any probabilistic system is governed by Mathematical Expectancy (\(E\)) per dollar risked:

E = (W imes R) - (L imes 1.0)

Where:

  • \(W\) = Win Rate (probability of a winning trade)
  • \(L\) = Loss Rate (\(1 - W\))
  • \(R\) = Payoff Ratio (Average Win / Average Loss)

The 90% Win Rate Disaster Scenario

Consider a martingaling scalping system:

  • Win Rate (\(W\)): 90% (0.90)
  • Average Profit: 0
  • Average Loss (when stop eventually hits or catastrophic move occurs): 20
  • Payoff Ratio (\(R\)): 0.083
  • Expectancy: \((0.90 imes 10) - (0.10 imes 120) = 9 - 12 = -\.00\) per trade!

Despite winning 9 out of every 10 trades, the strategy is mathematically guaranteed to wipe out account equity over sufficient iterations.