The Deel Kick Off contest attached to the 2026 World Cup pays a shared pool to entrants who correctly predict four outcomes at once: the champion, the Player of the Tournament, the top scorer, and that scorer’s exact goal count. Winning requires a single joint four-tuple to resolve correctly, so the problem is a conjunction rather than four separate forecasts. We describe an engine that runs one Monte-Carlo simulation of the full 48-team tournament fifty thousand times and selects the most probable joint tuple from the simulated frequency table, rather than stitching together four marginal favourites. Across the four World Cups from 2010 to 2022, the engine champion probability records a mean log-loss of 1.897 against the devigged closing line at 2.199, beating the market in three of the four years. The dominant source of joint uncertainty is the identity of the top scorer, whose modal candidate holds 24 percent of the probability across an effective field of roughly eleven scorers, while the goal-count distribution places on average 62 percent of its mass on the empirically dominant five-to-eight-goal band. The selected 2026 ticket carries a joint probability of 0.94 percent, roughly ten to twenty times a casual entry’s chance and still small in absolute terms. The principal limitation is structural: the 48-team format has no historical precedent, so the bracket path itself cannot be backtested, and the engine never locks a real contest entry.
A free-entry contest run alongside the 2026 World Cup, the “Deel Kick Off” pool, is reported to award up to 150,000 dollars. To win a share, an entrant must correctly name four things before the tournament begins: the champion, the Player of the Tournament, the Golden Boot winner, and the exact number of goals that top scorer finishes on. The pool is split among every entrant who gets all four right. A single operator holds one ticket, with no second entry to hedge.
The structure changes the problem. A leaderboard rewards being approximately right about many independent questions; this contest rewards being exactly right about one compound event. The payout depends on the joint probability that all four answers resolve together, not on the four marginal probabilities considered one at a time. The naive entry picks the favourite for each question separately. That entry is usually suboptimal, because the four marginal favourites rarely form the single most probable joint outcome once the questions are correlated through a shared tournament.
The contribution of this paper is one engine and one validated claim about it: selecting the argmax of a simulated joint distribution, rather than the product of marginal favourites, produces a defensible four-tuple whose champion component beats the devigged betting market on historical World Cups (Eq. 2). We describe the simulation, the calibration evidence that earns trust in the joint estimate, and the honest size of the resulting probability.
The remaining sections proceed in order. Section 3 places the engine against the football-forecasting and odds-devigging literature. Section 4 specifies the simulation, the team-strength model, the player models, and the scoring rules. Section 5 reports the calibration results and the selected 2026 ticket. Sections 6 through 8 interpret the findings, enumerate what the work does not establish, and state where the next iteration should go.
Statistical models of football scores begin with Maher (1982), who modelled goals as independent Poisson counts driven by team attack and defence parameters. Dixon & Coles (1997) refined that model with a low-score dependence correction and a time-decay weighting, and they framed the result explicitly as a test of betting-market efficiency. The Elo rating system, originally designed for chess (Elo, 1978), provides an alternative team-strength estimate that updates on match results alone and avoids the score-line modelling that Poisson approaches require.
Tournament-level forecasting has tended to publish marginal predictions. Groll et al. (2019) combined a random forest with ranking and Poisson components to forecast match outcomes and then simulated the bracket to produce per-team title probabilities for international tournaments. That design answers the champion question well. It does not address a conjunction contest, where the object of interest is a joint tuple across heterogeneous questions rather than a single marginal.
Recovering probabilities from bookmaker odds requires removing the bookmaker margin. Proportional normalisation is the simplest devig; Shin (1993) derived a model that attributes part of the margin to informed traders, and Štrumbelj (2014) compared devigging methods empirically and found the basic and Shin variants competitive for football. We use proportional devigging as the baseline and report sensitivity to the assumed margin.
The scoring rules used throughout are standard. The logarithmic score (Good, 1952) and the Brier score (Brier, 1950) are both proper, meaning a forecaster minimises expected penalty by reporting true beliefs. We report log-loss as the primary metric because it penalises confident errors heavily, which is the relevant failure mode for a single-ticket conjunction bet.
