Preprint: SSRN Working Paper No. 7013338 — https://papers.ssrn.com/sol3/papers.cfm?abstract_id=7013338
Companion code for:
F. R. Araujo da Silva, A Hybrid Prior-Performance Monte Carlo Model for Forecasting FIFA World Cup Knockout Outcomes: Methodology and Retrospective Validation 1986–2026. ORCID: 0000-0003-4938-5856
A transparent Monte Carlo model that forecasts the FIFA World Cup champion from the first knockout round. Each team gets a strength rating blending season-long priors (FIFA ranking, squad market value), group-stage performance (expected goals, goals, individual production), and a goalkeeper/defensive-pedigree term. Strength differences drive a Poisson goal engine with extra-time and penalty resolution; the fixed bracket is simulated many times to estimate championship probabilities.
No knockout-stage result is ever used as a model input.
Requirements
Python 3.8+ (standard library only — no external packages).
Usage
python worldcup_model.py # backtests (1986–2022) + 2026 prediction python worldcup_model.py --loocv # also run leave-one-out cross-validation
Files
| File | Description |
|---|---|
worldcup_model.py |
Model, simulation engine, backtests, prediction |
data.py |
Per-tournament inputs and fixed brackets |
Method summary
Strength rating:
R_i = 1500 + 250 * (Attack_i - Defense_i)
Attack_i = 0.70*rank + 0.20*value + 0.13*xGF + 0.05*goals + 0.03*star
Defense_i = 0.55*xGA - 0.35*gk_pedigree
(z-scored signals; for pre-2002 tournaments rank+value are replaced by a single pedigree rating carrying their combined weight.)
Match: expected goals lambda = clip(1.35 * exp(0.5*tanh((R_a - R_b)/400)), 0.25, 3.5),
independent Poisson draws, reduced-rate extra time, then a coin-flip shootout.
Validation
- Champion in the model's top two in 10/10 tournaments, 1986–2022.
- Out-of-sample (1986–1998, never used for tuning): top-two 4/4.
- Leave-one-tournament-out CV (2002–2022): top-two in 5/6 held-out folds.
Data sources
FIFA/Coca-Cola Men's World Ranking; Transfermarkt squad valuations; FIFA official match statistics; published xG trackers (2010–2026, estimated for ≤1998); RSSSF archive and ESPN for historical brackets and group-stage results.
License
MIT (code). Statistical data are public domain / cited to their sources.