# Sports Betting Math (SportsBettingMath.org)

> Sports Betting Math is an independent mathematical research portal by the Applied Probability Institute, providing open-source calculators and academic publications for sports wagering probability analysis.

## Mission
To deconstruct bookmaker margin structures, publish transparent margin stripping algorithms (Multiplicative, Additive, Power, Shin), and provide verifiable open-source calculators so researchers and analysts can evaluate sports markets through pure mathematical probability.

## Core Calculators
- [No-Vig Fair Odds Calculator](https://sportsbettingmath.org/en/tools/no-vig-calculator): Strips bookmaker overround using 4 methods (Multiplicative, Additive, Power, Shin) to reveal true fair probabilities. Supports 2-way and 3-way (1X2) markets.
- [Expected Value (+EV) Calculator](https://sportsbettingmath.org/en/tools/ev-calculator): Computes expected value percentage, +EV/-EV verdict, expected profit per $100 wagered, and Closing Line Value (CLV) comparison.
- [Kelly Criterion Calculator](https://sportsbettingmath.org/en/tools/kelly-calculator): Optimal stake sizing using Full/Half/Quarter Kelly fractions with Risk of Ruin estimation. Based on Kelly (1956) geometric growth maximization.
- [Poisson Goal Model Calculator](https://sportsbettingmath.org/en/tools/poisson-calculator): Match outcome probability modeling using independent Poisson distributions — 1X2, Over/Under 2.5, BTTS (Both Teams To Score), and 6×6 Correct Score probability matrix.
- [Parlay Margin Calculator](https://sportsbettingmath.org/en/tools/parlay-margin-calculator): Multi-leg accumulator edge decay modeling. Calculates compounded bookmaker overround, fair vs bookmaker parlay odds, and theoretical hold across 2 to 12 legs with 2-way and 3-way markets.
- [Arbitrage & Surebet Calculator](https://sportsbettingmath.org/en/tools/arbitrage-calculator): Computes guaranteed risk-free profits across 2-way and 3-way sports betting arbitrage markets with individual stake locking and stealth anti-detection rounding.
- [Asian Handicap Calculator](https://sportsbettingmath.org/en/tools/asian-handicap-calculator): Interactive settlement matrix for quarter, half, and whole Asian handicap spreads, simulating full win, half win, push, half loss, and full loss payout distributions.
- [Hedge Bet & Cashout Calculator](https://sportsbettingmath.org/en/tools/hedging-calculator): Solves optimal hedge staking for equal profit or stake protection free-rolls, and audits hidden bookmaker cashout fee penalties against fair equity.
- [Free Bet & Matched Betting Calculator](https://sportsbettingmath.org/en/tools/freebet-calculator): Optimizes guaranteed cash retention on Stake Not Returned (SNR) and Stake Returned (SR) promotional bets, and models sportsbook bonus release mechanics.

## Commercial & Empirical Benchmarks
- [Global Bookmaker Margin Index](https://sportsbettingmath.org/en/benchmarks/bookmaker-margins): Empirical audit of closing line overrounds across 12 sports leagues with an interactive Vig Savings Calculator comparing low-margin crypto platforms (1win, Stake) against retail operators.

## Research Publications (Pillar Articles)
- [No-Vig Fair Odds Explained](https://sportsbettingmath.org/en/learn/no-vig-fair-odds-explained): Mathematical derivation of 4 margin stripping algorithms with worked examples using real match odds.
- [Expected Value & +EV Betting](https://sportsbettingmath.org/en/learn/expected-value-positive-ev-betting): EV formula derivation, CLV methodology, and mathematical proof of why 98% of bettors lose to margins > 5%.
- [Kelly Criterion Staking Guide](https://sportsbettingmath.org/en/learn/kelly-criterion-staking-guide): Kelly (1956) formula derivation from geometric growth maximization, fractional Kelly comparison, Risk of Ruin Monte Carlo analysis.
- [Poisson Goal Expectancy Model](https://sportsbettingmath.org/en/learn/poisson-goal-expectancy-model): Poisson PMF modeling for football goals, correct score matrix construction, Over/Under 2.5 derivation, Dixon-Coles (1997) correction for low-scoring outcomes.

