Appendix: Scores

This appendix documents score formulas used by the reports. Scores are ranking heuristics, not probabilities of future profit. For example, a score of 0.80 should not be read as an 80% probability of future success; it only ranks candidates inside this research process.

Score Usage Map

This table separates scores that drive the main ranking from diagnostic scores that are shown for inspection only.

Score / Metric	Used In	Affects Final Ranking?	Range	How To Read It
`efficiency_score`	Step 02, rolling/OOS/regime windows, WFA metric selection	No, not directly	0..1	General single-period quality score; higher is better.
`balanced_score`	Step 02 metric winners, WFA metric selection	No	0..1	Geometric balance across return, drawdown, profit factor, and Sharpe.
`profit_quality_score`	Step 02 metric winners, WFA metric selection	No	Unbounded	Drawdown-adjusted absolute-profit heuristic; compare within one run only.
`robustness_score`	Step 04, Step 06	Yes	0..1	Combined rolling plus fixed-OOS robustness.
`regime`	Step 05, Step 06	Yes	0..1	Weighted market-regime performance score.
`parameter_stability`	Step 06	Yes	0..1	Plateau / local-neighborhood stability score.
`strategy_composite_score`	Step 06, Step 11 summary	Main final ranking	0..1	Final composite ranking score.
`statistical_confidence_score`	Step 06 diagnostics	No	0..1	Sample-quality diagnostic based on trades, Wilson win-rate bound, expectancy, and OOS positivity.
`trade_distribution_score`	Step 06 diagnostics	No	0..1	Trade-level distribution diagnostic for concentration, tails, median, skew, and sample size.
`sltp_robustness_score`	Step 03/04 SL/TP validation	No, except for SL/TP shortlist inclusion	0..1	Checks whether an SL/TP overlay survives validation relative to its own baseline.
`leverage_score`	Step 08	No	0..1	Soft leverage suitability score; hard leverage status should be checked separately.
`adaptability_score`	Step 10	No	0..1	Classic train/test WFA adaptability diagnostic.

Common Scale Notes

Most composite scores are bounded to 0..1; higher is better.
Unbounded metrics such as profit_quality_score, max_drawdown_relative_score, Sharpe, and Sortino are useful for ranking, but their absolute values are not directly comparable to bounded scores.
When a bounded score is shown, values above roughly 0.70 are usually strong, 0.55-0.70 are promising, 0.40-0.55 are borderline, and values below 0.40 are weak. Some sections use stricter or looser thresholds where appropriate.

Score Dependency Map

strategy_composite_score
  = robustness_score + regime + parameter_stability

robustness_score
  = rolling_robustness_score + oos_robustness_score

regime
  = weighted per_regime_score + positive_regime_ratio + covered_weight

parameter_stability
  = local-neighborhood quality + good-neighbor ratio + density + center position

diagnostic-only scores
  = statistical_confidence_score, trade_distribution_score, leverage_score, adaptability_score

Metric Winner / Parameter Optimization Scores

These scores are mostly used in Step 02 to find metric winners and diagnostic candidates. They rank candidates by different definitions of quality, not by robustness.

Efficiency Score

efficiency_score =
  0.30 * return_quality_score
+ 0.30 * risk_adjusted_score
+ 0.25 * drawdown_score
+ 0.10 * expectancy_score
+ 0.05 * trades_score

return_quality_score = 0.65 * profit_score + 0.35 * profit_factor_score
drawdown_score = 0.55 * drawdown_depth_score + 0.25 * drawdown_duration_score + 0.20 * underwater_score
positive_bounded_score(x) = max(x, 0) / (1 + max(x, 0))
signed_bounded_score(x) = 0.5 + 0.5 * x / (1 + abs(x))

Sub-scores:

profit_score: bounded version of total return; grows with positive return but saturates.
profit_factor_score: bounded version of profit factor; rewards gross profit exceeding gross loss.
risk_adjusted_score: signed bounded Sharpe-style component; negative Sharpe pushes it below 0.5.
drawdown_depth_score: 1 - max_drawdown; deeper drawdown lowers the score.
drawdown_duration_score: 1 - drawdown_duration_pct; long time underwater is penalized.
underwater_score: 1 - underwater_mean; persistent underwater depth is penalized.
expectancy_score: bounded positive expectancy; zero or negative expectancy contributes nothing.
trades_score: bounded trade count support; very low trade count lowers confidence in the candidate.

Interpretation:

Range	Meaning
> 0.65	Strong candidate on the tested period: good return/risk balance, acceptable drawdown, and enough trades.
0.45 - 0.65	Usable/interesting but needs OOS, regime, and trade-distribution confirmation.
< 0.45	Weak quality score; usually too low unless there is a specific reason to inspect it.

