cost-density-net-rr-calculator

<essential_principles> Core Principles of the Cost Density Model

1. Core Formula

All calculations are based on the following relationship:

Cost Density = (c/V + s)           # 成本密度（pips 等效）
x = Cost Density / P               # 負載係數
RR_net = (RR_g - x) / (1 + x)      # 淨風險報酬比
WR_min = (1 + x) / (1 + RR_g)      # 最低勝率
P_critical = CostDensity × (RR_g + 2) / RR_g  # 效率減半點

2. Parameter Definitions

Parameter	Definition	Unit
RR_g	Gross risk-reward ratio (target/stop-loss)	Unitless
P	Stop-loss size	pips/points
c	Round-turn commission (per lot)	Account currency
s	Round-turn spread	pips/points
V	Value per pip (per lot)	Account currency/pip
R	Fixed risk (optional, cancels out)	Account currency

3. Key Insights

Hyperbolic decay: As P → 0, x → ∞, RR_net → -1
R independence: RR_net does not depend on fixed risk R
Scissors effect: Short timeframes simultaneously increase the cost burden and reduce signal quality

4. Unit Consistency Rules

P and s must use the same basis (both pips or both points)
c must be round-turn commission
V must be the value per pip per lot </essential_principles>

Compute - Calculate the cost density and efficiency metrics for a single parameter combination
Sweep - Scan the stop-loss range and generate an RR_net/WR_min curve table
Analyze - Interpret the results and provide strategy recommendations

Wait for a response before continuing.

After reading the workflow, please follow its steps exactly.

<reference_index> Reference Documents (references/)

Document	Content
formulas.md	Complete formula derivation and mathematical proof
theory.md	Market microstructure theory background and literature
</reference_index>

<workflows_index>

Workflow	Purpose
compute.md	Single calculation of cost density and efficiency metrics
sweep.md	Grid scan and threshold search
analyze.md	Result interpretation and strategy recommendations
</workflows_index>

<templates_index>

Template	Purpose
output-schema.yaml	Output JSON schema
input-schema.yaml	Input parameter schema
</templates_index>

<scripts_index>

Script	Purpose
cost_density.py	Python calculation implementation
cost_density.ts	TypeScript calculation implementation
</scripts_index>

<quick_start> Quick calculation (XAU/USD example):

Input:

{
  "RR_g": 3.0,
  "c": 7.0,
  "s": 1.5,
  "V": 10.0,
  "P": 20
}

Calculation:

cost_density = 7.0/10.0 + 1.5  # = 2.2 pips
x = 2.2 / 20                    # = 0.11
RR_net = (3.0 - 0.11) / (1 + 0.11)  # = 2.60
WR_min = (1 + 0.11) / (1 + 3.0)     # = 27.7%
P_critical = 2.2 * (3.0 + 2) / 3.0  # = 3.67 pips

Output:

{
  "cost_density": 2.2,
  "x": 0.11,
  "RR_net": 2.60,
  "WR_min": 0.277,
  "P_critical": 3.67,
  "Loss_RR": 0.133
}

</quick_start>

<success_criteria> When the Skill executes successfully:

Input parameters pass validation (unit consistency)
Correctly calculate cost_density, x, RR_net, WR_min
Identify whether it is in the high-friction zone (P < P_critical)
Output conforms to outputs_schema
Provide zh-TW explanatory notes </success_criteria>

About this skill