Science of Sports Betting

Master essential concepts, and mathematical, behavioral, and statistical techniques for developing a systematic approach to winning.

Course 1: Top-Down

Middling, arbitrage, reverse engineering, bankroll management, bet sizing, closing line value.
Includes free access to Foundations for Sports Betting.

Rolling enrollment. Begin today.

Course 2: Bottom-Up

Calibration, backtesting, shrinkage, linear regression, logistical regression, statistical distributions, case studies.

Rolling enrollment. Begin today.

Course 1 Top-Down

Critical betting concepts, including bet types (moneyline, spread, total), odds formats (American, decimal, fractional), conversion between odds formats, vig, overround, breakeven probability, arbitrage and middles, synthetic hold and vig, useful rules of thumb, Excel calculator for odds conversion, breakeven probability, vig, and arbitrage.
Understanding sports betting markets, reverse engineering market lines, alternative lines, systematic market analysis, NBA alternative lines case study, empirical distributions, statistical assumptions, random variables, distributions, probability, expected value, edge, standard deviation and variance, Gaussian distribution, applying the empirical and Gaussian distributions, adjusting the empirical distribution for reverse engineering, exploratory data analysis, exploratory observations about hockey scoring, introduction to data analysis in R, NHL historical odds data.
Different approaches to profitable sports betting (top-down, bottom-up, hybrid), inter-book mispricings, line grinding, intra-book coherence, palps, dynamic pricing, line movements, steam chasing, fundamental modeling and origination, methods of evaluation: naive backtesting, coherent backtesting, shrinking, closing line value, sample size needed to accurately evaluate edge, volatility of backtesting, practical advice and caveats, market coherence, calibration tables, z-scores, goodness-of-fit test, chi-square test, p-value.
Regression: definition, interpretation, residuals, and other key concepts, illustration of regression on spreads, interpreting regression output in Excel,market efficiency, market resistance, market support, parimutuel and fixed odds, fractional odds, definition of closing line value: definition, conceptual motivation, and empirical justification, real-data demonstration of closing line value, CLV framework for moneylines, quantifying closing line value, relationship between CLV and EV, real data illustration.
Closing line value for spreads and totals, derivation of the magic CLV formula, methods for calculating CLV: alternative lines, full, partial graded and partial market, CLV calculation in NFL spreads and totals, alternative lines approach, naive empirical and centered empirical approaches, partial graded: historical empirical and historical Gaussian approaches, partial market, teasers, definition of middling, valuing points, Gaussian distribution for valuing points in NBA, valuing points in NFL, top-down approach for middling NHL season-long points totals, consequences of mislocating the middle, middling player props, risks and challenges in estimating variance, sensitivity analysis, caveats of middling.
Record keeping, logging bets, St. Petersburg paradox, additive vs. multiplicative dynamics, maximizing growth rate, loss aversion, prospect theory, maximum utility, illustration of overbetting and its consequences, basics of optimal betting, motivation for Kelly criterion, components of an edge: information, execution, and modeling; where to find an edge, review of arbitrage, relation between arbitrage, Kelly criterion, and hedging, hedging versus holding, real-time hedging.
“JM” is a renowned sports bettor and market maker leading a dynamic licensed Maltese syndicate that is set up to specialize in US sports trading.

