The Applied Probability Institute is an independent quantitative research collective dedicated to open-access mathematical modeling, empirical market benchmarks, and reproducible stochastic algorithms across sports wagering markets and competitive information economics.
| Repository | Focus & Domain | Language / Stack | License |
|---|---|---|---|
no-vig-fair-odds |
Margin stripping algorithms (Multiplicative, Additive, Power, Shin's insider fraction |
Python 3.11 / SciPy | MIT |
kelly-criterion-sim |
Log-wealth maximization, fractional Kelly scaling & Monte Carlo risk-of-ruin engine | Python 3.11 / NumPy | MIT |
poisson-match-models |
Independent & bivariate Poisson goal expectancy distributions for 1X2 and over/under markets | Python 3.11 / Poisson | MIT |
research-papers |
10,000 EPL fixture closing line benchmark dataset, reproducibility notebooks & BibTeX citations | Open Access / CSV / Py | CC-BY-4.0 |
-
Margin Decomposition & Market Clearing: Quantitative extraction of true implied probability densities from multi-way bookmaker price vectors utilizing Multiplicative, Power, and Shin's informed trader parameter (
$z$ ) equilibrium models. -
Optimal Capital Growth & Drawdown Control: Theoretical parameterization of John L. Kelly Jr.'s log-optimal betting criterion (
$f^* = \frac{bp - q}{b}$ ), fractional volatility reduction ($f_{\text{half}} = 0.50 \cdot f^*$ ), and asymptotic Brownian ruin boundaries under finite bankroll horizons. -
Discrete Goal Expectancy & Count Distributions: Stochastic modeling of association football and ice hockey scorelines via bivariate Poisson processes (
$\lambda_H, \lambda_A$ ) accounting for low-scoring covariance and draw deflation. - Empirical Closing Line Efficiency: Longitudinal econometric tracking of Closing Line Value (CLV), measuring pricing efficiency, liquidity formation, and the favorite-longshot bias across Tier-1 European football competitions.
All research papers, empirical benchmark datasets, and interactive zero-runtime JavaScript calculators are accessible open-access at sportsbettingmath.org:
- No-Vig Fair Odds Calculator: sportsbettingmath.org/tools/no-vig-calculator/
- Kelly Criterion Bankroll Tool: sportsbettingmath.org/tools/kelly-calculator/
- Bivariate Poisson Match Forecaster: sportsbettingmath.org/tools/poisson-calculator/
- Arbitrage & Market Inefficiency Scanner: sportsbettingmath.org/tools/arbitrage-calculator/
- 10,000-Match Overround & CLV Study: sportsbettingmath.org/research/overround-decomposition-study/
- Bookmaker Margins Benchmark: sportsbettingmath.org/benchmarks/bookmaker-margins/
If you utilize our algorithms, simulation suites, or benchmark datasets in your academic research or financial modeling, please cite:
@article{api2026overround,
title={Empirical Margin Decomposition, Closing Line Efficiency, and Information Fraction Estimation in European Football Wagering: A 10,000-Match Study},
author={{Applied Probability Institute}},
journal={Applied Probability Institute Research Hub},
year={2026},
url={https://sportsbettingmath.org/research/overround-decomposition-study/}
}