Two roads to the same champion: a homegrown World Cup model side by side with Goldman Sachs

Goldman Sachs and a single operator working with AI coding agents each built a Monte-Carlo forecaster for the champion of the 2026 World Cup. We set the two side by side on the one question both answer, who wins, and report what each side did and what it cost. The two agree. Both make Spain the favourite, at 24.0 percent for the homegrown Kickoff engine and 25.7 percent for Goldman Sachs, which is about one and a half times the betting market’s price. Both also part from the market in the same places, rating Spain and Argentina above it and England and Portugal below it, and both put about two-fifths of the title on Spain and Argentina together. They disagree most on France, where the Goldman Sachs count of elite scorers lifts France to 18.9 percent against Kickoff’s 12.0. On a seven-part assessment the two finish even, with strengths that do not overlap: Goldman Sachs leads on the size of its sample and the breadth of its inputs, Kickoff on calibration evidence, leakage control and reproducibility. Kickoff was built in nine days on free public data, and it beat the betting market in three of the four past World Cups it was tested on. Accuracy cannot settle the comparison yet, because no World Cup has had 48 teams before and the two forecasts were frozen on different dates.

The 2026 World Cup is the first to field 48 teams: twelve groups of four, the top two plus the eight best third-placed teams advancing to a round of 32, then a knockout to the final, with finalists playing eight matches. Two separate efforts built a probabilistic forecaster for its champion on the same skeleton: a rating of each team’s strength (Elo), turned into expected goals (a Poisson model), and played through the actual bracket thousands of times (a Monte-Carlo simulation). One is Goldman Sachs Global Investment Research, whose 29 May 2026 note extends a recurring World Cup research product (Hatzius, Pierdomenico, and Stehn, 2026). The other is Kickoff, an engine that a single operator built in nine days with AI coding agents on free public data, and that the conjunction paper MKT-004 (Atol Research, 2026) used to select a contest ticket. Both forecasters accept the group draw of 5 December 2025 as a fixed input, so any divergence between them is a property of the models rather than of the draw.

The two systems can be compared on one question only, each team’s probability of winning the title, which we call the champion marginal, and the comparison holds them to it. Goldman Sachs has the better-resourced and better-estimated model: it fits an interpretable regression on roughly twenty thousand matches and uses more inputs than Kickoff chooses to. Kickoff supplies what the public Goldman Sachs note does not: evidence that its probabilities are calibrated, a frozen forecast that later information cannot leak into, and a way for anyone to reproduce it. On a seven-part assessment the two finish even, with each side’s edges falling on different parts.

The contribution is the comparison itself. A forecasting system assembled by one person with coding agents on zero-cost data holds level with a model from one of the best-resourced research divisions in finance, on a task where that division has more than a decade of published work. Section 3 places both models in the football-forecasting and prior-ATOL literature, and Section 4 describes the two systems, the validation metrics and the reproducibility protocol. Section 5 reports the head-to-head probabilities, the shared lean against the market, the validation evidence, the build ledger and the assessment. Section 6 interprets the France divergence and the contrast between breadth and discipline, while Sections 7 and 8 state the limitations and what remains for the in-tournament sequel to settle.

Probabilistic football forecasting rests on two building blocks that both models reuse. The first is the Poisson goals model (Dixon and Coles, 1997), which turns estimates of team strength into odds on every scoreline, with a correction for low scores and more weight on recent matches. The second is the Elo rating system (Elo, 1978), a strength rating that updates after every result, which both models use as the main driver of expected goals. Forecast quality is measured with proper scoring rules, the Brier score (Brier, 1950) and the logarithmic score, which reward probabilities that come true as often as they say and punish confident misses.

Goldman Sachs has published a World Cup forecast under the title “The World Cup and Economics” across several tournaments, with the chief economist as the through-line and the model extended at each edition (Bloomberg, 2026). The 2026 note states that it is similar to the models for prior World Cups but extended along several dimensions, and it backtests its own 2018 and 2022 forecasts (Hatzius, Pierdomenico, and Stehn, 2026). The note is a research product of a large institution with proprietary data and a named author team.

Within the ATOL corpus, the Kickoff engine was introduced in MKT-004 (ATOL Research, 2026), which used its joint simulation to pick a four-outcome contest ticket and reported the champion backtest reused here. The construction context, a single operator directing a fleet of AI coding agents across production repositories, is documented in MKT-005 (Atol Research, 2026). Prior ATOL papers compare a model against a market baseline; none places an ATOL system beside an external institutional forecaster. We fill that gap, and in doing so turn a question about accuracy into a question about what one person can now build.

