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Outcome Dependence, Overround Allocation and Informational Efficiency in Fixed-Odds Association Football Markets: Evidence from 45,550 Matches
Author: Jakub Rybaczuk (Windsor, Ontario) · Status: working paper, not peer reviewed · Version: v2.2 (24 October 2026) · Licence: CC BY-NC 4.0 (non-commercial)
Summary
This paper uses 45,550 matches from 22 European leagues (2019-20 to 2024-25) with closing prices from Pinnacle, Bet365 and market average/maximum to study four questions.
- Same-game dependence. Result × total and result × BTTS outcomes are strongly dependent. For example, draw & under 2.5 occurs 1.465× [1.437, 1.492] as often as independence implies. A parlay priced as the product of its two legs would be mispriced.
- Draw model. A pre-registered bivariate Poisson score model, selected on 2019-23 only, beats an independent Poisson grid on 2023-25 out-of-sample data on all three pre-stated metrics.
- Margin and efficiency. Retail books track Pinnacle and load about 6% overround in a power/Shin-like way. Bet365 closes 67.5% of its gap to Pinnacle by kick-off. There is no favourite-longshot bias at the Pinnacle close. 0/7 feature hypotheses (kit colour, fatigue, referees) and 0/10 candidate unpriced variables survive multiplicity correction.
- Line shopping. In-sample and exploratory, CLV is significantly positive in 22/25 configurations. ROI is significant in 0/25 (positive in 14/25). v2.2 fresh holdout (22 divisions, 25 Jul 2025 to 14 Oct 2026, never used for tuning, Betfair Exchange reference): the frozen screen's CLV is −1.60% [95% CI −2.37, −0.80] over 1,314 bets, and ROI is +1.6% [−6.2, +9.4]. The in-sample edge is not confirmed out of sample.
- Dead rubbers (v2+). The Betfair Exchange close matched Pinnacle on 10,642 matches. v2.2 re-ran this on pre-July-2025 data only (7,680 matches), and it still passes. Caveat: Pinnacle odds after July 2025 are unreliable in the source. On that basis, a pre-registered re-test ran on 2025-26 and failed: gain +0.33×10⁻⁴ [−0.93, +1.53], p = .27, and the effect had the opposite sign.
- Out-of-sport extensions (v2+, §6.7). Draw & under replicates on 2025-26 at 1.496×. MLB 2025 win & over is 0.90–0.92× (q < .05). For the NHL 2018-22 puck-line favourite, cover & over is 1.454× (z = +11.3, all four seasons). NBA and NFL are null. Elo never beats the closing market. Same-game parlay pricing remains untested.
v2.2 also removes look-ahead features: the dead-rubber flag now uses pre-season schedules (still null), the kit test is withdrawn, and the popular-club surcharge is withdrawn (−0.08 pp, se 0.06, with training-only popularity). Dependence z-scores are now reported on held-out rows only.
Methods: Shin, power and additive de-vigging; match-clustered bootstrap; Benjamini–Hochberg and Holm correction; pre-registered season splits.
Files
| File | Description |
|---|---|
correlated_outcomes_v2.2.pdf |
Full paper, v2.2 (26 pp.) |
correlated_outcomes_v2.2.md |
Markdown source, v2.2 |
Intended use and limitations
This is a research paper on market efficiency. It is not betting advice, and nothing in it shows a profitable strategy. The results were transcribed from saved script outputs, and the work was done with AI research assistants (see §9.3). Proprietary operational parameters are deliberately withheld (§9.4): line-shopping thresholds, blend weights, staking settings and SGP-engine parameters. Every reported statistic can be reproduced from public data by following the stated procedures.
Responsible gambling
This is not betting advice, and no strategy here should be used to place bets. Gambling involves the risk of losing money. If gambling is causing you or someone you know harm, free and confidential help is available. In Ontario, call ConnexOntario at 1-866-531-2600 (24/7). Elsewhere, contact your local helpline.
Data and credits
Football results and odds: football-data.co.uk. The raw data is not redistributed here; download it from the source. football-data.co.uk states no licence for its data.
MLB 2025, NHL 2025-26, NBA 2024-26 and NFL 2025 closing odds: Hugging Face datasets by minmaxxxer (https://huggingface.co/minmaxxxer), licensed CC BY 4.0, used with attribution.
NHL odds 2018-19 to 2021-22: Wildgoose, N. & Chezum, B. (2023). Market Efficiency: The Efficiency of Online Sportsbooks in the NHL Betting Market. Harvard Dataverse, V1. https://doi.org/10.7910/DVN/39ZFRO. Licensed CC BY-NC 4.0, non-commercial only. This data is not redistributed in this repository. Obtain it from Dataverse under its own licence.
Odds are facts compiled by third parties from bookmaker prices. No bookmaker or the NHL endorses this work. Third-party data is subject to its own terms and is not redistributed here.
Licence of this paper: because the paper uses CC BY-NC data, it is released under CC BY-NC 4.0. No commercial use is permitted. No raw data of any kind is included in this repository.
Citation
@misc{rybaczuk2026outcome,
title = {Outcome Dependence, Overround Allocation and Informational Efficiency in Fixed-Odds Association Football Markets: Evidence from 45,550 Matches},
author = {Rybaczuk, Jakub},
year = {2026},
note = {Working paper, v2.2},
howpublished = {Hugging Face}
}
Changelog
- v2.2: out-of-sample re-test (edge did not hold), popularity and kit claims withdrawn; dataset page renamed to correlated-outcomes-fixed-odds.
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