Team strength is estimated from the martj42 open dataset of international results (Jürisoo, 2024), covering matches from 1872 to the present. Player scoring rates for the historical calibration come from the companion martj42 goalscorers dataset, while the 2026 live ticket uses declared tier priors instead, because per-90 ingestion was blocked in the build environment, a substitution recorded in Section 7. The match-calibration window begins in 2014 and contains 11,734 matches, of which 1,767 played after 2024-09-06 form the held-out test set (Tab. 1). Historical champion odds for the beat-the-line test are transcribed from public vegasinsider.com outright-history tables and cover the realized champion and the documented pre-tournament favourite only; the full free field is unavailable, a gap discussed in Section 7. The 2026 market comparison uses the devigged Polymarket outright winner market. All inputs are frozen to a content-addressed snapshot before kick-off, so no post-kick-off information enters the locked pick.
Two team-strength models sit behind a common interface: an Elo system (Elo, 1978) and a Dixon-Coles Poisson model (Dixon & Coles, 1997). On held-out per-match outcomes, Dixon-Coles is the better-calibrated model, with a log-loss of 0.867 against Elo’s 0.894 and an expected calibration error of 0.037 against 0.056 (Tab. 1).
The contest scores the champion rather than individual matches, and on that target the two models invert their per-match ranking (Fig. 2). Backtesting the champion marginal with no leakage over 2010 to 2022 gives Elo a mean log-loss of 1.889 and Dixon-Coles 2.504; the market sits at 2.199. This 1.889 comes from the engine-selection backtest; the market-comparison backtest in Section 5.2 reports the Elo champion log-loss as 1.897 against the same market value, the two differing by Monte-Carlo seed and the size of the comparison field and both rounding to roughly 1.9 nats. Dixon-Coles over-rates CONMEBOL sides, because high-scoring intra-confederation qualifiers inflate their attack ratings, and a live run over-rated Brazil severely relative to the market, an artifact of that inflation rather than a real edge. The bracket therefore uses Elo, which is the model validated as market-beating on the tournament target. Dixon-Coles is retained for the per-match comparison it wins.
data/engine_logloss.csv.The simulator reproduces the 2026 format exactly: twelve groups of four, the FIFA tiebreaker order, the eight best third-placed teams resolved through the encoded combination table, and the Round of 32 through the final with extra time and penalties. Each of fifty thousand simulations threads a single seeded random number generator, so a given snapshot and seed reproduce an identical output. Player goals are drawn from a Poisson process whose rate combines a per-player scoring rate, real for the historical backtests and a declared tier prior for the 2026 ticket, with expected matches played, the latter being a function of how far the player’s team advances in that simulation. The scoring rate is recency-weighted with a one-year half-life, in the spirit of the time-decay weighting of Dixon & Coles (1997); Section 5.5 reports the calibration gain that justifies the choice. A designated-penalty-taker signal was tested and rejected, because concentrating a team’s penalties on its backward-looking taker pulls probability away from the breakout scorers who tend to win the Golden Boot. The Player of the Tournament model scores candidates from team success, individual goal contribution, and a star-prior term calibrated against the historical Golden Ball vote.
The primary metric is the logarithmic score over realized outcomes, written for the realized-outcome probabilities as
\mathrm{LL} = -\frac{1}{N} \sum_{i=1}^{N} \log \hat{p}_i \tag{1}
where the hat-p term is the probability the forecaster assigned to the outcome that actually occurred. Lower is better, and a confident wrong forecast is penalised sharply (Good, 1952).
The pick is the argmax of the simulated joint frequency table,
\hat{t} = \arg\max_{t \in \mathcal{T}} \hat{P}(t), \qquad t = (\mathrm{winner}, \mathrm{POTT}, \mathrm{scorer}, \mathrm{goals}) \tag{2}
where the probability is estimated by counting how often each complete tuple occurs across the simulations. Selecting the four marginal favourites separately optimises four copies of (Eq. 1) independently and ignores the correlation among the questions, which is why it does not in general return the argmax of (Eq. 2).
Market probabilities are recovered from decimal odds by proportional devigging,
q_j = \frac{1/o_j}{\sum_{k} 1/o_k} \tag{3}
with the denominator equal to the booksum, or overround. The historical comparison assumes an overround of 1.30 for the outright market; the sign of the beat-the-line result holds across 1.20 to 1.40. Shin (1993) and Štrumbelj (2014) describe margin models that reallocate the overround unevenly, which we leave as a refinement.
