Sports Betting
Math
Fair Odds Engine & +EV Calculator Suite
Deconstruct bookmaker margins using advanced probability models, multiplicative overround stripping, and Poisson goal matrices. Identify positive expected value (+EV) and protect bankroll growth with proven mathematical rigor.
EMPIRICAL PROOF // VIG STRIPPING
How Bookmakers Hide Their Overround
Compare retail odds with true fair probability. When both sides are priced at 1.91 (-110), the true fair odds are 2.00 (+100) and the bookmaker extracts 4.71% vig on every wager.
Research Pillars
Explore the four mathematical disciplines that define quantitative sports analysis, odds de-vigging, and edge quantification.
No-Vig Fair Odds & Bookmaker Overround Decomposition
Mathematical methods for stripping bookmaker margins from odds: Multiplicative, Additive, Power, and Shin's method. Reveals the true implied probability behind every sports betting line.
P_fair = (1 / O_i) / Σ(1 / O_k) Expected Value Formula & Why 98% of Bettors Lose to the Margin
Formal derivation of EV = (P_win × (Odds - 1)) - (P_loss × 1). Demonstrates the mathematical inevitability of long-term loss when betting into margins exceeding 5%.
EV = (P × O) - 1 Kelly Criterion Staking: Full, Half & Quarter Kelly with Risk of Ruin Analysis
Optimal geometric growth bet sizing derived from Kelly's 1956 paper. Covers fractional Kelly variants, tilt protection, drawdown limits, and risk of ruin simulation.
f* = (b·p - q) / b Poisson Goal Expectancy Engine: 1X2, Over/Under & Correct Score Probabilities
Poisson distribution modeling for football and hockey outcomes. Calculates independent goal probabilities for 1X2, Over/Under 2.5, correct score matrices, and BTTS markets.
P(X=k) = (λ^k · e^-λ) / k! MATHEMATICAL AXIOMS
Three Immutable Laws of Sports Betting Markets
Overround Compounds Inevitably
Betting into a standard 5% juice line requires a win-rate above 52.38% just to break even. Over 1,000 wagers, the expected loss to overround exceeds the entire initial bankroll.
Log-Wealth Maximization
Kelly's 1956 formula proves that bet sizing proportional to your edge guarantees maximum long-term geometric compounding while mathematically eliminating the risk of ruin.
The Sharp Market Oracle
The final price before kickoff aggregates all available market information. Consistently beating the closing line is the only reliable predictor of long-term profitability.
Calculate Your Edge on
Top Sportsbooks
Apply de-vigged fair odds, Poisson goal expectations, and Kelly criterion stakes directly into live betting markets.
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