你的策略勝率 87%？Z-score 說：那是幻覺 — 統計檢驗入門

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import math

def z_score(wins: int, total: int) -> tuple[float, float]:
    """計算勝率的 Z-score 和 p-value"""
    if total == 0:
        return 0.0, 1.0
    p_hat = wins / total
    z = (p_hat - 0.5) / math.sqrt(0.25 / total)
    # 單尾 p-value（用常態分佈近似）
    p_value = 0.5 * math.erfc(z / math.sqrt(2))
    return z, p_value

# 範例：8 筆贏 7 筆
z, p = z_score(wins=7, total=8)
print(f"Z = {z:.2f}, p = {p:.3f}")
# 輸出: Z = 2.12, p = 0.017 — 看起來顯著？
# 但只有 8 筆，Bayesian 調整後會大幅修正

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from scipy import stats

def z_test_proportion(wins: int, total: int, null_p: float = 0.5):
    """完整的比例檢定，回傳 Z-score、p-value 和信賴區間"""
    p_hat = wins / total
    se = math.sqrt(null_p * (1 - null_p) / total)
    z = (p_hat - null_p) / se
    p_value = 1 - stats.norm.cdf(z)  # 單尾
    # 95% 信賴區間
    ci_se = math.sqrt(p_hat * (1 - p_hat) / total)
    ci_lower = p_hat - 1.96 * ci_se
    ci_upper = p_hat + 1.96 * ci_se
    return {
        "z_score": round(z, 3),
        "p_value": round(p_value, 4),
        "win_rate": round(p_hat * 100, 1),
        "ci_95": (round(ci_lower * 100, 1), round(ci_upper * 100, 1)),
        "significant": p_value < 0.05
    }

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def bayesian_win_rate(wins: int, total: int, alpha: float = 1, beta: float = 1) -> float:
    """
    用 Beta 先驗調整勝率。
    alpha=1, beta=1 是均勻分佈（無資訊先驗）。
    alpha=2, beta=2 讓收斂更積極。
    """
    return (wins + alpha) / (total + alpha + beta) * 100

# 批次計算所有策略
strategies = [
    {"name": "CEX Volume + Funding", "wins": 5, "total": 11},
    {"name": "TradingView 信號",      "wins": 5, "total": 8},
    {"name": "Pipeline",              "wins": 2, "total": 7},
    {"name": "其他",                   "wins": 2, "total": 7},
]

for s in strategies:
    raw = s["wins"] / s["total"] * 100
    adj = bayesian_win_rate(s["wins"], s["total"])
    z, p = z_score(s["wins"], s["total"])
    print(f"{s['name']:20s}  原始 {raw:5.1f}%  調整 {adj:5.1f}%  Z={z:+.2f}  p={p:.3f}")

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import math

def min_trades_for_significance(true_wr: float, alpha: float = 0.05) -> int:
    """給定策略的真實勝率，計算達到顯著性所需的最少交易筆數"""
    z_alpha = 1.645  # 單尾 95% 門檻
    # 從 Z = (p - 0.5) / sqrt(0.25/n) 反推 n
    n = math.ceil((z_alpha / (true_wr - 0.5)) ** 2 * 0.25)
    return n

# 算出不同勝率需要的筆數
for wr in [0.55, 0.60, 0.65, 0.70]:
    n = min_trades_for_significance(wr)
    print(f"真實勝率 {wr:.0%} → 至少需要 {n} 筆")

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def overfit_index(is_pf: float, oos_pf: float) -> dict:
    """
    計算過擬合指數。
    is_pf: 樣本內 Profit Factor（回測）
    oos_pf: 樣本外 Profit Factor（實盤或 WFO 驗證）
    """
    if oos_pf <= 0:
        return {"ofi": float("inf"), "risk": "CRITICAL", "action": "策略無效，停止使用"}

    ofi = is_pf / oos_pf
    if ofi < 1.5:
        risk, action = "LOW", "穩健，可增加倉位"
    elif ofi < 2.0:
        risk, action = "MEDIUM", "謹慎，維持小倉"
    elif ofi < 3.0:
        risk, action = "HIGH", "高過擬合風險，減少參數或增加樣本"
    else:
        risk, action = "CRITICAL", "嚴重過擬合，不建議上實盤"

    return {"ofi": round(ofi, 2), "risk": risk, "action": action}

# 範例：回測 PF=2.5，實盤 PF=1.1
result = overfit_index(is_pf=2.5, oos_pf=1.1)
print(f"OFI = {result['ofi']} ({result['risk']})")
print(f"建議：{result['action']}")
# 輸出: OFI = 2.27 (HIGH)
# 建議：高過擬合風險，減少參數或增加樣本

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交易 < 5 筆     → "數據不足"
p ≥ 0.05        → "統計不顯著"
OFI > 2.0       → "過擬合"
調整 WR ≥ 62%   → "穩健 ✓"
調整 WR ≥ 58%   → "可接受"
其他            → "待觀察"

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def strategy_health_check(wins: int, total: int,
                          is_pf: float = None, oos_pf: float = None):
    """一站式策略統計健檢"""
    raw_wr = wins / total * 100 if total > 0 else 0
    adj_wr = bayesian_win_rate(wins, total)
    z, p = z_score(wins, total)
    min_n = min_trades_for_significance(raw_wr / 100) if raw_wr > 50 else "N/A (WR ≤ 50%)"

    report = {
        "trades": total,
        "raw_win_rate": f"{raw_wr:.1f}%",
        "bayesian_win_rate": f"{adj_wr:.1f}%",
        "z_score": round(z, 3),
        "p_value": round(p, 4),
        "significant": p < 0.05,
        "min_trades_needed": min_n,
    }

    if is_pf and oos_pf:
        ofi = overfit_index(is_pf, oos_pf)
        report["overfit_index"] = ofi

    # 綜合判定
    if total < 5:
        report["verdict"] = "數據不足"
    elif p >= 0.05:
        report["verdict"] = "統計不顯著"
    elif is_pf and oos_pf and ofi["risk"] in ("HIGH", "CRITICAL"):
        report["verdict"] = "過擬合風險"
    elif adj_wr >= 62:
        report["verdict"] = "穩健 ✓"
    elif adj_wr >= 58:
        report["verdict"] = "可接受"
    else:
        report["verdict"] = "待觀察"

    return report

# 使用範例
result = strategy_health_check(wins=7, total=8, is_pf=2.5, oos_pf=1.1)
for k, v in result.items():
    print(f"  {k}: {v}")