# Anthropic Claude — End-to-End Predictive Framework for the 2026 FIFA World Cup **Model identification — Brand: Anthropic · Model: Claude (Claude Agent SDK, Cowork research preview build) · Generated: June 10, 2026** ## Abstract This paper presents a fully independent, deterministic-baseline predictive framework for all 104 matches of the 2026 FIFA World Cup, built on an independent bivariate Poisson scoring engine with an exponential strength link. Per the user-calibrated interview, team strength ratings weight recent continental evidence (Euro 2024, Copa América 2024, 2025–26 Nations League and qualifying form) at 70% against historical World Cup pedigree at 30%; host advantage is tiered ($\gamma_{MEX}=1.25$, $\gamma_{USA}=1.15$, $\gamma_{CAN}=1.10$) and decays for Mexico/Canada in knockout rounds played on U.S. soil; club-season fatigue ($\phi$) and travel/climate friction ($\tau$) enter as multiplicative attenuators. The model uses the official December 5, 2025 Final Draw, FIFA's published Round-of-32 allocation, and Annex C third-place combinatorics. Primary conclusions: **Spain** is the baseline champion (defeating Argentina on penalties after a 1–1 final at MetLife Stadium), France finishes third, and the expected per-match result hit rate of the baseline is ≈ 51.7%. ## 1. Methodology & Theoretical Framework The framework is a **calibrated independent Poisson goals model**. Each team $i$ carries a decomposed rating triple — Offensive Rating $O_i$, Defensive Rating $D_i$, and Overall Strength $R_i$ on a 0–100 scale — where the overall rating implements the user's interview calibration: $$R_i = 0.70 \cdot R_i^{recent} + 0.30 \cdot R_i^{hist}$$ $R_i^{recent}$ encodes continental-cycle evidence (Euro 2024, Copa América 2024, UEFA Nations League 2025, AFCON/Gold Cup form, and 2024–26 qualifying), anchored to the April 2026 FIFA ranking (France 1, Spain 2, Argentina 3, England 4, Portugal 5, Brazil 6); $R_i^{hist}$ encodes historical World Cup performance. Offensive and defensive ratings are the attack/defense decomposition of the same evidence and are the quantities consumed by the scoring engine. **Core metrics.** The engine consumes (i) the $O_i/D_i$ decomposition above (an Elo-family strength encoding standing in for xG/xGA attack-defense splits), (ii) the tiered host coefficient $\gamma$, (iii) a club-fatigue attenuator $\phi_i \in [0.980, 1.000]$ penalizing squads with the heaviest 2025–26 European club minute loads (Spain, England, France, Portugal at 0.980; minute-light squads at 1.000), and (iv) a travel/climate friction term $\tau_i \in [0.980, 1.000]$ reflecting that the United States hosts 78 of 104 matches: CONCACAF-based squads acclimated to summer heat and the venue footprint carry $\tau = 1.000$, while long-haul, cool-climate squads (e.g., Australia, Japan) carry $\tau = 0.980$. **Host-field scaling per user input (moderate, tiered).** Group stage: $\gamma_{MEX}=1.25$ (Estadio Azteca altitude at 2,240 m + crowd), $\gamma_{USA}=1.15$, $\gamma_{CAN}=1.10$. Because Mexico and Canada host only 13 matches each and the knockout tree migrates onto U.S. soil, the coefficient decays by round: Mexico 1.20 (R32, Mexico City) → 1.15 (R16) → 1.05 (QF onward); Canada 1.08 (R32) → 1.04 thereafter; the United States retains 1.15 throughout, including the East Rutherford final. **Extra time and penalties.** For knockout matches the 90-minute scoreline distribution is computed first. The probability that the home side ultimately advances is $$P_{adv} = P_{win90} + P_{draw90} \cdot \omega, \qquad \omega = \frac{P_{win90}}{P_{win90} + P_{loss90}}$$ i.e., conditional on a level 90 minutes, advancement odds in extra time/penalties inherit the relative 90-minute dominance ratio $\omega$ (a logistic-equivalent reduction that avoids inventing an independent shootout skill parameter). The published scoreline is the modal exact score among the union of (winner-victory cells) and (draw cells): when the tie sits inside the volatility band $|P_{adv} - 0.5| < 0.08$ **and** the joint modal scoreline is level, the model publishes the draw scoreline and designates the ET/penalties winner; otherwise it publishes the winner's modal victory scoreline. This produced 11 ET/penalty designations across 32 knockout matches (34%), consistent with the 2018–2022 empirical base rate. ### 1.1 Mathematical Formulation Goal-scoring intensities use an exponential strength link with multiplicative structural adjustments: $$\lambda_{H} = \mu \cdot \exp\!\left(\kappa \cdot \frac{O_H - D_A}{100}\right) \cdot \gamma_H \cdot \phi_H \cdot \tau_H$$ $$\lambda_{A} = \mu \cdot \exp\!\left(\kappa \cdot \frac{O_A - D_H}{100}\right) \cdot \gamma_A \cdot \phi_A \cdot \tau_A$$ with baseline intensity $\mu = 1.28$ goals/team/match (modern World Cup average) and differential sensitivity $\kappa = 2.3$. Goals are independent Poisson draws: $$P(X = k) = \frac{\lambda^k \cdot e^{-\lambda}}{k!}, \qquad P(i, j) = \frac{\lambda_H^i e^{-\lambda_H}}{i!} \cdot \frac{\lambda_A^j e^{-\lambda_A}}{j!}$$ Outcome probabilities integrate the truncated grid ($k \le 10$): $$P_{H} = \sum_{i>j} P(i,j), \quad P_{D} = \sum_{i=j} P(i,j), \quad P_{A} = \sum_{i