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# B-Score Pro Suite (Standard & MTF)
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## 1. Summary (Introduction)
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The **B-Score Pro Suite** is an institutional-grade, high-performance statistical arbitrage oscillator comprising two advanced indicators:
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* `BScore_Pro` (Standard)
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* `BScore_MTF_Pro` (Multi-Timeframe)
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The standard standard score (Z-Score) measures price distance from a lagging centerline (SMA, EMA). During strong trend expansions, these lagging centerlines cause standard Z-Scores to remain pinned at extremes, producing premature counter-trend signals.
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The B-Score (Butterworth Filter Z-Score) resolves this limitation by employing **John Ehlers' Higher-Order Butterworth Filter** (supporting 2-pole and 3-pole transfer functions) as its dynamic centerline.
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Unlike other averages, the Butterworth filter is designed to be **maximally flat in the pass-band**, providing an exceptionally sharp frequency cut-off. By calculating the Root-Mean-Square (RMS) standard deviation of the absolute distance between the price and this fourier-aligned centerline, the B-Score normalizes volatility expansions cleanly. It produces an ultra-responsive, zero-mean, highly defined cycle oscillator.
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The suite features dynamic Heikin Ashi price integration, a customizable **5-Zone Swapped Thermal Color Histogram**, a volume-weighted Signal Line, and advanced multi-timeframe step-blocking algorithms to prevent real-time drawing warping.
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---
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## 2. Mathematical Foundations
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The statistical calculations operate on closing prices $P_t$ (Standard or Heikin Ashi) over an active rolling lookback window of size $N$ (`InpPeriod`):
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### A. Dynamic Low-Lag Centerline ($\mu_{B, t}$)
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The baseline central curve is represented by the selected Butterworth Filter type (2-pole or 3-pole) calculated recursively over the cutoff period $P_{\text{Cutoff}}$ (`InpButterPeriod`):
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$$\mu_{B, t} = \text{ButterworthFilter}(P_t, \text{Poles}, P_{\text{Cutoff}})$$
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### B. Smoother Standard Deviation ($\sigma_{B, t}$)
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Instead of calculating price dispersion around a static mean, the B-Score calculates the Root-Mean-Square (RMS) standard deviation of the absolute distance between the price ($P$) and the responsive Butterworth centerline ($\mu_B$) over the rolling window of size $N$:
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$$\text{Difference}_i = P_i - \mu_{B, i}$$
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$$\sigma_{B, t} = \sqrt{\frac{1}{N} \sum_{k=0}^{N-1} (P_{t-k} - \mu_{B, t-k})^2}$$
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### C. Final Normalized B-Score
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The current price distance is divided by the smoother standard deviation to yield the normalized B-Score value in Sigma units:
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$$\text{B-Score}_t = \frac{P_t - \mu_{B, t}}{\sigma_{B, t}}$$
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To protect the system from division-by-zero exceptions during periods of absolute price consolidation, the calculator incorporates an active protection layer:
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$$\text{B-Score}_t = 0.0 \quad \text{if } \sigma_{B, t} \le 1.0 \times 10^{-9}$$
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### D. Signal Line Generation
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To filter out high-frequency noise and generate crossover triggers, a smoothed Signal Line is calculated directly on top of the B-Score output buffer (`BufferBScore[]`) using the integrated `CMovingAverageCalculator` (supporting standard MAs and volume-weighted **VWMA**):
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$$\text{Signal}_t = \text{MA}(\text{B-Score}, \text{SignalPeriod})_t$$
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---
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## 3. Visual & Architectural Highlights
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The suite integrates several advanced MQL5 architectural design patterns:
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* **Swapped 5-Zone Thermal Color Histogram:**
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To maintain perfect consistency with Heikin Ashi candle colors and represent progressive momentum build-up, the indicator implements a Swapped Thermal Palette (Blue for Bullish expansion, Red/Coral for Bearish expansion). The color transition logic is dynamically linked to the inputs:
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* **$B \ge \text{InpLevelClimaxHigh}$:** `clrDeepSkyBlue` (Bullish Climax / Extreme High)
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* **$B \in [\text{InpLevelFlowHigh}, \text{InpLevelClimaxHigh})$:** `clrLightSkyBlue` (Bullish Flow / Warning High)
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* **$B \in (\text{InpLevelFlowLow}, \text{InpLevelFlowHigh})$:** `clrGray` (Neutral Zone / Random Noise)
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* **$B \in (\text{InpLevelClimaxLow}, \text{InpLevelFlowLow}]$:** `clrCoral` (Bearish Flow / Warning Low)
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* **$B \le \text{InpLevelClimaxLow}$:** `clrOrangeRed` (Bearish Climax / Extreme Low)
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* **Dynamic Levels Configuration:**
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To bypass the visual limitations of hardcoded levels, the suite exposes all 6 statistical significance boundaries to the input panel under `"Indicator Levels"`. The centerline grid is programmatically constructed inside `OnInit()` using:
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```mql5
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IndicatorSetInteger(INDICATOR_LEVELS, 6);
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IndicatorSetDouble(INDICATOR_LEVELVALUE, 0, InpLevelFlowHigh);
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```
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* **Strict Chronological Sorting Safeguards:**
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To prevent calculation corruption caused by reverse-chronological array states (often forced by custom templates or third-party indicators on the active chart), the suite enforces chronological sorting (`ArraySetAsSeries(..., false)`) on all price inputs inside `OnCalculate()`.
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* **Memory Safety Validation (Pointer Guards):**
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To shield the terminal from runtime memory violations, a robust pointer-safety layer validates all dynamic objects via `CheckPointer()` before any calculation sequence is allowed to execute.
