Art of Sports Betting Analytics

Review of the hidden generator, Bayesian inference, prediction updating, skill versus performance, outcome as unobservable plus measurables plus noise, a basketball in-game totals case study, priors, market information, market efficiency, modeling objectives, distribution of points by quarter, simplicity versus accuracy tradeoff, extrapolation, credibility of new information, correlation, and the fundamental question of inference.

Review of the credibility scale, examples of high and low credibility in sports, credibility and outcome biases, posteriors, the Ballast model, judgment balance prompt, automatic credibility adjustment, model fitting, data-driven selection, an NBA historical example, numerical optimization, objective functions, squared versus absolute errors, Solver, model error, overfitting, backtesting considerations, outliers, and sensitivity analysis.

Model evaluation, positive expected value, advantage betting, definitions, event space, probability, summary statistics, indicator variables, information compression, distribution functions, the Normal curve, discrete versus continuous distributions, mass and cumulative functions, and examples including uniform, binomial, Poisson, Normal, discrete Normal, Gamma, and Beta distributions.

Review of distributions through domains, parameters, shapes, and fitting methods; matching averages and standard deviations; imputing from market odds; a golf example; solving for parameter values; joint probabilities and distributions; empirical distributions; strength-of-schedule style course comparisons; NHL and NBA examples; American-to-decimal conversion; and best-fit optimization.

Review of fitting parameters, maximum likelihood estimation, an NHL example, vanishing floating-point computations, logarithms and exponentials, log-likelihood, mass and density functions, unconstrained maximization with Solver, the relationship with regression, generalized linear models, transformations, an NHL Poisson example, model error, black swans, antifragility, and practical issues such as line shading, early foul trouble, overtime, and hot-hand expectation effects.

Conditional probability, the law of total probability, Bayes theorem, conditional versus unconditional likelihood, priors, posteriors, correlated parlays, prior and posterior distributions, a sharpness-detection example, an NFL quarterback passing-ability example, expected points added per dropback, sums of normally distributed variables, and the homework bridge into the Bayesian Methods portion of the program.

Review of the homework from Course 1, law of total probability, prior and posterior probability, conditional probability, Bayes theorem, an NFL season win totals case study, epistemology, process or aleatory uncertainty, parameter or epistemic uncertainty, Bayesian inference, the hidden generator, overdispersion, Binomial distribution, latent variables, mixed models, noise versus signal, hyperparameters, prior and posterior distributions, and Bayesian updating.

Review of latent variables and mixed models, posterior distribution issues, conjugate priors, prior and posterior hyperparameters, Normal-Normal mixtures, model learning speed, the Beta prior, distribution calibration assumptions, the relationship between the ballast model and mixed models, Binomial-Beta and Beta-Binomial structures, Poisson-Gamma and Negative Binomial models, and Gamma-Gamma and Compound Gamma formulations.

Maximum likelihood with discrete and continuous distributions, an NFL quarterback ratings case study with latent variables and hyperparameters, an NCAA basketball case study with a Binomial-Beta mixed model, properly weighting prior-year win percentages, and practical model issues such as away-home dependence, strength of schedule, margin of victory, and recency.

Rufus Peabody is widely regarded as one of the world's top professional bettors. He is a co-founder of Massey-Peabody Analytics and of Unabated.com, and is co-host of the Bet the Process podcast.

Pairwise comparison models, Bradley-Terry, double Beta distributions, NFL Bayesian power rankings, and the refinements needed to make ranking systems more stable, interpretable, and useful in real betting analysis.

Review of generalized linear models, an introduction to conjugate GLMs, applications to NFL and other sports, and the challenges of working with dynamic covariates in realistic betting environments.