SPORTS BETTING MATH APPLIED PROBABILITY INSTITUTE
INDEPENDENT MATHEMATICAL RESEARCH

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.

4 Calculators
16 Research Pages
4 Languages
12+ Formulas
0% Data Transmitted
100% Client-Side
Open Source
Est. 2026
1 Understand the Math
2 Use the Tools
3 Find +EV Edges

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.

Retail Bookmaker Line VIG: 4.71%
Side A (Implied: 52.36%) 1.91 (-110)
Side B (Implied: 52.36%) 1.91 (-110)
Total bookmaker book: 104.71% — an insurmountable hurdle for recreational bettors.
Multiplicative De-Vig
P_fair = P_implied / 1.0471
Zero-Vig Fair Odds FAIR: 100.00%
True Probability Side A 2.00 (50.00%)
True Probability Side B 2.00 (50.00%)
De-vigged baseline reveals pure event probability for identifying +EV wagers.
RESEARCH ARCHITECTURE

Research Pillars

Explore the four mathematical disciplines that define quantitative sports analysis, odds de-vigging, and edge quantification.

📐 PILLAR 01 // FAIR ODDS & MARGIN ANALYSIS
PILLAR 1

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.

Core Formula: P_fair = (1 / O_i) / Σ(1 / O_k)
📈 PILLAR 02 // EXPECTED VALUE & +EV IDENTIFICATION
PILLAR 2

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%.

Core Formula: EV = (P × O) - 1
🎯 PILLAR 03 // KELLY CRITERION & BANKROLL OPTIMIZATION
PILLAR 3

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.

Core Formula: f* = (b·p - q) / b
PILLAR 04 // POISSON DISTRIBUTION & MATCH MODELING
PILLAR 4

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.

Core Formula: P(X=k) = (λ^k · e^-λ) / k!

MATHEMATICAL AXIOMS

Three Immutable Laws of Sports Betting Markets

01 // The Vig Tax

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.

02 // Kelly Sizing

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.

03 // Closing Line Value

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.

TEST YOUR MATHEMATICAL EDGE

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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