The engine is a standalone Python package (kickoff) at commit 63e6d53, type-checked under mypy strict and exercised by a full test suite. A hard calibration gate blocks any pick lock unless every blocking check passes on real evidence. The reproducibility notebook in this paper loads the committed datasets, recomputes every number this paper derives from them, and regenerates each figure specification; it runs top to bottom on a clean kernel with pandas alone.
On the held-out test set, Dixon-Coles is the better per-match forecaster across all three metrics (Tab. 1). Both models clear the uninformative baseline by a wide margin: a uniform one-third forecast scores a log-loss of 1.099, against 0.867 for Dixon-Coles. The expected calibration error of 0.037 indicates a forecast whose stated probabilities track realized frequencies closely.
Table 1. Held-out match-outcome calibration on 1,767 international matches played after 2024-09-06. Lower log-loss and ECE are better.
| Engine | Brier | Log-loss | ECE | n |
|---|---|---|---|---|
| Elo | 0.524 | 0.894 | 0.056 | 1,767 |
| Dixon-Coles | 0.508 | 0.867 | 0.037 | 1,767 |
Across 2010, 2014, 2018, and 2022, the engine champion probability records a mean log-loss of 1.897 against the devigged closing line at 2.199, and it beats the market in three of those four years (Fig. 1). The single loss is 2018, where the model under-rated eventual champion France relative to the market. The margin of roughly 0.30 nats is the headline calibration result, because the champion is the contest question with a liquid market to test against, and the comparison is the closest thing available to an out-of-sample audit of the engine.
data/champion_vs_market_history.csv.The Golden Boot has historically landed on a range of totals, so the exact goal count carries real spread. The model places on average 62 percent of its probability mass on the five-to-eight-goal band across the four past tournaments, rising from 51 percent in 2010 to 84 percent in 2022 (Fig. 3). The realized winning count fell inside that band in every one of the four cases. The count is therefore well located; the larger source of joint uncertainty is which player tops the scoring chart, addressed in Section 5.5.
data/q4_goal_count_band.csv.The Player of the Tournament model is calibrated against the historical Golden Ball vote with coefficients alpha 0.5, beta 2, and gamma 4, the last reflecting a star-biased media electorate. The realized Golden Ball winner ranked inside the model top five in all four tournaments and first in both Messi years (Tab. 2).
Table 2. Player-of-the-Tournament calibration against the historical Golden Ball winner, by tournament. The realized winner ranked inside the model top five every year and first in both Messi years.
| Year | Golden Ball winner | Model rank | Model probability |
|---|---|---|---|
| 2010 | Diego Forlán | 5 | 7.6% |
| 2014 | Lionel Messi | 1 | 38.0% |
| 2018 | Luka Modrić | 5 | 4.7% |
| 2022 | Lionel Messi | 1 | 48.3% |
For 2026 the engine over-rates Spain and Argentina relative to the devigged Polymarket market and under-rates France, England, and Portugal (Fig. 4). The disagreement on Spain is the largest, at 24.0 percent model against 15.9 percent market. The selected ticket is Spain as champion, Erling Haaland as both Player of the Tournament and top scorer, and seven as the exact goal count (Tab. 3). Its joint probability is 0.94 percent, with a 95 percent confidence interval of 0.86 to 1.03 percent, roughly ten to twenty times the 0.05-to-0.10 percent chance of a casually constructed entry. The goal count is a near-tie: the strict argmax is eight goals at 0.95 percent, and the pick is tilted to seven, the less public count, to reduce pool-splitting in a shared-payout contest. The remaining alternatives each differ from the pick by a single component.
data/wc2026_winner_marginal.csv.Table 3. The selected 2026 ticket and its nearest alternatives, from a frozen run of 50,000 simulations (snapshot c7f3f5afa805, seed 20260611). Joint P is the simulated probability that all four components resolve correctly. The pick tilts off the strict argmax (eight goals) to seven, the less public count.