4.1 The two systems

Goldman Sachs fits a Poisson goals regression, in which the expected number of goals a team scores depends mainly on the difference between the two teams’ Elo ratings. Four further terms adjust it: scoring talent, the count of the team’s players among the top fifty scorers in the major European leagues, capped at four; momentum, from goals scored over the last ten matches and conceded over the last five; mentality, including a slump for the reigning champion and a boost for a first World Cup; and geography, through a host effect and adjustments for distance, altitude, and temperature (Hatzius, Pierdomenico, and Stehn, 2026). The fitted scorelines feed 50,000 simulated runs of the 48-team bracket, and the model is re-run after each match day during the tournament.

Kickoff runs an Elo-anchored Monte-Carlo engine over the same bracket structure. Two match engines sit behind one interface: a World-Football-Elo win, draw, and loss model, and a Dixon-Coles bivariate Poisson with the low-score correction and time-decayed weighting. For the champion forecast Kickoff uses the Elo engine, because it scores better on past champions it was not fitted to, with a log-loss of 1.889 against 2.504 for Dixon-Coles. Dixon-Coles over-rated South American (CONMEBOL) sides, whose attack ratings are inflated by high-scoring qualifiers within their own confederation. Knockout ties are resolved by an explicit extra-time and penalty-shootout model rather than by a rule of thumb that discards draws. Features that made the forecast less calibrated were dropped, among them an adjustment for the opponent’s defence and a term for a designated penalty taker, each of which worsened the goal-count log-loss that decides whether a feature stays. Table 2 and Table 3 summarize the two systems.

Table 2. Data and inputs for the two forecasters.

Table 3. Methodology contrast for the two forecasters.

4.2 Validation metrics

Both systems can be scored by the logarithmic loss assigned to the realized outcome,

where $p_{i, y_i}$ is the probability the forecaster placed on the outcome $y_i$ that event $i$ resolved to. For the champion backtest, an event is a tournament and the realized outcome is the actual winner, so the score is the negative logarithm of the probability the forecast gave the team that won: the more it gave, the lower the score. Goldman Sachs reports a different quantity, the correlation between predicted and actual goal difference, which is 0.49 across all World Cup games since 1978 (Hatzius, Pierdomenico, and Stehn, 2026). That correlation is informative about scorelines but does not test calibration, and the note publishes no calibration metric, confidence interval, or acceptance threshold.

Kickoff measures calibration directly, through the Brier score (Brier, 1950), log-loss, and expected calibration error. It benchmarks its champion probabilities against the devigged closing line, the last market prices before the tournament with the bookmaker’s margin taken out so that they sum to one, and a blocking calibration check refuses to lock a forecast that fails it.

4.3 Reproducibility protocol

The Kickoff forecast is pinned to a content-addressed snapshot of its inputs and a fixed random seed. Re-executing the frozen package returns byte-identical output on repeated invocation,

python -m vkickoff report --outright --no-live --no-callog \
  --frozen-board --json --seed 20260611 --snapshot c7f3f5afa805

which on 12 June 2026 produced a board with SHA-256 digest beginning d9023739 on two consecutive runs, with Spain the champion at 24.0 percent and the same lean against the market reported below. The champion probabilities in Table 1 come from the engine’s 30,000-simulation run before kickoff, recorded in the snapshot’s dry-run report. The shippable package reproduces the favourite and the ranking, and agrees with that board to within one percentage point on the less likely teams; the difference comes from the simulation count and a later build. The Goldman Sachs forecast carries no such protocol: it is re-run daily inside the bank, and no party outside Goldman Sachs can regenerate its board for any date.

4.4 Verification of the Goldman Sachs figures

The Goldman Sachs champion probabilities for the top eight teams were verified against the 29 May 2026 note and against reputable secondary coverage (Bloomberg, 2026). The figure for Colombia, which sits outside the note’s published top eight, is taken from the internal head-to-head comparison and is flagged in the limitations rather than asserted as independently confirmed. Goldman Sachs material is used at fair-use scale, the headline champion probabilities, the named covariates, and the stated sample, with full attribution; the note’s exhibits are not reproduced.

4.5 Software environment

The analysis regenerates the deviation table and every figure with Python 3.12 and pandas, with no network access. The model runs themselves come from the World Cup engine described in MKT-004.

