How the model works
ParallaxEdge produces independent, calibrated forecasts for every match, and publishes the reasoning and the track record behind them. Here’s how.
A Bayesian core
Our primary engine is a Bayesian hierarchical model in the Dixon-Coles tradition. It estimates each team's attacking and defensive strength while accounting for the correlation between low-scoring outcomes that simpler Poisson models miss.
The Bayesian framing matters because it carries uncertainty through the whole pipeline. We don't just produce a number — we produce a distribution. That's what makes honest confidence bands, not false precision, possible on every forecast.
Built on recent international football
The model is trained on roughly 1,700 recent international matches across eight competitions — the World Cup and its qualifiers, the Nations League, and the continental championships (the Euros, Copa América, the Africa Cup of Nations, the Asian Cup, and the Gold Cup). Where shot-quality data exists it blends expected goals with actual results; where it doesn't, it learns from results alone — with per-competition effects, so a qualifier and a World Cup knockout aren't treated as the same kind of match.
Every input is validated and versioned before it reaches the model, so any forecast can be reproduced from the exact data it was built on. When we publish a score, it's traceable, not a moving target.
Calibrated, and scored in public
We measure forecast quality with the Brier score, the standard for probabilistic predictions. Lower is better, and it rewards calibration over bravado: a model that confidently calls the wrong outcome is punished more than one that expressed appropriate uncertainty.
Out of sample — on matches the model never trained on — it scores about 0.31. Just as important, it's well-calibrated: when it says 60%, that outcome happens about 60% of the time. Once the tournament begins, every forecast is scored in the open, per competition, including the misses. If the model drifts, the score shows it before we do.
A probability isn't a prediction
When the model gives a team a 15% chance and they win, the model wasn't wrong — a 15% event is supposed to happen about one time in seven. Read a single result as a pass/fail grade and you'll mislearn from it every time. A probability is a statement about how often something happens across many similar situations, not a verdict on the one match in front of you. Half the value of a forecast lives in the games it says are close.
So how do you actually judge a forecaster? Not on whether the favorite won on Saturday — on whether its probabilities hold up over hundreds of games. That's exactly what calibration and proper scores like the Brier score measure: when it says 30%, do those things happen about 30% of the time? A model is genuinely wrong when it's miscalibrated — its 30%s landing at 50%, its 80%s at 60% — not when a fairly-priced underdog has its day. We publish the running score so the honest version of “were we right?” is the one on display.
Independent of the market
Our forecasts are generated by our own model. We show the market's implied probabilities alongside ours for comparison — but we never derive our numbers from them. The point of comparison is insight, not imitation.
ParallaxEdge is built to help you understand the game.
Every forecast, explained
A probability with no explanation is just a number to trust or ignore. Every ParallaxEdge forecast ships with the specific factors that drove it — a key injury, fixture congestion, a tactical mismatch, home advantage — each ranked, with a direction and a magnitude, in plain language.
The goal isn't to make you trust the model blindly. It's to show enough of its reasoning that you can judge it for yourself.
The full model — calibrated probabilities and the factors behind them — launches with the World Cup opener, free.
Join the waitlist