| Rank | Winner | POTT | Top scorer | Goals | Joint P | Note |
|---|---|---|---|---|---|---|
| 1 | Spain | Erling Haaland | Erling Haaland | 7 | 0.94% | selected (Q4 tilt to less public count) |
| 2 | Spain | Erling Haaland | Erling Haaland | 8 | 0.95% | strict argmax (near-tie) |
| 3 | Spain | Erling Haaland | Erling Haaland | 6 | 0.64% | goals = 6 |
| 4 | Spain | Erling Haaland | Erling Haaland | 9 | 0.64% | goals = 9 |
| 5 | Argentina | Erling Haaland | Erling Haaland | 7 | 0.61% | winner = Argentina |
The largest single source of joint uncertainty is the identity of the top scorer, and the engine’s final scorer model makes that race more open than a career-volume baseline would. Integrating the adopted recency weighting flattened the 2026 scorer marginal: the modal candidate fell from 28.5 to 23.8 percent, the inverse-Herfindahl effective field rose from 7.8 to 11.4 scorers, and the top-five cumulative mass fell from 66.7 to 55.6 percent (Fig. 5, Tab. 4). Because no four-tuple that names a scorer can exceed that scorer’s marginal, the flatter marginal lowered the joint-argmax probability from 1.02 to 0.95 percent. Better current-form modelling did not raise the headline; it revealed that the Golden Boot race is more competitive than career goal volumes imply.
data/scorer_concentration.csv.Table 4. Concentration of the 2026 top-scorer marginal, career-volume baseline against the integrated one-year recency model. A higher effective field and a lower modal share mean a more open race.
| Measure | Career-volume baseline | Post-recency (1y) |
|---|---|---|
| Modal scorer share | 28.5% | 23.8% |
| Top-5 cumulative mass | 66.7% | 55.6% |
| Effective field (1/HHI) | 7.8 | 11.4 |
| Joint-argmax P(win) | 1.02% | 0.95% |
The recency weighting was adopted because it improves scorer calibration on the realized Golden Boots of 2010 to 2022. Mean scorer log-loss falls from 12.656 at an all-equal baseline to 12.051 at a one-year half-life, the best of the tested half-lives (Tab. 5). The probability the model assigns to the player who actually won rises under recency in the two most recent cases: it nearly triples for Kane in 2018, from 0.7 to 1.8 percent, and nearly doubles for Mbappé in 2022, from 1.7 to 3.2 percent (Fig. 6). A designated-penalty-taker signal moved calibration the wrong way and was rejected, because it entrenches the backward-looking taker over the breakout scorer who tends to win.
Table 5. Recency-weight tuning for the scorer model, mean scorer log-loss over the 2010 to 2022 realized Golden Boots. Lower is better; the one-year half-life was adopted.
| Arm | Half-life | Mean scorer log-loss |
|---|---|---|
| Baseline (all-equal) | none | 12.656 |
| Recency | 1 year | 12.051 |
| Recency | 2 years | 12.189 |
| Recency | 3 years | 12.284 |
data/scorer_recency_peryear.csv.Selecting from the joint frequency table, rather than from four separate marginals, is what produces the pick. Four of the top five tuples share Spain, Haaland, and Haaland and differ only in the goal count (Tab. 3), which shows where the residual uncertainty concentrates once the champion and the scorer are fixed. A marginal-favourite entry would pick each component from its own most-likely value and could easily land on a tuple that no single simulation path actually produced often. Reading the pick off the joint frequency table avoids that failure by construction. The scorer marginal is the binding term: even the modal candidate holds only 23.8 percent after recency (Fig. 5), the ceiling the joint argmax presses against, which is why the headline sits below one percent rather than higher.
The beat-the-line result gives the champion component an external check that the other three questions lack. A model that beats a liquid, devigged market on the most-traded question over four tournaments has demonstrated more than internal consistency (Fig. 1). The same engine then carries the player questions, where no comparable free market exists, so the calibration evidence for those rests on the goal-count band (Fig. 3) and the Golden Ball rank history rather than on a market test.
The honest reading of the 0.94 percent is that it is a real edge of small absolute size on a sample of one. An edge of roughly ten to twenty times a casual entry is large in relative terms and still leaves the most likely outcome as a loss. Across a single ticket on a single tournament, variance dominates, and no result here should be read as a prediction that the ticket wins. That the integrated scorer model lowered the headline from 1.02 percent rather than raising it is the calibration working as intended: a more honest marginal, not a more winnable one.
The 48-team bracket has no precedent. The 2026 format has zero prior instances, so the component models can be backtested but the bracket structure cannot. The historical tests in Section 5 use the 32-team format, and the path probabilities for the new structure are calibrated only indirectly, through the market anchor and internal consistency.