Course 2 Bottom-Up

Review of top-down approach, introduction to bottom-up modeling, hybrid approach, key elements of bottom-up approach: data, modeling, scalability, core data considerations, data acquisition and quality control, data management, file management, directory structure, CSV, databases, data updating: manual and automated methods, response variables, crucial modeling considerations, common distributions (Gaussian, binomial, multinomial, Poisson, logistic), methods (ad hoc, linear regression, logistic regression, deep learning), model development life cycle, application of modeling life cycle to NBA totals: data exploration, model development, evaluation, premature averaging, new data exploration, different response variables, in-sample backtest, out-of-sample backtest, testing assumptions, extracting insights from model differences, positive and negative correlation, variable identification and design, interaction terms.
Review of bottom-up modeling, best practices and precautions, role of narrative, independent vs. comparative evaluations, coherence checks, explanation checks, residual sum of squares, market checks: backtesting, shrinkage, CLV, flat vs. Kelly betting, real-data illustration, variable development, moving averages and weight averages, out-of-sample vs. in-sample testing, common pitfalls, ROI backtests, calibration, extreme probabilities and extreme residuals, player-specific variables, important differences between backtesting and live betting.
Explanation of shrinkage, applications for model evaluation, model refinement, model comparison, and live bet execution, loss functions: squared deviation, absolute deviation, and log loss, application of shrinkage to modeling totals, comparison between calibration and shrinkage for model evaluation, shrinkage weight as a model evaluation metric, variable selection using shrinkage, using shrunk results to evaluate bets, practical implications, illustration of ROI with and without shrinking, shrinkage using regression, model assumptions underlying different shrinkage approaches, comparison of different approaches, additional shrinking possibilities and review.
Objectives in optimal betting, ingredients of optimal betting, the classical Kelly criterion formula and its implications, illustration of Kelly criterion, fractional Kelly, conceptual and theoretical justification for fractional Kelly, practical considerations of Kelly betting, limitations of the Kelly criterion, Kelly criterion for multiple independent outcomes, implementation of joint Kelly criterion in Mathematica, Kelly criterion for parlays, positive and negative correlation, multiplicative advantage and disadvantage, computing growth rate under negative correlation, multiplayer events, illustration in golf betting, expected value, edge and growth rate under negative correlation, computing growth rate under positive correlation, same-game parlays and related outcomes, illustration in NHL same-game alternative totals, expected value, edge and growth rate under positive correlation, computing odds and growth rate in parimutuel betting, application to horse racing, relationship between Kelly criterion and maximum EV in parimutuel betting, application of Kelly criterion to motivating question, review of the Kelly principle, formal and practical considerations for bet sizing.
Modeling framework: structuring and fitting, review of linear regression, regression for binary outcomes, logistic regression: definition, assumptions and fitting, shrinkage for probabilities and moneylines, log loss function, linear shrinkage, relationship between probability shrinkage and fractional Kelly, shrinkage of log probabilities, benefits and implications, consensus lines, models for player/team relative ability, application to MLB team strength, model assessment and practical implications, relationship between edge and shrinkage weight, binomial distribution, Poisson distribution, Gaussian approximation to the binomial distribution, Poisson regression: definition, basic properties, and core assumptions, application of Poisson regression to baseball run totals, generalize linear models, hybrid modeling, robustness checks, some machine learning techniques.
Four in-depth case studies showing real applications of course concepts in profitable betting: examples from NFL, NBA, NHL and MLB: NBA case study using a hybrid approach to implement deep learning on proprietary NBA data from Vantage Sports, NBA event-level data, performance under proprietary data vs. public data, MLB case study to model league leaders by fitting a bottom up model under a shortened season, finding edges in unprecedented situations, naive modeling of extreme values, inefficient and ill-fated attempts, extreme value theory, top-down model for coherence in NHL moneyline, puck line and totals, Skellam distribution, application of shrinkage, leveraging parameter uncertainty to price extreme outcomes in NFL season-long win totals markets, Bayesian modeling, consensus lines, parameter uncertainty, prior distributions, beta-binomial distribution, reverse engineering to estimate model parameters, summary of core course concepts and key takeaways.
Dr. William T. Ziemba is the Alumni Professor (Emeritus) of Financial Modeling and Stochastic Optimization in the Sauder School of Business, University of British Columbia and the author of several of the most famous books on gambling.


Harry Crane is Associate Professor and Chancellor’s Excellence Scholar in Statistics, Co-Director of the Graduate Program in Statistics, and Affiliated Faculty in the Graduate Program in Philosophy at Rutgers University.

He is currently Fellow at the London Mathematical Laboratory, and has previously held positions as a Visiting Scholar in Mathematics at UC Berkeley, Research Associate at the RAND Corporation, and Research Fellow at the Foreign Policy Research Institute. He is also a co-founder of Researchers.One, a platform for scholarly publication and initiative for intellectual reform.

Harry received his PhD in Statistics from the University of Chicago and BA in Mathematics, Economics and Actuarial Science from the University of Pennsylvania.

He has profitably applied statistical and other techniques to successful sports betting and other advantage gambling opportunities and has discussed these experiences on the Business of Betting podcast, the Pinnacle podcast, the Political Trade Podcast, the Artful Trader, Old Bull TV, and other media outlets.