Balanced Score

balanced_score = geometric_mean(
  profit_score,
  drawdown_depth_score,
  drawdown_duration_score,
  profit_factor_score,
  sharpe_score
)

Sub-scores: this is a geometric mean, so one very weak component pulls the whole score down. It intentionally rewards candidates that are decent across return, drawdown, profit factor, and Sharpe rather than excellent in only one dimension. Balanced Score uses its own bounded component transforms; its profit_factor_score is not identical to the component used inside Efficiency Score.

Interpretation:

Range	Meaning
> 0.60	Balanced across several dimensions.
0.35 - 0.60	Acceptable but has at least one weaker dimension.
< 0.35	Not balanced; one or more components are poor.

Profit Quality Score

profit_quality_score = profit_draw * log(profit_factor + 1) * log(min(10, expectancy) + 2) * log(1.2 + win_rate) * trade_penalty

profit_draw = profit_total_abs - (max_drawdown * profit_total_abs) * (1 - 0.055)
trade_penalty = max(1 - abs(trades - 50) / 50, 0.1) when trades < 50, otherwise 1

Sub-scores:

profit_draw: absolute profit reduced by a drawdown penalty.
log(profit_factor + 1): rewards profit factor while compressing extreme values.
log(min(10, expectancy) + 2): rewards expectancy but caps runaway values.
log(1.2 + win_rate): small win-rate quality multiplier.
trade_penalty: penalizes very low trade counts relative to the target of 50 trades.

Interpretation:

Range	Meaning
> 0	Passes this drawdown-adjusted profitability heuristic.
approx. 0	Marginal; profit and drawdown adjustment roughly cancel out.
< 0	Losses or drawdown adjustment dominate.

Caveat: this score is unbounded and capital-size dependent. It is useful for ranking candidates within the same run, but it should not be compared directly to bounded 0..1 scores.

Sharpe Metric

sharpe = mean(period_return) / std(period_return) * sqrt(bars_per_year)
bars_per_year = (365 * 24 * 3600) / median_bar_seconds  # derived from actual data interval

This is a raw risk-adjusted performance metric, not a bounded score.

Interpretation:

Range	Meaning
> 1.0	Good risk-adjusted equity performance.
0.5 - 1.0	Acceptable but not strong.
< 0.5	Weak risk-adjusted performance.

Trade-Based Sharpe Metric

sharpe_trade_based = mean_period_pnl / std(individual_trade_returns) * sqrt(bars_per_year)

This is a raw trade-distribution metric, not a bounded score.

Interpretation:

Range	Meaning
Higher	Better consistency across individual trades.
Low / negative	Trade outcomes are noisy or negative after normalization.

Sortino Metric

sortino = mean(period_return) / std(negative_period_return) * sqrt(bars_per_year)

This is a raw downside-adjusted performance metric, not a bounded score.

Interpretation:

Range	Meaning
> 1.5	Good downside-adjusted performance.
0.75 - 1.5	Acceptable but not strong.
< 0.75	Weak downside-adjusted performance.

Trade-Based Sortino Metric

sortino_trade_based = mean_period_pnl / std(losing_trade_returns) * sqrt(bars_per_year)

This is a raw trade-distribution metric, not a bounded score.

Interpretation:

Range	Meaning
Higher	Better consistency after focusing only on losing-trade volatility.
Low / negative	Losing trades are too volatile relative to daily PnL.

Max Drawdown Relative Score

max_drawdown_relative_score = profit_total / max_drawdown^2

This metric is unbounded. It is intentionally aggressive: very small drawdown can produce very large values.

Interpretation:

Range	Meaning
Higher	Better return per squared unit of drawdown.
Very high	Can be good, but inspect whether max_drawdown is tiny due to too few trades.
<= 0	No positive drawdown-adjusted return.

Robustness Related Scores

These scores evaluate whether a candidate remains acceptable across rolling windows and fixed OOS periods.

Combined Robustness Score

robustness_score = (0.50 * rolling_robustness_score + 0.50 * oos_robustness_score) / 1.00

Interpretation:

Range	Meaning
> 0.70	Robust across both rolling and fixed OOS validation.
0.55 - 0.70	Promising but needs detailed inspection.
0.40 - 0.55	Borderline; usually not enough without strong qualitative reasons.
< 0.40	Poor robustness.

Rolling Robustness Score

rolling_robustness_score =
  0.35 * mean_window_efficiency
+ 0.25 * worst_window_efficiency
+ 0.20 * positive_window_ratio
+ 0.10 * consistency_score
+ 0.10 * drawdown_stability_score

consistency_score = clip(1 - std(window_efficiency), 0, 1)
drawdown_stability_score = clip(1 - std(window_max_drawdown), 0, 1)

Sub-scores:

mean_window_efficiency: average quality across rolling windows.
worst_window_efficiency: weakest rolling window; prevents one bad period from being hidden by the mean.
positive_window_ratio: fraction of rolling windows with positive profit.
consistency_score: rewards low dispersion of efficiency scores across windows.
drawdown_stability_score: rewards stable drawdown behavior across windows.