The Golden Boot market is unverified. No free historical market for the top-scorer count was found, so that component of the edge is asserted from the goal-count calibration rather than tested against a price. The contest’s player questions therefore carry weaker external validation than the champion question does.
Player rates depend on example priors. Per-player scoring rates in the shipped configuration derive from declared tier priors, because live per-90 ingestion was blocked in the build environment. A real entry would replace those priors with observed rates and verify every candidate against the final squads. Recency weighting (Section 5.5) sharpens the scorer marginal but does not remove its diffuseness, and the top-scorer identity remains the largest residual uncertainty in the ticket.
The historical sample is four tournaments. A mean log-loss over four World Cups cannot separate a stable edge from a fortunate draw with high confidence. The result is suggestive and directionally consistent, and it is not a large-sample claim.
The market anchor is champion-only and thinly sourced. Historical outright odds were available for the champion and one favourite per year, not the full field, and the comparison assumes a 1.30 overround. The sign of the result is robust across plausible overrounds, while the exact margin is not.
A conjunction contest rewards the joint, and the engine described here selects the joint rather than four marginal favourites. The design earns trust from one external check: the champion probability beats the devigged closing line on three of the last four World Cups, at a mean log-loss of 1.897 against 2.199. The goal-count band is well located, with 62 percent of model mass on the empirically dominant five-to-eight band, while the dominant residual uncertainty is the identity of the top scorer, whose modal candidate holds only 23.8 percent of the probability once the scorer model is recency-weighted.
The selected 2026 ticket is Spain, Haaland, Haaland, and seven goals, at a joint probability of 0.94 percent. That figure is a defensible model estimate of a small absolute chance, roughly ten to twenty times a casual entry, on a sample of one. Integrating a better-calibrated scorer model lowered it from 1.02 percent, which is the calibration becoming more honest rather than the ticket becoming less winnable.
The next iteration should replace the example player priors with observed scoring rates, source a wider historical field for the market comparison, and pre-register the 2026 ticket before kick-off so the single live outcome becomes an honest, if small, addition to the calibration record.
All datasets are enumerated in data/manifest.yaml. They are outputs of the world-cup engine at commit 63e6d53; the 2026 tables come from a frozen run (snapshot c7f3f5afa805, seed 20260611, 50,000 simulations).
| Dataset id | File | Contents |
|---|---|---|
| match-calibration | data/match_calibration.csv | Held-out per-match calibration of Elo and Dixon-Coles on 1,767 international matches |
| champion-vs-market-history | data/champion_vs_market_history.csv | Model and devigged-market champion probabilities and log-losses, 2010 to 2022 |
| engine-logloss | data/engine_logloss.csv | Per-match and champion log-loss for both engines and the market |
| q4-goal-count-band | data/q4_goal_count_band.csv | Goal-count band mass and realized-count mass by tournament |
| pott-calibration | data/pott_calibration.csv | Model rank and probability for each realized Golden Ball winner |
| wc2026-winner-marginal | data/wc2026_winner_marginal.csv | Engine and devigged-market champion probabilities for the twelve leading 2026 teams |
| joint-ticket | data/joint_ticket.csv | The joint-argmax 2026 tuple and its four nearest runners-up |
| scorer-concentration | data/scorer_concentration.csv | Top-scorer marginal concentration before and after recency (modal share, effective field, top-5 mass, joint-argmax probability) |
| scorer-recency | data/scorer_recency.csv | Recency-weight tuning, mean scorer log-loss by half-life arm |
| scorer-recency-peryear | data/scorer_recency_peryear.csv | Per-tournament probability on the realized Golden Boot, baseline vs recency |
Market odds are transcribed from public sources and reproduced as factual data points; their upstream providers are named per dataset in the manifest. The reproducibility notebook is at notebook.ipynb.
See references.yaml. Inline citations: Maher (1982), Dixon & Coles (1997), Elo (1978), Brier (1950), Good (1952), Shin (1993), Štrumbelj (2014), Groll et al. (2019), Jürisoo (2024).
research/markets/tournament-forecasting/MKT-004-conjunction-world-cup/.
Manifest:
data/manifest.yaml.
Notebook:
notebook.ipynb.