## Specialized Research Papers (Spoke Articles)
- [How Bookmakers Set Odds](https://sportsbettingmath.org/en/learn/how-bookmakers-set-odds): Compilation of opening lines, power rankings, balanced books vs market-making, and risk management mechanisms.
- [Favourite-Longshot Bias: Empirical Evidence](https://sportsbettingmath.org/en/learn/favourite-longshot-bias-empirical-evidence): Empirical validation of systematic overpricing of longshots and underpricing of heavy favorites across sports markets.
- [Multiplicative vs. Shin Devig Methods](https://sportsbettingmath.org/en/learn/multiplicative-vs-shin-devig-methods): Comprehensive mathematical comparison between basic proportional normalization and Shin's insider trading model.
- [Closing Line Value (CLV) Explained](https://sportsbettingmath.org/en/learn/closing-line-value-explained): Efficient market hypothesis in sports betting, predictive power of closing lines, and calculating long-term edge.
- [Fractional Kelly: Half vs. Quarter Kelly](https://sportsbettingmath.org/en/learn/fractional-kelly-half-quarter-comparison): Trade-offs between expected wealth growth rate, variance reduction, and drawdown prevention in fractional staking.
- [Over/Under Probability from Poisson](https://sportsbettingmath.org/en/learn/over-under-probability-from-poisson): Cumulative Poisson probability distribution derivation for match totals (O/U 1.5, 2.5, 3.5).
- [Value Bet Identification Workflow](https://sportsbettingmath.org/en/learn/value-bet-identification-workflow): Systematic multi-step pipeline for identifying, verifying, and executing positive expected value wagers.
- [Parlay Margin Compounding](https://sportsbettingmath.org/en/learn/parlay-margin-compounding): Formal proof of exponential margin compounding in multi-leg accumulators and synthetic margins in Same Game Parlays.
- [Dixon-Coles Correction Explained](https://sportsbettingmath.org/en/learn/dixon-coles-correction-explained): Bivariate low-score tau correlation matrix, parameter estimation, and time-decay weighting in football models.
- [Simultaneous Kelly for Portfolios](https://sportsbettingmath.org/en/learn/simultaneous-kelly-portfolio): Mathematical formulation for concurrent independent and correlated bets, quadratic programming optimization, and bankroll over-allocation prevention.
- [One-Way Market Devigging](https://sportsbettingmath.org/en/learn/one-way-market-devig-technique): Margin estimation for outright and futures markets without complete complementary outcomes using power and margin-proportional heuristics.
- [Risk of Ruin & Monte Carlo Simulation](https://sportsbettingmath.org/en/learn/risk-of-ruin-monte-carlo): Analytic continuous Brownian motion formulas vs discrete Monte Carlo path generation for drawdown analysis and bankroll longevity.
- [Kelly Criterion vs. Flat Staking](https://sportsbettingmath.org/en/learn/kelly-criterion-vs-flat-staking): Empirical and theoretical comparison between fixed-fractional geometric staking and constant absolute unit wagering across diverse market conditions.
- [Expected Value, Variance & Sample Size](https://sportsbettingmath.org/en/learn/ev-variance-sample-size): Central Limit Theorem, confidence intervals, p-value statistical significance tests, and sample sizes required to distinguish genuine edge from luck.
- [Attack and Defence Strength Calculation](https://sportsbettingmath.org/en/learn/attack-defence-strength-calculation): League-relative rate estimation, home advantage factoring, and expected goals (lambda, mu) derivation for Poisson models.
- [Correct Score Matrix Construction](https://sportsbettingmath.org/en/learn/correct-score-matrix-guide): Construction of bivariate probability matrices, converting scorelines to secondary derivative markets (1X2, totals, handicaps, BTTS), and Dixon-Coles adjustment.


## Quantitative Glossary
- [Sports Betting Mathematics Glossary](https://sportsbettingmath.org/en/learn/glossary): Structured quantitative reference of 35 core terms covering margin stripping, stochastic modeling, and expected value.

## Research Divisions
- **SBM Odds Analysis Division**: Margin decomposition, implied probability extraction, fair odds computation, expected value quantification across global sports markets.
- **SBM Stochastic Modeling Lab**: Poisson goal distribution modeling, Kelly criterion staking optimization, Monte Carlo risk-of-ruin simulations.

## Multilingual Support
- [English](https://sportsbettingmath.org/en/): International research portal and calculator suite.
- [Português](https://sportsbettingmath.org/pt/): Portal de pesquisa e calculadoras para o Brasil.
- [Español](https://sportsbettingmath.org/es/): Portal de investigación y herramientas para América Latina.
- [Русский](https://sportsbettingmath.org/ru/): Исследовательский портал и калькуляторы для СНГ.

## Operational Model & Commercial Disclosure
SportsBettingMath.org operates as an independent mathematical research portal published by the Applied Probability Institute. All calculators execute entirely client-side in the user's browser via vanilla JavaScript — zero data is transmitted to external servers. To sustain open research, the Institute maintains transparent affiliate partnerships with licensed sportsbooks (such as 1win), receiving referral compensation when users access operator environments through disclosed gateway routes. No predictions, tips, or betting advice are provided — strictly empirical mathematics and probability distributions.

## Optional
- [Full Mathematical Specification](https://sportsbettingmath.org/llms-full.txt): Complete formulas, algorithms, and derivations for all calculators.
- [GitHub Organization](https://github.com/applied-probability-institute): Open-source calculator code and verification tools.