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---
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## 4. Advanced MQL5 MTF Implementation Details
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`BScore_MTF_Pro` resolves standard MTF calculation and display limitations by implementing a synchronized multi-timeframe pipeline:
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### A. Forming LTF Block Flat-Force (The Warping Solution)
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To prevent real-time step warping and slope distortion on lower timeframe charts, the indicator implements a step-blocking algorithm. On every tick, the indicator isolates the beginning of the active forming HTF block and forces the calculations to rewrite that block completely, keeping the visual lines perfectly flat and historically stable:
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```mql5
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int first_bar_of_forming_htf = rates_total - 1;
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while(first_bar_of_forming_htf > 0 &&
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iBarShift(_Symbol, g_calc_timeframe, time[first_bar_of_forming_htf], false) == 0)
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{
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first_bar_of_forming_htf--;
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}
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first_bar_of_forming_htf++; // Dynamic anchor start of current forming block
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if(start > first_bar_of_forming_htf)
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start = first_bar_of_forming_htf;
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```
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### B. State Mocking for IIR State Stability
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Since the Butterworth Filter equations inside the calculator are highly recursive, calling calculations continuously on the live forming bar on every tick would corrupt the feedback states ($F_{t-1}, F_{t-2}, F_{t-3}$). To avoid this, we perform **State Mocking** by passing `prev_calculated = g_htf_count` during live ticks. This processes the forming index exactly once, protecting closed historical registers from accumulation errors.
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---
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## 5. Parameters
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### A. BScore Settings
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* **Butterworth Period (`InpButterPeriod`):** The cutoff period ($P$) for the underlying Butterworth filter centerline (Default: `20`).
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* **Butterworth Poles (`InpPoles`):** Selects between a 2-pole (`POLES_TWO = 2`) or 3-pole (`POLES_THREE = 3`) IIR transfer function. Default: `POLES_TWO`.
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* **Volatility Lookback (`InpPeriod`):** The rolling window size ($N$) for the standard deviation calculations (Default: `20`, Range: $\ge 2$).
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* **Price Source (`InpSourcePrice`):** Selects the pricing input, supporting Standard and Heikin Ashi price series (Default: `PRICE_CLOSE_STD`).
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### B. Signal Line Settings
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* **Show Signal Line (`InpShowSignal`):** Toggle to enable/disable the Signal Line (Default: `true`).
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* **Signal Line Period (`InpSignalPeriod`):** The lookback period for the Signal Line MA (Default: `5`).
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* **Signal Line MA Type (`InpSignalType`):** Select the MA type for the Signal Line (Default: `SMA`). Supports `VWMA`.
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### C. MTF Specific Settings (MTF Version Only)
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* **Target Timeframe (`InpTimeframe`):** The target higher timeframe to calculate B-Scores on (Default: `PERIOD_H1`).
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### D. Indicator Levels Settings
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* **High Warning Level (`InpLevelFlowHigh`):** Volatility band indicating positive structural expansion (Default: `1.5`).
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* **Low Warning Level (`InpLevelFlowLow`):** Volatility band indicating negative structural expansion (Default: `-1.5`).
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* **High Climax Level (`InpLevelClimaxHigh`):** Extreme bullish exhaustion threshold (Default: `2.0`).
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* **Low Climax Level (`InpLevelClimaxLow`):** Extreme bearish exhaustion threshold (Default: `-2.0`).
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* **High Exhaustion Level (`InpLevelExtremeHigh`):** Advanced statistical exhaustion threshold (Default: `2.5`).
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* **Low Exhaustion Level (`InpLevelExtremeLow`):** Advanced statistical exhaustion threshold (Default: `-2.5`).
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* **Levels Color (`InpLevelColor`):** Customize the color of the horizontal line layout (Default: `clrSilver`).
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* **Levels Style (`InpLevelStyle`):** Customize the line style of the horizontal line layout (Default: `STYLE_DOT`).
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---
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## 6. Quantitative Trading Strategies
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### A. The Butterworth Extreme Exhaustion Trigger
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Nesting the statistical standard deviation over Ehlers' maximally flat Butterworth centerline creates highly responsive overbought and oversold extreme boundaries. By waiting for the B-Score to cross back into the neutral zone, traders avoid premature counter-trend entries.
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1. Wait for the B-Score to enter the Extreme Zone (**DeepSkyBlue** $\ge \text{InpLevelClimaxHigh}$ or **OrangeRed** $\le \text{InpLevelClimaxLow}$).
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2. Wait for the B-Score histogram to contract and **cross back over the Signal Line** (typically configured as a 5-period TMA or EMA).
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3. **Execution:** Open a mean-reversion trade (Short if high, Long if low) on the crossover bar. Place the stop-loss strictly beyond the extreme candle's high/low.
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### B. Top-Down Macro Volatility Alignment (MTF Core Strategy)
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Using the B-Score on a higher timeframe ensures that lower timeframe trade executions are aligned with large-scale institutional volatility cycles.
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1. **Macro Volatility Deviation (H1/H4):** Apply `BScore_MTF_Pro` set to H1 or H4 on an M5/M15 execution chart. Configure it with a `VWMA` signal line.
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2. **The Setup:** Wait for the macro **H1 B-Score** to enter the **Bear Extreme Zone (OrangeRed $\le \text{InpLevelClimaxLow}$)**, indicating that the macro price is extremely cheap relative to institutional fair value.
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3. **Execution:** On the lower M5 chart, only look for buy setups. Once the local M5 B-Score crosses back above its own **InpLevelFlowLow (-1.5)** level (or crosses its signal line), execute **BUY** orders, riding the wave of macro mean-reversion back to the macro fair value.
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