Peer-reviewed studies, preprints and classic methods papers on pricing, efficiency, risk and research practice. Each entry is our summary, with the original link and a plain statement of what the study does not show.
Summaries are original paraphrases of published abstracts and records; no paper text is reproduced. Bibliographic details were checked against publisher, index and author listings on 25 October 2026. Where a paper was later corrected, the correction is shown. Preprints are labelled as not peer reviewed.
9 sources
The model describes score outcomes well, and the authors report a positive return when its probabilities were used to select bets against bookmaker odds in their historical evaluation.
Does not show: That a Dixon–Coles model beats today's football markets after margins, limits and competition.
To a first approximation, wagering prices are efficient forecasts of outcomes and absorb information as lines move, while documented exceptions such as the favourite–longshot bias remain important.
Does not show: That every market or price is efficient, or that the anomalies it lists can be exploited today.
The authors report that the strategy was profitable in a historical simulation, in a simulation on more granular odds data and in a short real-money trial, and that bookmakers restricted their accounts during the trial.
Does not show: That cross-bookmaker discrepancies remain available or executable at meaningful stakes today.
Bettor disagreement combined with bookmaker risk aversion can generate a favourite–longshot pattern (worse returns on long shots) without assuming that bettors love risk.
Does not show: That backing favourites is profitable, or how large the bias is in any particular market today.
Apparent inefficiencies appear in individual seasons but do not persist systematically across seasons or leagues, and simulations show that significant single-season results are likely even in a fully efficient market.
Does not show: That no bettor can ever find an edge; it shows that single-season evidence is weak.
Sportsbook forecasts were mostly reliable, yet line changes were negatively autocorrelated (overreaction), forecast quality did not always improve toward game time, and simple strategies would have earned significant hypothetical profits.
Does not show: That football markets behave the same way, or that the hypothetical strategies were executable at scale.
Bookmakers facing less competition set prices with a favourite–longshot bias, while the competitive market shows little of it; the model's prediction about returns on draws is also supported. Working-paper versions describe a sample of tens of thousands of matches (later drafts cite over 150,000).
Does not show: That a favourite strategy beats competitive markets; the bias is concentrated where competition is weaker.
Tests based on normalised probabilities behave well; tests based on raw inverse odds do not, and are biased against finding a favourite–longshot bias.
Does not show: Any profitable strategy; it shows how test design can change conclusions.
A bookmaker protecting against insiders sets odds that produce a favourite–longshot bias; the model underlies the Shin de-vig method.
Does not show: How much insider trading exists in a given market.
