1% risk · 2R reward · ~40% win — positive expectancy under randomness
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Mathematical form:
Example: 0.40×2R − 0.60×1R = +0.20R → positive expectancy.
Threshold: R > (1−P)/P → at P=0.40 need R>1.5, baseline uses 2R.
| Domain | Metric | Symbol | Formula | Meaning |
|---|---|---|---|---|
| Distribution | Stability Index | S | σₘ/μₜ | Average deviation stability |
| Volatility Density | Vd | σ/MAD | Noise uniformity ratio | |
| Signal Consistency Ratio | SCR | Nvalid/Ntotal | Behavioral precision | |
| Efficiency | Expectancy Coefficient | Ec | (W×R)-(L×1) | Expected return per risk |
| Risk–Reward Efficiency | RRE | mean(R)/mean(1) | Risk–return harmony | |
| Systemic Cost Ratio | SCR₂ | (slip+comm+behav)/gross | Systemic friction cost | |
| Robustness | Max Drawdown Ratio | MDDr | Dmax/Epeak | Depth of capital contraction |
| Recovery Factor | RF | Net/Dmax | Recovery resilience | |
| Behavioral Durability Index | BDI | Nplan/Ntotal | Psychological consistency | |
| Capital | Flow Velocity | CFV | Cturn/Etotal | Capital turnover rhythm |
| Compounding Growth Rate | CGR | (Eend/Estart)^(1/n)−1 | Rate of compounded survival | |
| Capital Persistence Ratio | CPR | Tabove/Ttotal | Continuity of capital stability |
PCI = (D+E+R+C)/4 → ≥0.70 Survival Zone · 0.50–0.70 Adaptive Drift · <0.50 Collapse
| Field | Concept |
|---|---|
| F1 | Mathematics — probabilistic logic |
| F2 | Physics — capital as energy |
| F3 | Behavior — psychological control |
| F4 | Time — temporal averaging |
| F5 | System — boundary constraints |
| F6 | Evolution — adaptive logic |
| F7 | Data Awareness — feedback loop |
| F8 | Inner Balance — entropy control |
| F9 | Outer Balance — environmental fit |
Authorship and data integrity anchored by verifiable identifiers.
DOI (concept): 10.5281/zenodo.17458961
DOI (version): 10.5281/zenodo.17458788
ArDrive: 88270e0a-7583-468d-9050-c38f20ad3892
SHA-256: E19AB011C7E5C261C87201B24A2FBFB63A3A0A7312A59392B98616544F630075