5.1 The same favourite

Both models make Spain the favourite for the 2026 title, with about a one-in-four chance: 24.0 percent from Kickoff and 25.7 percent from Goldman Sachs (Fig. 1, Tab. 1). The betting market gives Spain 15.9 percent, so both models rate its chances about one and a half times as high. Both also rate Argentina highly, second for Kickoff at 16.8 percent and third for Goldman Sachs at 14.3 percent. The market gives Argentina 8.5 percent, little more than half of either model’s figure. The two models were estimated on different data with different inputs, so their agreement comes from a common recipe reaching the same answer twice, rather than from a shared input.

Table 1. Champion probabilities for the 2026 World Cup: the Kickoff engine, the Goldman Sachs model, and the devigged market, for the nine teams that anchor the comparison.

5.2 The same lean against the market

The two models also part from the betting market in the same places. Both rate Spain and Argentina above the market, by 5.8 to 9.8 points, and both rate England and Portugal below it, by 4.5 to 5.9 points (Fig. 2). Goldman Sachs reads its own market comparison the same way, describing itself as overweight Spain and Argentina and underweight England and Portugal (Hatzius, Pierdomenico, and Stehn, 2026). Two models built apart that lean against the bookmakers in the same direction corroborate each other. They also put almost the same weight on the pair: Spain and Argentina together hold 40.8 percent of Kickoff’s title probability and 40.0 percent of Goldman Sachs’s (Tab. 1).

5.3 Where they diverge

The two models disagree most on France. Goldman Sachs makes France its second favourite at 18.9 percent, while Kickoff gives it 12.0 percent, a gap of 6.9 points (Fig. 1, Tab. 1). They also fall on opposite sides of the market on France, with Goldman Sachs 2.3 points above it and Kickoff 4.6 points below (Fig. 2). The next largest gaps, Brazil at 3.1 points in Goldman Sachs’s favour and Argentina at 2.5 in Kickoff’s, are less than half as wide (Tab. 1). In proportion, the team Kickoff favours most over Goldman Sachs is Colombia, at 4.2 percent against 2.0, more than twice as much.

5.4 Validation evidence

The Kickoff champion forecast has a track record against the betting market. Run on the 2010, 2014, 2018, and 2022 World Cups with only what was known before each tournament, it gave the eventual winner more probability than the devigged closing line in three of the four, and less only in 2018, when France won (Fig. 3). In 2022, for example, it gave Argentina 23.6 percent before the tournament, nearly three times the market’s 8.1 percent. Scored by log-loss, where lower is better, the engine averages 1.897 across the four tournaments against the market’s 2.199.

Match by match, Dixon-Coles is the better-calibrated of Kickoff’s two engines: on 1,767 held-out matches its log-loss is 0.867, against 0.894 for Elo (Tab. 4). Its expected calibration error, the average gap between the probabilities it states and the frequencies that follow, is 0.037 against Elo’s 0.056. The champion forecast still uses Elo, because Dixon-Coles distorts the champion probabilities (Section 4.1). Goldman Sachs reports a single validation number, a correlation of 0.49 between predicted and actual goal difference, and publishes no calibration metric or interval (Hatzius, Pierdomenico, and Stehn, 2026). On whether these champion probabilities are calibrated, so that a team given 20 percent wins about one time in five, Kickoff supplies evidence and the public Goldman Sachs note does not.

Table 4. Validation evidence published by each system. The Kickoff per-match and backtest figures are computed against held-out data and the devigged closing line; the Goldman Sachs figure is the goal-difference correlation reported in the note.

5.5 What it cost

The two systems differ most in what they took to build (Fig. 4, Tab. 5). One operator working with AI coding agents built Kickoff in nine days, from the first commit on 2 June 2026 to the frozen pre-kickoff snapshot on 11 June. It runs to about 28,000 lines of code, a quarter of them tests, over 58 commits. Its data cost nothing, because the martj42 international-results file and the eloratings.net ratings are both free (Jürisoo, 2024). On the Goldman Sachs side we state only what is public: three named Global Investment Research authors, a footing in proprietary data, and a research product with a lineage to the 2014 and 2018 editions (Hatzius, Pierdomenico, and Stehn, 2026; Bloomberg, 2026). The contrast is stark without any estimate of Goldman Sachs’s headcount, hours, or budget.

Table 5. Construction ledger for the two forecasters. The Kickoff column is derived from the world-cup and poly git histories and the frozen snapshot date; the Goldman Sachs column states only public facts.