Interpretation:

Range	Meaning
> 0.70	Strong rolling stability across windows.
0.50 - 0.70	Moderate stability; inspect worst-window and equity behavior.
< 0.50	Fragile across rolling windows or too dependent on specific periods.

OOS Robustness Score

oos_robustness_score =
  0.35 * mean_oos_efficiency
+ 0.25 * worst_oos_efficiency
+ 0.20 * positive_oos_ratio
+ 0.10 * oos_consistency_score
+ 0.10 * oos_drawdown_stability_score

Sub-scores:

mean_oos_efficiency: average quality across fixed OOS periods.
worst_oos_efficiency: weakest fixed OOS period.
positive_oos_ratio: fraction of OOS periods with positive profit.
oos_consistency_score: rewards low dispersion of OOS efficiency scores.
oos_drawdown_stability_score: rewards similar drawdown depth across OOS periods.

Interpretation:

Range	Meaning
> 0.70	Strong fixed-OOS confirmation.
0.50 - 0.70	Mixed but potentially acceptable; inspect each OOS period separately.
< 0.50	Weak OOS confirmation; likely period-sensitive.

Regime Related Scores

These scores evaluate how candidates behave across manually defined market regimes.

Regime Score

per_regime_score =
  0.35 * profit_score
+ 0.30 * survival_score
+ 0.25 * drawdown_score
+ 0.10 * efficiency_score

regime_score = 0.75 * weighted_regime_score + 0.15 * positive_regime_ratio + 0.10 * covered_weight

Sub-scores:

profit_score: bounded positive return inside one regime.
survival_score: equals 1 for profitable regimes; negative returns reduce survival.
drawdown_score: penalizes deep regime drawdowns.
efficiency_score: carries the general quality score into the regime calculation.
weighted_regime_score: average per-regime score using configured regime weights.
positive_regime_ratio: fraction of regimes where profit is positive.
covered_weight: how much configured regime weight had usable data.

Interpretation:

Range	Meaning
> 0.70	Works well across the configured regime mix.
0.50 - 0.70	Acceptable but may have weak regimes.
< 0.50	Regime-sensitive or poor in important regimes.

Parameter Stability Related Scores

These scores estimate whether a candidate sits in a stable parameter neighborhood or a sharp isolated optimum.

Parameter Stability / Plateau Score

score_column = robustness_score
radius = 2 grid steps
good_neighbor_threshold = quantile(score_column, 0.75)

parameter_stability =
  0.40 * neighbor_quality
+ 0.30 * good_neighbor_ratio
+ 0.20 * density_score
+ 0.10 * center_score

Sub-scores:

neighbor_quality: average score of nearby parameter combinations.
good_neighbor_ratio: share of nearby combinations above the configured score quantile.
density_score: whether enough neighbors exist inside the configured radius.
center_score: rewards candidates closer to the local neighborhood center instead of edge points.

Fallback behavior: if a proper plateau grid is unavailable, the report falls back to a simpler parameter-center score. If parameter information is not usable, the neutral fallback is 0.5.

Interpretation:

Range	Meaning
> 0.70	Candidate sits in a healthy plateau; nearby parameters are also good.
0.45 - 0.70	Some stability, but not a clear plateau.
< 0.45	Likely sharp optimum or edge of the tested parameter space.

Final Ranking Scores

These scores combine the previous validation layers into the final ranking used by the pipeline.

Strategy Composite Score

strategy_composite_score =
  0.60 * robustness_score
+ 0.25 * regime
+ 0.15 * parameter_stability

Interpretation:

Range	Meaning
> 0.70	Strong overall finalist by this pipeline's ranking logic.
0.55 - 0.70	Good candidate, but inspect components before trusting it.
0.40 - 0.55	Borderline.
< 0.40	Weak finalist.

Diagnostic Scores

These scores do not directly replace the main ranking logic. They help diagnose sample quality, trade distribution, and hidden risks.

Statistical Confidence Score

target_trades = 100
statistical_confidence_score =
  0.35 * trade_count_score
+ 0.25 * win_rate_wilson_lower_bound
+ 0.25 * expectancy_score
+ 0.15 * positive_oos_ratio

trade_count_score = total_trades / (target_trades + total_trades)

Sub-scores:

trade_count_score: saturating sample-size support.
win_rate_wilson_lower_bound: conservative lower confidence bound for observed win rate.
expectancy_score: bounded positive weighted expectancy.
positive_oos_ratio: fraction of OOS periods with positive return.

