World Cup Predictor

This is a simple predictor for FIFA World Cup matches that implements a probabilistic Poisson's model based on ELO rating differences to calculate the most likely outcomes.

Probabilistic Model

The model uses Poisson distributions to calculate the probability each team scores a given number of goals.

Let X be the random variable representing the number of goals scored by team A, and Y the random variable representing the number of goals scored by team B.

We asume that

$$ X \sim \text{Poiss}(\lambda_{1}), \quad Y \sim \text{Poiss}(\lambda_{2}) $$

To estimate the two goal rates, two constraints were used.

The first constraint computes the probability of team A victory according to the ELO rating:

$$ p_{A} = \frac{1}{1 + 10^{-\left( R_{A} - R_{B} \right)/400}} $$

where $R_{A}, R_{B}$ are the ELO ratings of team A and team B, respectively.

Then constraint is then

$$ \mathbb{P} (X > Y) = p_{A} $$

The second constraint asumes that the expected number of goals per match in this World Cup is 2.6. So,

$$ \mathbb{E} \left[ X + Y \right] = \lambda_{1} + \lambda_{2} = 2.6 $$

Then, a root finder algorithm is used to get the to parameters of the distributions.

Finally, the most likely match outcomes are computed from the resulting distributions.

Data

The data is extracted from this open web site.

Usage

Example:

uv run main.py COL ARG