5.6 Assessment

Scored only as forecasters of the champion, the two systems finish even, each leading where the other is weaker (Tab. 6). Goldman Sachs leads on three dimensions: the size of its estimation sample and its statistical power, the inference and interpretability of its model, and the richness of its inputs. Kickoff leads on four: calibration evidence, rigor against the market benchmark, leakage control and reproducibility, and an honest statement of its limits. Three edges to four is still a tie, because breadth of estimation and discipline of evaluation are different goods that do not add up to one score. Goldman Sachs has the better-estimated model, and Kickoff the better-validated one.

Table 6. Seven-dimension assessment of the two systems as champion-marginal forecasters, scored one to five per dimension with the edge attributed.

France is the cleanest test of what a richer set of inputs buys. The Goldman Sachs scoring-talent term rewards France’s deep roster of elite forwards in Europe’s top five leagues, which lifts France to 18.9 percent, above the market (Fig. 2). The Kickoff champion engine has no such term and prices France near the level its Elo rating implies, below the market. Only the tournament can show whether the term captures attacking quality that Elo misses or fits a plausible story too closely. No other team isolates the difference between the two methods as cleanly as France does.

That difference is breadth against discipline. Goldman Sachs invests in breadth of explanation: more covariates, a larger sample, interpretable marginal effects, and a daily re-run that incorporates new information. Kickoff invests in discipline of evaluation: a minimal covariate set, a calibration gate that can veto a feature or a forecast, a frozen snapshot, and a seed that makes the result reproducible. Each choice has a cost. The Goldman Sachs covariates rest in places on small samples without published intervals, and the daily re-run is not a frozen, leakage-controlled protocol. The Kickoff parsimony may leave real signal on the table, as the France case suggests, and its champion forecast uses the less inferential of its two engines.

What the comparison establishes sits above either model. One operator with AI coding agents assembled a forecaster in nine days, on data that cost nothing, and it holds level with a model from a top research division that has published on this problem since 2014. The two agree on the champion, agree on where they part from the market, and split a seven-part assessment three edges to four. A practitioner choosing between them is choosing between explanatory richness and evaluative rigor: the Goldman Sachs model is the one to read for an account of why a team is strong, and the Kickoff model is the one to trust for a probability that has been tested for calibration and can be reproduced.

The deepest limitation is shared and structural. The 48-team format has no prior instance, so neither model’s bracket-path distribution (the third-place combination table and the eight-match finalist path) can be validated on history; both are at best market-anchored and internally consistent. The comparison is therefore confined to the champion marginal, the one axis both models answer.

The Goldman Sachs side carries the limitations of an unvalidated small-sample design. Several covariates rest on few observations (the reigning-champion slump on roughly a dozen prior champions) and come without reported regularization, standard errors, or out-of-sample stability tests, while the note publishes no calibration metric or confidence interval. These are characterizations of the public note, not of any internal Goldman Sachs work that may exist but is not published.

The Kickoff side has a thinner evidence base than Goldman Sachs’s proprietary inputs, a deliberately narrow feature set, and a champion forecast that uses the Elo engine rather than the more inferential Dixon-Coles. Its published board of record is a 30,000-simulation run. The shippable package reproduces the ranking and Spain at 24.0 percent but differs by under one percentage point on the less likely teams, a residual from the build and the simulation count (Section 4.3).

Two caveats apply to the head-to-head numbers themselves. The two forecasts were frozen on slightly different dates and market snapshots, which injects a small non-model wedge into any gap between them. And the Goldman Sachs figure for Colombia, outside the note’s published top eight, comes from the internal head-to-head transcription rather than from independent verification.

This comparison is pre-kickoff by construction: both published boards predate the opening match, and neither side’s probabilities are updated here with realized results. Scoring the two forecasts against what actually happens is the job of the in-tournament scorecard, the planned MKT-004 sequel, and is out of scope here.

On the one question both models answer, who wins the 2026 World Cup, Goldman Sachs and Kickoff are peers. They share an Elo-Poisson-Monte-Carlo backbone, name the same favourite in Spain, lean against the bookmakers in the same direction, and split a seven-part assessment three edges to four. Goldman Sachs is the better-estimated model and Kickoff is the better-validated one, and the choice between them is a choice between explanatory richness and evaluative rigor rather than a choice between right and wrong.

What remains open is the part neither model can settle from the armchair. France, where the two disagree most, will be priced correctly by one of them and not the other only once the matches are played, and the broader accuracy question waits on the tournament. One result does not wait: the price of building a forecaster that holds its own against Goldman Sachs has fallen to one operator, a fleet of coding agents, nine days, and free data.