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.
PROPORTIONAL MODEL EXAMPLE
How Bookmakers Hide Their Overround
At 1.91 on both outcomes, overround is 4.712042%. Proportional normalization assumes 50% per side, giving fair odds 2.00 and an expected loss of 4.50% per unit wagered. The prices alone do not prove that the true probabilities are 50/50.
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. Each produces probability estimates under its own margin-allocation assumptions.
P_fair = (1 / O_i) / Σ(1 / O_k) 
Expected Value, Overround & Model Assumptions
Formal derivation of EV = (P_win × (Odds - 1)) - (P_loss × 1). Distinguishes quoted overround from model expected loss and explains why the probability estimate determines selection EV.
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 Models for Evaluating a Bet
Overround and expected loss
At 1.91, break-even probability is 1/1.91≈52.356%. With a50% win probability, each unit has EV=-4.50%. Over 1000 fixed one-unit bets the expected loss is 45 units; the fraction of the starting bankroll depends on its size.
Log-Wealth Maximization
Kelly maximizes expected log growth for specified probabilities and payouts. Estimation error, finite-horizon losses and operational bankroll limits remain.
A Market Price Benchmark
A no-vig closing line is a model-based benchmark available after the market closes. CLV measures price improvement against it; it does not establish true probability or guarantee profit.
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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