2024-02-07
Understanding randomness in sports betting
Why you can rarely know whether a single bet was the right decision — even after you see the outcome.
Sports Betting & Prediction Markets
The science of betting markets.
I study the statistics and decision theory of sports betting and prediction markets — as a scientist, not a tout. The public conversation is crowded with picks, affiliate rankings, and models marketed as edge. I work the empty seat: the independent voice that says whether a model, a market, or a claim is actually real, and how you would ever know.
My peer-reviewed work formalizes optimal decision-making under uncertainty in betting markets. The throughline: a billion dollars of real money usually out-forecasts a spreadsheet, the closing line is the only honest benchmark, and a single tournament can never validate a probability. I care about calibration and honesty about variance — not selling winners.
Market vs. model
Closing-line value
Optimal staking
Calibration & wisdom of crowds
Positioning
Independent academic — the referee, not a player. No sportsbook affiliations.
I can speak on
- • Prediction markets vs. Wall Street models
- • Why betting markets are hard to beat
- • Forecasting, calibration, and variance
New research · September 2026
Preprint · under review
The profit–bias identity: bookmaker profit as the public’s prediction error
A sportsbook’s expected profit turns out to be an exact affine function of a single quantity: the share of money that lands on the losing side. Under a model of public belief, that quantity is precisely the probability that a representative bettor picks the wrong side — a Bayes error. A book’s revenue is therefore a continuously updated measurement of how often a large population forecasts incorrectly.
Generalizes Levitt
The standard account of bookmaker profit assumes where the money goes is independent of how games end. Relaxing that recovers it exactly as the independent case.
Three channels
The margin resolves into exactly three: the hold, price shading × the public’s lean, and the covariance between betting and outcomes.
A Simpson’s paradox
In 1,139 MLB games, the public’s apparent tendency to back losers is present when games are pooled and absent within every stratum.
What we found, precisely
The public leans heavily toward favorites, but we find no evidence of the price shading that Levitt’s account requires, and the realized margin is indistinguishable from the guaranteed hold.
This is a null on that specific mechanism, not a demonstration of accurate pricing. A margin test carries power against mispricing aligned with where the money sits (88% in simulation) and little against mispricing oriented independently of it (6%). A book could misprice substantially in ways unrelated to the public’s lean and leave no trace in its margin.
As featured in · CNN Business · June 2026
“Think you know who’s going to win the World Cup? So does Goldman Sachs.”
On Goldman Sachs’s World Cup prediction model, I told CNN it amounts to a “fun exercise” that sits further from reality than the prediction markets — because “the information going into the model is a tiny sliver of all the information in the possession of the millions of people who have bet into prediction markets.” Markets aren’t perfect either; they overreact to injuries and lean toward unlikely outcomes — and ultimately it’s impossible to know who was right.
The takeaway
The market is the benchmark; a published model is the thing being measured. Where Goldman diverged — Spain near double the market, England roughly half — it was betting against a billion-dollar market with no stated justification.
Signature theses
The recurring ideas I bring to every model, market, and claim.
Market beats model
Aggregated, money-backed forecasts price in information no hand-built model can see. The bar isn’t picking the favorite — it’s beating the closing market price.
Closing-line value is the only benchmark
The closing line is the single number that actually predicts outcomes. Beating it consistently is the real evidence of edge; everything else is narrative.
Single-tournament probabilities are unfalsifiable
A “26% to win the World Cup” number can never be validated — the tournament runs once. Many published forecasts are confident about quantities that are, in principle, uncheckable.
De-vig before you compare
Sportsbook odds sum past 100%; near-zero-vig exchanges already read as probabilities. Comparing the two without removing the vig is the most common way analyses go wrong.
Wisdom of crowds, with caveats
Aggregated independent forecasts converge to a robust estimate — but herding and favorite–longshot bias are real. The market is the best available estimate, not the truth.
Calibration over picks
A good forecaster is judged by calibration and honesty about variance, not by a winning week. You usually cannot know from one outcome whether a decision was right.
Foundational work
The peer-reviewed and open-source backbone behind the commentary.
PLOS ONE · 2023
A statistical theory of optimal decision-making in sports betting
A decision-theoretic framework for when a bet is objectively good or bad, independent of whether it wins — and what that implies for staking and evaluation under uncertainty.
Preprint · 2026 · under review
The profit–bias identity in sports betting: bookmaker profit as the public’s prediction error
Bookmaker profit is an exact affine function of the share of money on the losing side — the public’s Bayes error. Generalizes the standard model of bookmaker profit, and shows that the public’s apparent tendency to back losers is a Simpson’s paradox.
In progress
Ongoing research
A quantile-regression model for NFL point spreads with full backtesting. Deep-dives will appear here as they’re ready.
Writing
Accessible essays on the statistics of betting. A newsletter is in the works.
2024-12-02
The economics of teaser bets
Testing the “crossing key numbers” conventional wisdom on NFL teaser legs across multiple seasons.
For journalists
I’m a standing resource for stories on betting models, prediction markets, and forecasting — the independent academic angle, not a tipster’s. Quick to respond, comfortable on deadline, and happy to translate the statistics into plain English.