When expectancy and drawdown limits disagree

Three filters before an order is sent

The historical workflow treats expected value, risk-reward geometry, and a hard drawdown bound as three separate pre-trade filters. Expected value is a pre-trade mean outcome computed from win bias and payoff multiple. It is used as a first filter that opposite styles can still share.

Win bias is the fraction of outcomes that hit the payoff side of a style. The risk-reward ratio is the payoff multiple that, together with win bias, sets both the expected-value reading and the width of the equity path. A drawdown limit is a cap on peak-to-trough equity loss used to reject a style whose path can sink far below the shared mean.

Opposite mixes can share one mean

Two opposite payoff-and-hit-rate mixes can return the same expected-value reading when expectancy is computed as win bias times one plus the payoff multiple, minus one. Under a 2.63 percent win rate with a 35-to-1 payoff and a 47.4 percent win rate with a 1-to-1 payoff, that shared expected value is a 5.26 percent loss.

Path-volatility after the mean filter

With that expected value held fixed, the high-payoff mix produced a series standard deviation near 5.77 percent versus about 0.99 percent for the near-even mix, so changing the risk-reward pairing still moves path noise after the expectancy filter is passed. Path-volatility is how far realized equity wanders around the expected-value mean across a long sequence of bets.

Across 1,000 repetitions of 1,000-bet sequences, profit-and-loss scatter around the common mean was much wider for the high-payoff mix, with a distribution standard deviation of 34.8 percent versus 8.7 percent. A volatility identity that scales with one plus the payoff multiple and with the square root of win-rate variance predicted roughly a 5.8-to-1 noise gap between the two mixes, consistent with the simulated standard deviations.

Why a drawdown limit still splits the styles

The high-payoff mix reached a maximum drawdown of 68.6 percent, against 15.4 percent for the near-even mix, so a drawdown-limit screen would not treat the two styles as interchangeable. High-payoff paths with a 2.63 percent win rate included losing streaks longer than 100 consecutive losing bets at least five times inside one 1,000-bet run.

Realized win rate drifted away from the design bias, stretching the high-payoff style from about 51.1 percent profit at a 4.4 percent realized win rate to about a 49.6 percent loss at a 1.4 percent realized win rate.