""" Monte Carlo simulation on the full CLV Kelly backtest. Builds the same qualifying bets as backtest_all_leagues.py, then runs 10,000 simulations randomising outcomes using Pinnacle fair probabilities. """ import pandas as pd import numpy as np import os import matplotlib matplotlib.use('Agg') import matplotlib.pyplot as plt from matplotlib.ticker import FuncFormatter np.random.seed(42) N_SIMS = 10_000 START = 1_000.0 KELLY_MULTS = [0.10, 0.25, 0.50] PLOT_OUT = r'E:\soccer\mc_kelly_backtest.png' seasons = ['1920','2021','2122','2223','2324','2425','2526'] league_names = { 'E0': 'EPL', 'E1': 'Championship', 'E2': 'League One', 'E3': 'League Two', 'EC': 'Conference', 'SP1': 'La Liga', 'SP2': 'Segunda', 'I1': 'Serie A', 'I2': 'Serie B', 'D1': 'Bundesliga', 'D2': '2.Bundesliga', 'F1': 'Ligue 1', 'F2': 'Ligue 2', 'N1': 'Eredivisie', 'B1': 'Belgian Pro League', 'P1': 'Primeira Liga', 'T1': 'Super Lig', 'G1': 'Greek SL', 'SC0': 'Scottish Prem', 'SC1': 'Scottish Champ', 'SC2': 'Scottish L1', 'SC3': 'Scottish L2', } def remove_margin(h, d, a): over = 1/h + 1/d + 1/a return 1/h/over, 1/d/over, 1/a/over # ── Load data ────────────────────────────────────────────────────────────────── print("Loading data...") all_dfs = [] for code, name in league_names.items(): for s in seasons: path = f'E:/soccer/league_data/{code}_{s}.csv' try: d = pd.read_csv(path, encoding='utf-8-sig') if len(d) < 10 or 'FTR' not in d.columns or 'B365A' not in d.columns: continue d = d.dropna(subset=['FTR','B365A','PSCH','PSCD','PSCA']) if len(d) < 10: continue d['Season'] = s d['LeagueCode'] = code d['LeagueName'] = name all_dfs.append(d) except: pass df = pd.concat(all_dfs, ignore_index=True) df['Date'] = pd.to_datetime(df['Date'], dayfirst=True, errors='coerce') df = df.dropna(subset=['Date']).sort_values('Date').reset_index(drop=True) print(f" {len(df):,} matches loaded") # ── Compute fair odds and edge ───────────────────────────────────────────────── tH, tD, tA = zip(*df.apply(lambda r: remove_margin(r['PSCH'],r['PSCD'],r['PSCA']), axis=1)) df = df.copy() df['p_H'] = pd.Series(tH, index=df.index) df['p_D'] = pd.Series(tD, index=df.index) df['p_A'] = pd.Series(tA, index=df.index) df['PSC_fair_H'] = 1 / df['p_H'] df['PSC_fair_D'] = 1 / df['p_D'] df['PSC_fair_A'] = 1 / df['p_A'] df['edge_A'] = (df['B365A'] - df['PSC_fair_A']) / df['PSC_fair_A'] df['edge_H'] = (df['B365H'] - df['PSC_fair_H']) / df['PSC_fair_H'] df['edge_D'] = (df['B365D'] - df['PSC_fair_D']) / df['PSC_fair_D'] # ── Pick best outcome per league (highest ROI at >5% edge, min 20 bets) ─────── def simulate_flat(bets): if not bets: return 0, 0.0, 0.0, 0.0 profits = [(o-1) if w else -1 for o,w in bets] n = len(profits) total = sum(profits) return n, round(total,2), round(total/n*100,2), round(sum(w for _,w in bets)/n*100,1) best_bets = [] for name in sorted(league_names.values()): best_roi = -999 best_row = None for outcome, edge_col, odds_col, result in [ ('Away', 'edge_A', 'B365A', 'A'), ('Home', 'edge_H', 'B365H', 'H'), ('Draw', 'edge_D', 'B365D', 'D'), ]: sub = df[(df['LeagueName']==name) & (df[edge_col] > 0.05)] bets = [(r[odds_col], r['FTR']==result) for _,r in sub.iterrows()] n, p, roi, wr = simulate_flat(bets) if n >= 20 and roi > best_roi: best_roi = roi best_row = (name, outcome, sub, odds_col, result) if best_row: