The 1:1 range projection is the target rule both books recommend (book 1 ch.8
discards point-and-figure counting as too subjective and keeps the vertical
projection). Tested as a complete trade on 4 symbols x M15/H1: enter on the
range breakout, stop at the far side of the range, target k x risk.
A driftless market gives P(win) = 1/(1+k) and expR = 0 at EVERY k, so the
benchmark here is analytic - no permutation null needed. Result: expR sits on
that benchmark at every k on every symbol. Target placement does not move
expectancy, which is what a martingale already said.
But the law itself is measurable, and it is not 1:1. Regressing
log(MFE) on log(range height) with log(ATR) as a FREE regressor (a shared ATR
denominator correlates the errors and biases the exponent towards the
hypothesis, so it cannot be used to argue against it):
b = 0.10 .. 0.92, centred ~0.6
b = 1 rejected in 5 of 8 at >2sd, never significantly above 1
b = 0 rejected in 7 of 8
So a bigger cause does produce a bigger effect - sub-proportionally. The 1:1
projection systematically over-reaches after a large consolidation and
under-reaches after a small one. Median travel in risk-multiples falls
monotonically across height quartiles in 8 of 8 runs.
Also adds the volume-profile machinery the second book is built on and which
nothing in the EA has: tick-level volume-at-price on a fixed absolute grid,
per-session VPOC/value area by the standard Market Profile walk, naked VPOCs,
and HVN/LVN from a rolling causal composite.
Two biases are left in deliberately, both against the hypothesis: a bar
spanning stop and target books the loss, and spread is charged on entry and
both barriers. Unresolved trades are marked to market at the horizon rather
than discarded - discarding them deletes slow winners and manufactures a
false deficit at large k.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
