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arxiv: 2605.16066 · v1 · pith:ARXCWXVFnew · submitted 2026-05-15 · 📊 stat.AP

A market-calibrated accelerated failure time model for in-play football forecasting

Lawrence Clegg , Zixing Song , John Cartlidge This is my paper

Pith reviewed 2026-05-19 18:53 UTC · model grok-4.3

classification 📊 stat.AP
keywords in-play football forecastingaccelerated failure time modelbetting market calibrationWeibull modelpost-shot expected goalsPremier Leaguecontinuous-time goal models
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The pith

Calibrating a Weibull accelerated failure time model to pre-match betting prices and adding post-shot expected goals nearly matches betting exchange accuracy for in-play football forecasts.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes that an accelerated failure time model for goal arrivals in football can be made competitive with betting exchange prices for in-play forecasting by calibrating its team strength parameters directly to pre-match market odds and incorporating post-shot expected goals as a dynamic covariate. This combination captures both the aggregated wisdom of the betting market before kick-off and the evolving match state during play. Evaluated minute by minute across 140 English Premier League games, the resulting forecasts reach 70.2 percent classification accuracy, nearly identical to the 70.6 percent from Betfair prices themselves. The work also demonstrates through comparisons that the market calibration step contributes more to accuracy than the specific choice of scoring model.

Core claim

The central claim is that jointly fitting team-strength parameters to 1X2 and over/under Betfair prices via squared-error minimisation, then incorporating post-shot expected goals in a Weibull AFT model, produces in-play forecasts that almost match betting exchange accuracy while retaining interpretability. Comparison with other calibrated models shows market calibration drives the accuracy gain. A betting simulation yields positive returns, indicating market inefficiency.

What carries the argument

Market calibration of team strength parameters to pre-match betting prices combined with post-shot expected goals as a time-varying covariate in a Weibull accelerated failure time model.

Load-bearing premise

That jointly fitting team-strength parameters to pre-match 1X2 and over/under Betfair prices via squared-error minimisation produces values that remain valid for in-play forecasting once post-shot expected goals are added as a time-varying covariate.

What would settle it

Testing the calibrated model forward on a new set of Premier League matches and checking whether classification accuracy remains near 70 percent and whether simulated betting returns against in-play odds stay positive.

Figures

Figures reproduced from arXiv: 2605.16066 by John Cartlidge, Lawrence Clegg, Zixing Song.

Figure 1
Figure 1. Figure 1: Cumulative goals and PSxG for Arsenal vs. Everton (2–1, 19 May 2024) against the population mean PSxG. The dotted line indicates the population mean PSxG trajectory, estimated from the training data. matches preceding the evaluation period: 3.1 minutes for the first half and 6.2 for the second. We restrict this computation to the same-season data because of FIFA’s 2023 effective playing time directive, whi… view at source ↗
Figure 2
Figure 2. Figure 2: Total-goals distribution across the 𝑁 = 140 calibrated matches. Bars show, left to right: uncalibrated Weibull sim￾ulations, calibrated Weibull simulations, Betfair over/under-implied probabilities, and empirical season proportions (hatched). Simulated values aggregate 10,000 simulations per match; the final bucket aggregates five or more goals. the most accurate pre-match forecaster (Forrest et al., 2005;… view at source ↗
Figure 3
Figure 3. Figure 3: Market calibration adjustments to team scoring parameters for gameweek 25 (first evaluation gameweek, 10 matches). Each paired row shows the shift from model-estimated to market-calibrated 𝜂 for the home (blue) and away (orange) team. Posi￾tive values indicate the market assigns a slower scoring rate than the model. Rows ordered by total absolute shift. 𝜂𝐴 = 𝜇 + 𝑎𝐴 + 𝑑𝐻, we find for each match the calibrat… view at source ↗
Figure 4
Figure 4. Figure 4: Left: first half (minutes 0–44). Right: second half (minutes 45–95). Top: log-loss at each evaluation minute. Bottom: log-loss difference relative to Betfair (Δ < 0 indicates the model outperforms the market) [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Cumulative profit for Weibull𝜅,𝜓 against Betfair in-play odds (𝑁 = 140 matches), under unit and Kelly staking. Commis￾sion of 2% applied to net match winnings. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 EV threshold 0 5 10 15 20 25 ROI (%) 13368 5916 3215 2226 1713 (A) Unit staking 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 EV threshold 0 5 10 15 20 25 ROI (%) 13423 6051 3352 2343 1811 (B) Kelly stakin… view at source ↗
Figure 6
Figure 6. Figure 6: ROI at different expected value (EV) thresholds. Grey numbers indicate bet counts. Positive ROI persists across a range of thresholds, indicating the edge is not confined to marginal bets. past this point, perhaps reflecting the winner’s curse (Capen et al., 1971): at seemingly large edges, the filter disproportionately selects bets where the model’s probability, rather than the market’s, is furthest from … view at source ↗
read the original abstract

In-play football forecasting models have struggled to match the accuracy of betting exchange prices, which aggregate information from many market participants. We close this gap by combining two extensions to a Weibull accelerated failure time model: calibrating team strength parameters to Betfair Exchange prices at kick-off to capture pre-match market information, and including post-shot expected goals as a time-varying covariate to capture in-play information. The calibration approach, where we jointly fit team-strength parameters to 1X2 and over/under betting markets via squared-error minimisation, applies to any intensity-based goal arrival model and enables stronger in-play forecasting. Evaluated across 140 English Premier League matches at minute intervals, the calibrated model almost matches Betfair's classification accuracy (70.2% versus 70.6%) while retaining interpretable team-level parameters and covariate effects. A comparison with two alternative continuous-time scoring models, both calibrated to the same pre-match odds, confirms that market calibration is the dominant driver of predictive accuracy. A betting simulation against Betfair in-play odds yields a 4.5% return on investment (Sharpe ratio 5.94) over 17,458 bets, suggesting an inefficiency within in-play football markets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a Weibull accelerated failure time model for in-play football goal arrivals that jointly calibrates team-strength parameters to pre-match Betfair 1X2 and over/under prices via squared-error minimization and adds post-shot expected goals as a time-varying covariate. Evaluated at minute intervals across 140 English Premier League matches, the model reaches 70.2% classification accuracy (versus Betfair's 70.6%) and produces a 4.5% ROI (Sharpe ratio 5.94) over 17,458 simulated bets against in-play odds. Comparisons with two other continuous-time models calibrated to the same pre-match odds indicate that market calibration is the primary driver of accuracy gains.