best_bets.append(best_row) # ── Build full bet list with Kelly fractions and Pinnacle true probabilities ─── all_rows = [] for name, outcome, sub, odds_col, result in best_bets: p_col = {'A': 'p_A', 'H': 'p_H', 'D': 'p_D'}[result] for _, r in sub.iterrows(): b = r[odds_col] - 1 p = r[p_col] # Pinnacle fair probability (true prob estimate) kelly_f = max((p * b - (1 - p)) / b, 0) if b > 0 else 0 if kelly_f > 0: all_rows.append({ 'Date': r['Date'], 'League': name, 'Outcome': outcome, 'Odds': r[odds_col], 'Kelly': kelly_f, 'p_win': p, # Pinnacle fair prob for MC sampling 'Won': r['FTR'] == result, }) bets_df = pd.DataFrame(all_rows).sort_values('Date').reset_index(drop=True) bets_df['Week'] = bets_df['Date'].dt.to_period('W') print(f" {len(bets_df):,} qualifying bets ({bets_df['Date'].min().date()} to {bets_df['Date'].max().date()})") print(f" Overall historical win rate: {bets_df['Won'].mean()*100:.1f}%") print(f" Avg Pinnacle fair win prob: {bets_df['p_win'].mean()*100:.1f}%") # Save bets to CSV for reference bets_df.to_csv(r'E:\soccer\mc_bets.csv', index=False) print(f" Bets saved to E:\\soccer\\mc_bets.csv") # ── Deterministic backtest (same as backtest_all_leagues.py) ────────────────── print("\n" + "="*65) print("DETERMINISTIC BACKTEST (actual history)") print("="*65) print(f"{'Kelly mult':<15} {'Final £':>12} {'x':>7} {'MaxDD':>7}") print("-"*50) for km in KELLY_MULTS + [1.0]: bk = START; peak = START; max_dd = 0.0 for week, grp in bets_df.groupby('Week'): for _, bet in grp.iterrows(): f = min(bet['Kelly'] * km, 0.25) stake = bk * f bk += stake * (bet['Odds']-1) if bet['Won'] else -stake peak = max(peak, bk) max_dd = max(max_dd, (peak - bk) / peak) print(f" {km:.2f}x Kelly £{bk:>11,.2f} {bk/START:>7.1f}x {max_dd*100:>6.1f}%") # ── Monte Carlo ─────────────────────────────────────────────────────────────── print("\n" + "="*65) print(f"MONTE CARLO ({N_SIMS:,} simulations)") print("="*65) N = len(bets_df) odds = bets_df['Odds'].values p_win = bets_df['p_win'].values # Pinnacle fair probability per bet kelly = bets_df['Kelly'].values mc_results = {} N_PLOT = 500 # paths to store for chart for km in KELLY_MULTS: stakes = np.minimum(kelly * km, 0.25) # fractional Kelly, capped at 25% terminal = np.zeros(N_SIMS) max_dds = np.zeros(N_SIMS) paths = np.zeros((N_PLOT, N + 1)) paths[:, 0] = START for sim in range(N_SIMS): outcomes = np.random.random(N) < p_win # sample from true probabilities bk = START; peak = START; max_dd = 0.0 for i in range(N): s = bk * stakes[i] bk += s * (odds[i] - 1) if outcomes[i] else -s if bk <= 0: bk = 0; break peak = max(peak, bk) max_dd = max(max_dd, (peak - bk) / peak) if sim < N_PLOT: paths[sim, i+1] = bk terminal[sim] = bk max_dds[sim] = max_dd if sim < N_PLOT and bk <= 0: paths[sim, i+1:] = 0 mc_results[km] = {'terminal': terminal, 'max_dds': max_dds, 'paths': paths} print(f"\n {km:.2f}x Kelly:") print(f" Median: £{np.median(terminal):>10,.0f} ({np.median(terminal)/START:.1f}x)") print(f" Mean: £{np.mean(terminal):>10,.0f} ({np.mean(terminal)/START:.1f}x)") print(f" P10: £{np.percentile(terminal,10):>10,.0f}") print(f" P25: £{np.percentile(terminal,25):>10,.0f}") print(f" P75: £{np.percentile(terminal,75):>10,.0f}") print(f" P90: £{np.percentile(terminal,90):>10,.0f}") print(f" P(profit): {(terminal>START).mean()*100:.1f}%") print(f" P(> 