Research Publications
Independent mathematical research, closed-form derivations, and empirical probability studies for sports wagering efficiency.
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_win × (Odds - 1)) - (P_loss × 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!