He is the author of Probabilistic Foundations of Statistical Network Analysis.


Twitter: @harrydcrane

Philip Maymin is a professor of analytics and the director of the Master of Science in Business Analytics program at the Fairfield University Dolan School of Business where among other things he teaches both an undergraduate sports analytics course and a graduate sports analytics course. He is the founding managing editor of Algorithmic Finance and the co-founder and co-editor-in-chief of the Journal of Sports Analytics. He is the Chief Technology Officer and Chief Operating Officer for, an Insight Partner with Essentia Analytics, an advisor to Athletes Unlimited, and an affiliate of the Langer Mindfulness Institute, and has been an analytics consultant with several NBA teams.

He holds a PhD in Finance from the University of Chicago, a Master’s in Applied Mathematics from Harvard University, and a Bachelor’s in Computer Science from Harvard University. He also holds a J.D. and is an attorney-at-law admitted to practice in California. He has been a portfolio manager at Long-Term Capital Management, Ellington Management Group, and his own hedge fund.

He was awarded a Wolfram Innovator Award in 2015. He has won numerous coding challenges and hackathons. He was named one of the Top 50 Data and Analytics Professionals in the US and Canada in 2018. He is the only person to have won both the Grand Prize for Best Research Paper (2018) and the Hackathon (2020) at the MIT Sloan Sports Analytics Conference.

He is the author of Financial Hacking.


Twitter: @pmaymin

Guest Lecturers

JM is a renowned sports bettor and market maker leading a dynamic licensed Maltese syndicate that is set up to specialize in US sports trading.

Dr. William T. Ziemba is the Alumni Professor (Emeritus) of Financial Modeling and Stochastic Optimization in the Sauder School of Business, University of British Columbia where he taught from 1968-2006.  His PhD is from the University of California, Berkeley.  He currently teaches part time and makes short research visits at various universities.  Recently he is the Distinguished Visiting Research Associate, Systemic Risk Centre, London School of Economics. He is the author, among other things, of Handbook of Investments: Sports and Lottery Betting Markets with Donald Hausch, The Kelly Capital Growth Investment Criterion with legendary hedge fund trader Edward Thorp and Leonard MacLean, and a memoirs financial history book Adventures of a Modern Renaissance Academic in Gambling and Investing. He also, along with Hausch, wrote the famous Beat the Racetrack book which was revised into Dr Z’s Beat the Racetrack which presented their place and show betting system and the Efficiency of Racetrack Betting Markets – the so-called bible of racetrack syndicates. Their 1986 book Betting at the Racetrack extends this efficient/inefficient market approach to simple exotic bets.  Ziemba is revising BATR into Exotic Betting at the Racetrack which adds Pick3,4,5,6, etc. 


Aaron Green
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The course was awesome!! Harry and Philip did a great job of laying the foundations while simultaneously providing value to more experienced bettors with advanced topics and guests. My motivation for taking the course came down to my interest in forecasting and markets in general. I think the lessons here are broadly applicable and will help me in my explorations on where to focus my time and energy on my next big project. I think regardless of whether or not I get into betting more seriously, my investment in your course is worth it...
Tom Quinn
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I have really enjoyed the course. The biggest negative I can think of is that I wish each class was 4 hours, which is definitely a compliment. Overall, great class. I went into the class thinking I needed to refresh / enhance my quant skills to continue to improve. My primary takeaway is that I need to improve my data management and efficiency more than anything.
Michelangelo Whitson
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Enjoyed the course - given me a lot of food for thought and opened my eyes to some different approaches to things too. I like the dynamic between Harry and Philip presenting the course, and if it weren't for the late night start/finish for me in the UK I might contribute more but it's fast-paced enough that there's plenty to digest too.
Caveman Sam
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The class exceeded my expectations! 10/10 would recommend to others. Outside of arbing, my knowledge on sports betting, prior to this class, was minimal. For the novice, this class is exactly what I was looking for. I come from other advantage play worlds so I signed up looking to add more tools to the toolkit. One aspect about the class I really enjoy is the level of detail you guys dive into by taking the time to prove concepts. A lot of “ah ha” moments. Overall the course has been invaluable. Thanks for putting this together!!

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