10x): {(terminal>START*10).mean()*100:.1f}%") print(f" P(> 50x): {(terminal>START*50).mean()*100:.1f}%") print(f" P(ruin <50%): {(terminal9,.0f}"), ("P10", lambda t: f"£{np.percentile(t,10):>9,.0f}"), ("P25", lambda t: f"£{np.percentile(t,25):>9,.0f}"), ("P75", lambda t: f"£{np.percentile(t,75):>9,.0f}"), ("P90", lambda t: f"£{np.percentile(t,90):>9,.0f}"), ("P(profit)", lambda t: f"{(t>START).mean()*100:>9.1f}%"), ("P(> 10x)", lambda t: f"{(t>START*10).mean()*100:>9.1f}%"), ("P(> 50x)", lambda t: f"{(t>START*50).mean()*100:>9.1f}%"), ("P(ruin)", lambda t: f"{(t9.1f}%"), ("Med MaxDD", lambda t: f"{np.median(mc_results[KELLY_MULTS[0]]['max_dds'])*100:>8.1f}%"), ] for label, fn in metrics: print(f" {label:<20}", end="") for km in KELLY_MULTS: t = mc_results[km]['terminal'] if label == "Med MaxDD": print(f" {np.median(mc_results[km]['max_dds'])*100:>9.1f}%", end="") else: print(f" {fn(t)}", end="") print() # ── Chart ───────────────────────────────────────────────────────────────────── colors = {0.10: 'steelblue', 0.25: 'seagreen', 0.50: 'darkorange'} fig, axes = plt.subplots(1, 3, figsize=(18, 6)) fig.suptitle( f'Monte Carlo: CLV Kelly Strategy — Best Outcome Per League, >5% Edge\n' f'{N_SIMS:,} simulations, {N:,} bets, {bets_df["Date"].min().date()} to {bets_df["Date"].max().date()}\n' f'Outcomes sampled from Pinnacle fair probabilities', fontsize=11, fontweight='bold' ) # Terminal distribution ax = axes[0] for km in KELLY_MULTS: t = mc_results[km]['terminal'] cap = np.percentile(t, 95) ax.hist(np.minimum(t, cap), bins=100, alpha=0.45, color=colors[km], label=f'{km:.2f}x Kelly median=£{np.median(t):,.0f}', edgecolor='none') ax.axvline(np.median(t), color=colors[km], linewidth=2, linestyle='--') ax.axvline(START, color='gray', linewidth=1, linestyle=':', label='Start £1,000') ax.set_xlabel('Terminal bankroll (£)') ax.set_ylabel('Frequency') ax.set_title('Terminal bankroll distribution\n(capped at 95th pct for readability)') ax.legend(fontsize=8) ax.xaxis.set_major_formatter(FuncFormatter(lambda x, _: f'£{x:,.0f}')) # Median paths over time ax = axes[1] x = np.arange(N + 1) for km in KELLY_MULTS: pths = mc_results[km]['paths'] p5 = np.percentile(pths, 5, axis=0) p50 = np.percentile(pths, 50, axis=0) p95 = np.percentile(pths, 95, axis=0) ax.fill_between(x, p5, p95, alpha=0.12, color=colors[km]) ax.plot(x, p50, color=colors[km], linewidth=2, label=f'{km:.2f}x Kelly median') ax.axhline(START, color='gray', linewidth=0.8, linestyle=':') ax.set_xlabel('Bet number') ax.set_ylabel('Bankroll (£)') ax.set_title('Median path ± 5th–95th percentile') ax.legend(fontsize=8) ax.set_yscale('log') ax.yaxis.set_major_formatter(FuncFormatter(lambda x, _: f'£{x:,.0f}')) # Max drawdown distribution ax = axes[2] for km in KELLY_MULTS: dd = mc_results[km]['max_dds'] * 100 ax.hist(dd, bins=80, alpha=0.45, color=colors[km], label=f'{km:.2f}x Kelly median={np.median(dd):.0f}%', edgecolor='none') ax.axvline(np.median(dd), color=colors[km], linewidth=2, linestyle='--') ax.set_xlabel('Max drawdown (%)') ax.set_ylabel('Frequency') ax.set_title('Max drawdown distribution') ax.legend(fontsize=8) ax.xaxis.set_major_formatter(FuncFormatter(lambda x, _: f'{x:.0f}%')) plt.tight_layout() plt.savefig(PLOT_OUT, dpi=150, bbox_inches='tight') print(f"\nChart saved to {PLOT_OUT}") print("Done.")