Significance. If the pre-match calibrated parameters remain valid once realized post-shot xG trajectories are inserted, the work supplies a practical, interpretable route to combine market-implied information with in-play covariates. The concrete accuracy figures, direct comparison to betting-exchange benchmarks, and positive ROI constitute falsifiable, practically relevant evidence of both predictive performance and potential market inefficiency.

major comments (2)
  1. [Calibration section] Calibration section: Team-strength parameters are fitted by minimizing squared error to pre-match Betfair prices at kick-off (covariate = 0 or unconditional expectation). The manuscript provides no explicit invariance check showing that the same parameters, when driven by match-specific realized post-shot xG paths, continue to produce hazards consistent with the original market-implied probabilities. This leaves open the possibility that average future xG contributions are absorbed into the fitted strengths, undermining their use for in-play forecasting.
  2. [Results section] Results section: The claim that market calibration dominates accuracy gains rests on comparisons with two alternative continuous-time models, both calibrated to the same pre-match odds. Without reporting the accuracy of a non-calibrated Weibull AFT model that nevertheless includes the post-shot xG covariate, it is difficult to isolate whether the reported 70.2% accuracy stems primarily from calibration or from the addition of the time-varying covariate itself.
minor comments (2)
  1. [Abstract] Abstract and methods: The betting simulation reports a 4.5% ROI and Sharpe ratio 5.94 but does not specify stake sizing, whether odds are taken at the exact minute of each prediction, or how the 17,458 bets are distributed across matches.
  2. [Evaluation] Evaluation: Accuracy is stated as 70.2% versus 70.6% without accompanying standard errors, number of independent matches, or details on the precise classification rule (e.g., probability threshold for home-win calls).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which help clarify the interpretation of our calibration procedure and strengthen the evidence for our main claims. We respond to each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Calibration section] Calibration section: Team-strength parameters are fitted by minimizing squared error to pre-match Betfair prices at kick-off (covariate = 0 or unconditional expectation). The manuscript provides no explicit invariance check showing that the same parameters, when driven by match-specific realized post-shot xG paths, continue to produce hazards consistent with the original market-implied probabilities. This leaves open the possibility that average future xG contributions are absorbed into the fitted strengths, undermining their use for in-play forecasting.

    Authors: We acknowledge the value of an explicit invariance check. The calibration is performed once at kick-off against unconditional market prices, after which the post-shot xG enters only as a time-varying covariate that shifts the hazard during the match. To address the concern that average future xG effects might be absorbed into the strength parameters, we will add a short verification in the revised Calibration section (or an appendix). This will show that, when the calibrated parameters are driven by the unconditional expectation of the xG process, the resulting integrated hazards recover the original pre-match market probabilities on average. We view this as a useful clarification rather than a change to the core method. revision: yes

  2. Referee: [Results section] Results section: The claim that market calibration dominates accuracy gains rests on comparisons with two alternative continuous-time models, both calibrated to the same pre-match odds. Without reporting the accuracy of a non-calibrated Weibull AFT model that nevertheless includes the post-shot xG covariate, it is difficult to isolate whether the reported 70.2% accuracy stems primarily from calibration or from the addition of the time-varying covariate itself.

    Authors: We agree that reporting the non-calibrated Weibull AFT model that still includes the post-shot xG covariate would make the attribution clearer. In the revised Results section we will therefore add the classification accuracy, log-likelihood, and betting-simulation metrics for this baseline specification. This addition will allow readers to quantify the incremental contribution of market calibration over the covariate alone and will support (or, if necessary, qualify) the statement that calibration is the dominant driver. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central derivation calibrates team-strength parameters to pre-match Betfair 1X2 and over/under prices via squared-error minimization at kick-off (covariate at baseline), then augments the Weibull AFT model with an independent time-varying post-shot expected goals covariate for in-play updates. Evaluation compares the resulting in-play forecasts against Betfair's own classification accuracy on the same 140 matches and uses two alternative models (also pre-match calibrated) to attribute gains to calibration. No equation or claim reduces the in-play output to the pre-match fit by construction; the time-varying covariate path supplies new information not present in the calibration target. External market benchmark and controlled comparisons keep the chain self-contained without self-definitional, fitted-prediction, or self-citation reductions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the Weibull AFT functional form, the validity of squared-error calibration to market prices, and the assumption that pre-match market-implied strengths remain appropriate once in-play covariates are introduced.

free parameters (1)
  • team strength parameters
    Jointly fitted to pre-match 1X2 and over/under Betfair prices via squared-error minimisation.
axioms (1)
  • domain assumption Goal arrival times follow a Weibull distribution conditional on team strengths and covariates
    Core modeling choice of the accelerated failure time framework applied to football.

pith-pipeline@v0.9.0 · 5743 in / 1323 out tokens · 71359 ms · 2026-05-19T18:53:37.443947+00:00 · methodology

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Reference graph

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