Interpretation:

Range	Meaning
> 0.65	Reasonable sample support and OOS reliability.
0.45 - 0.65	Some support, but sample may still be thin.
< 0.45	Weak statistical confidence; be careful with conclusions.

Trade Distribution Score

trade_distribution_score =
  0.30 * concentration_score
+ 0.25 * median_score
+ 0.20 * tail_score
+ 0.15 * skew_score
+ 0.10 * sample_score

concentration_score = 1 - top_5_profit_share
tail_score penalizes 5% expected shortfall relative to mean absolute trade PnL

Sub-scores:

concentration_score: penalizes profit made by only a few top trades.
median_score: rewards positive median trade PnL.
tail_score: penalizes bad expected shortfall in the worst 5% trades.
skew_score: rewards positive skew and penalizes ugly left-tail distributions.
sample_score: small trade samples are penalized.

Interpretation:

Range	Meaning
> 0.65	Healthy trade distribution; profit is less concentrated and tails are less problematic.
0.45 - 0.65	Mixed distribution; inspect largest wins/losses.
< 0.45	Profit may be concentrated or tail risk may dominate.

SL/TP Related Scores

These scores validate whether SL/TP modifications found on the research period survive on independent periods.

SL/TP Robustness Score

SL/TP robustness validates Step 03 SL/TP candidates over independent OOS and rolling periods. OOS periods: ['20250101-20250701', '20250701-20260101']; rolling timerange: 20220101-20250101.

sltp_robustness_score =
  0.45 * sltp_rolling_survival_ratio
+ 0.35 * sltp_oos_survival_ratio
+ 0.20 * worst_score

sltp_improved = true when SL/TP metric value beats the baseline metric value
worst_score = 1 if worst segment improvement >= 0 else 0

Sub-scores:

sltp_rolling_survival_ratio: share of rolling validation windows where SL/TP improves its target metric.
sltp_oos_survival_ratio: share of fixed OOS periods where SL/TP improves its target metric.
worst_score: guardrail that fails when the worst segment is negative.

Caveat: this score only says whether the SL/TP overlay improves its own baseline on the selected target metric. A robust SL/TP improvement can still be attached to a weak baseline strategy, so inspect the resulting full-period and OOS metrics as well.

Interpretation:

Range	Meaning
> 0.70	SL/TP improvement survives well across validation segments.
0.50 - 0.70	Promising but mixed; inspect OOS and rolling details.
< 0.50	SL/TP improvement is not robust enough.

Leverage Related Scores

These scores estimate whether a candidate has enough adverse-excursion buffer for the configured leverage assumptions.

Leverage Score

leverage_score =
  0.35 * mae_safety_score
+ 0.25 * leveraged_drawdown_score
+ 0.20 * tail_risk_score
+ 0.20 * robustness_under_leverage_score

Sub-scores:

mae_safety_score: liquidation buffer based on MAE quantile versus liquidation distance.
leveraged_drawdown_score: drawdown safety at the tested leverage.
tail_risk_score: worst-trade/tail-loss safety at the tested leverage.
robustness_under_leverage_score: candidate robustness carried into leverage scoring.

Caveat: leverage_score is a soft ranking score. The hard leverage_status can still reject a candidate when liquidation, tail-loss, or drawdown guardrails fail.

Interpretation:

Range	Meaning
> 0.75	Looks suitable for the tested leverage assumptions.
0.55 - 0.75	Borderline; inspect MAE/tail-loss charts.
< 0.55	Unsafe or weak leverage suitability.

Walk-Forward Related Scores

These scores belong to the classic train/test walk-forward step and measure whether optimized train parameters transfer to the next test period.

Walk-Forward Adaptability Score

adaptability_score = 0.60 * mean(score_decay_closeness) + 0.40 * positive_test_ratio
score_decay = test_decay_score / train_decay_score
score_decay_closeness = clip(1 - abs(1 - score_decay), 0, 1)
For profit_quality_score, score_decay uses signed-log transformed Profit Quality:
profit_quality_score_log = sign(x) * log(1 + abs(x)).

Sub-scores:

score_decay: train-to-test transfer ratio. Values near 1 mean good transfer.
score_decay_closeness: bounded closeness to 1; both strong degradation and explosive improvement reduce confidence.
positive_test_ratio: fraction of forward test windows with positive profit.
test_score_worst: not part of adaptability_score directly, but should be inspected as worst-window failure risk.

Caveat: this step evaluates the adaptability of the re-optimization process, not the final shortlist ranking. It does not change strategy_composite_score. A high value means train-selected parameters transferred well to the next test windows under the tested selection metric.

Interpretation:

Range	Meaning
> 0.75	Good train-to-test adaptability.
0.60 - 0.75	Acceptable.
0.45 - 0.60	Weak / period-sensitive.
< 0.45	Poor adaptability.
< 0.30	Very poor adaptability.