The Science
GOLAZO prices every match with the same toolkit quants use to beat real sportsbooks. Every chart below is live — drag the sliders.
📈 1 · Elo ratings — measuring strength
Every nation carries an Elo rating. The probability that team A beats team B is the logistic curve
E_A = 1 / (1 + 10^(−(R_A − R_B + H) / 400))
Win-expectancy E = 1 / (1 + 10−Δ/400). A +120 edge ≈ 67% expectancy.
H is home-field advantage in Elo points (~70, ≈ 0.4 goals), applied only to the host nations. After each result ratings exchange points, R′ = R + K·G·(W − E): K weights match importance, G dampens blowouts. Drag the slider to see how an Elo gap maps to win-expectancy.
⚽ 2 · Poisson — how many goals?
A team that is expected to score λ goals actually scores k goals with Poisson probability
P(k) = e^(−λ) · λ^k / k!
P(k goals) = e−λ·λk/k!. The most likely scoreline shifts right as λ grows.
Football goals are close to Poisson. The Elo gap sets each side’s λ. Slide λ and watch the goal distribution shift.
🔢 3 · Dixon–Coles — the scoreline matrix
Two independent Poissons under-count 0-0 and 1-1 draws, so Dixon & Coles (1997) multiply the low-score cells by a correction τ(ρ):
P(x, y) = τ_ρ(x, y) · Poisson(x; λ_h) · Poisson(y; λ_a)
Most likely score 1–1 (12.2%). The 6×6 grid is the joint pmf with the Dixon–Coles low-score correction.
The normalised grid is the joint distribution of every scoreline — and from it we read 1X2, over/under, both-teams-to-score and the most likely score. Set the two λ’s and explore.
🎲 4 · Monte-Carlo — simulating the cup
We play all 104 matches thousands of times and count how often each team wins. The estimate of any probability converges as the number of simulations N grows:
P(event) ≈ (# sims with event) / N, error ∝ 1/√N
The estimate wobbles, then homes in on the truth. Monte-Carlo error shrinks like 1/√N.
Watch a single probability being estimated live — noisy at first, then converging on the truth. That’s why the tournament page runs thousands of sims.
🧮 5 · Odds, EV & Kelly — sizing the bet
Fair odds are o = 1/p. If you believe the true probability is p, your edge is EV = p·(o−1) − (1−p), and the growth-optimal stake is the Kelly fraction
f* = (p·(o − 1) − (1 − p)) / (o − 1)
Growth peaks at the Kelly fraction f* = (p·b − q)/b. Bet more and long-run growth falls; past 2f* you go broke.
The curve is your long-run log-growth versus how much of your bankroll you stake. It peaks exactly at f*. No edge (EV ≤ 0) → f* = 0, don’t bet. We suggest half-Kelly to tame variance.
🔮 6 · Brier score — grading your judgement
When you commit a probability vector over {home, draw, away}, we grade it with a strictly proper scoring rule you can only beat by being honest:
Brier = Σ_k (p_k − o_k)² Skill = 1 − Brier_you / Brier_ref
o_k is the actual outcome (one-hot). Averaged over your settled bets and benchmarked against a coin-flip prior, this Brier Skill Score ranks forecasting ability independently of how many coins you wagered. The skill leaderboard rewards calibration, not luck.