import warnings
import numpy as np
from numpy.typing import NDArray
from scipy.optimize import minimize
# from .probabilities import compute_dixon_coles_probabilities
from penaltyblog.models.base_model import BaseGoalsModel
from penaltyblog.models.custom_types import (
GoalInput,
ParamsOutput,
TeamInput,
WeightInput,
)
from penaltyblog.models.football_probability_grid import (
FootballProbabilityGrid,
)
from .gradients import dixon_coles_gradient
from .loss import dixon_coles_loss_function
from .probabilities import compute_dixon_coles_probabilities
[docs]
class DixonColesGoalModel(BaseGoalsModel):
"""
Dixon and Coles adjusted Poisson model for predicting outcomes of football
(soccer) matches
Methods
-------
fit()
fits a Dixon and Coles adjusted Poisson model to the data to calculate the team strengths.
Must be called before the model can be used to predict game outcomes
predict(home_team, away_team, max_goals=15)
predict the outcome of a football (soccer) game between the home_team and away_team
get_params()
Returns the fitted parameters from the model
"""
[docs]
def __init__(
self,
goals_home: GoalInput,
goals_away: GoalInput,
teams_home: TeamInput,
teams_away: TeamInput,
weights: WeightInput = None,
):
"""
Dixon and Coles adjusted Poisson model for predicting outcomes of football
(soccer) matches
Parameters
----------
goals_home : array_like
The number of goals scored by the home team in each match
goals_away : array_like
The number of goals scored by the away team in each match
teams_home : array_like
The name of the home team in each match
teams_away : array_like
The name of the away team in each match
weights : array_like, optional
The weight of each match, by default None
"""
super().__init__(goals_home, goals_away, teams_home, teams_away, weights)
self._params = np.concatenate(
(
[1] * self.n_teams,
[-1] * self.n_teams,
[0.25], # home advantage
[-0.1], # rho
)
)
def __repr__(self) -> str:
lines = ["Module: Penaltyblog", "", "Model: Dixon and Coles", ""]
if not self.fitted:
lines.append("Status: Model not fitted")
return "\n".join(lines)
assert self.aic is not None
assert self.loglikelihood is not None
assert self.n_params is not None
lines.extend(
[
f"Number of parameters: {self.n_params}",
f"Log Likelihood: {round(self.loglikelihood, 3)}",
f"AIC: {round(self.aic, 3)}",
"",
"{0: <20} {1:<20} {2:<20}".format("Team", "Attack", "Defence"),
"-" * 60,
]
)
for idx, team in enumerate(self.teams):
lines.append(
"{0: <20} {1:<20} {2:<20}".format(
team,
round(self._params[idx], 3),
round(self._params[idx + self.n_teams], 3),
)
)
lines.extend(
[
"-" * 60,
f"Home Advantage: {round(self._params[-2], 3)}",
f"Rho: {round(self._params[-1], 3)}",
]
)
return "\n".join(lines)
def __str__(self):
return self.__repr__()
def _gradient(self, params):
attack = np.asarray(params[: self.n_teams], dtype=np.double, order="C")
defence = np.asarray(
params[self.n_teams : 2 * self.n_teams], dtype=np.double, order="C"
)
hfa = params[-2] # Home field advantage
rho = params[-1] # Dixon-Coles rho adjustment
return dixon_coles_gradient(
attack,
defence,
hfa,
rho,
self.home_idx,
self.away_idx,
self.goals_home,
self.goals_away,
self.weights,
)
def _loss_function(self, params: NDArray) -> float:
"""
Internal method, not to called directly by the user
"""
# Get params
attack = np.asarray(params[: self.n_teams], dtype=np.double, order="C")
defence = np.asarray(
params[self.n_teams : 2 * self.n_teams], dtype=np.double, order="C"
)
hfa = params[-2]
rho = params[-1]
return dixon_coles_loss_function(
self.goals_home,
self.goals_away,
self.weights,
self.home_idx,
self.away_idx,
attack,
defence,
hfa,
rho,
)
[docs]
def fit(self):
"""
Fits the model to the data and calculates the team strengths,
home advantage and intercept. Must be called before `predict` can be used
"""
options = {
"maxiter": 1000,
"disp": False,
}
constraints = [
{
"type": "eq",
"fun": lambda x: sum(x[: self.n_teams]) - self.n_teams,
}
]
bounds = [(-3, 3)] * self.n_teams * 2 + [(0, 2), (-2, 2)]
with warnings.catch_warnings():
warnings.filterwarnings("ignore")
self._res = minimize(
self._loss_function,
self._params,
constraints=constraints,
bounds=bounds,
options=options,
# jac=self._gradient,
)
if not self._res.success:
raise ValueError(f"Optimization failed with message: {self._res.message}")
self._params = self._res["x"]
self.n_params = len(self._params)
self.loglikelihood = self._res["fun"] * -1
self.aic = -2 * (self.loglikelihood) + 2 * self.n_params
self.fitted = True
[docs]
def predict(
self, home_team: str, away_team: str, max_goals: int = 15
) -> FootballProbabilityGrid:
"""
Predicts the probability of each scoreline for a given home and away team
Parameters
----------
home_team : str
The name of the home team
away_team : str
The name of the away team
max_goals : int, optional
The maximum number of goals to consider, by default 15
Returns
-------
FootballProbabilityGrid
A FootballProbabilityGrid object containing the probabilities of each scoreline
"""
if not self.fitted:
raise ValueError(
"Model's parameters have not been fit yet. Please call `fit()` first."
)
if home_team not in self.teams or away_team not in self.teams:
raise ValueError("Both teams must have been in the training data.")
home_idx = self.team_to_idx[home_team]
away_idx = self.team_to_idx[away_team]
home_attack = self._params[home_idx]
away_attack = self._params[away_idx]
home_defense = self._params[home_idx + self.n_teams]
away_defense = self._params[away_idx + self.n_teams]
home_advantage = self._params[-2]
rho = self._params[-1]
# Preallocate the score matrix as a flattened array.
score_matrix = np.empty(max_goals * max_goals, dtype=np.float64)
# Allocate one-element arrays for lambda values.
lambda_home = np.empty(1, dtype=np.float64)
lambda_away = np.empty(1, dtype=np.float64)
compute_dixon_coles_probabilities(
float(home_attack),
float(away_attack),
float(home_defense),
float(away_defense),
float(home_advantage),
float(rho),
int(max_goals),
score_matrix,
lambda_home,
lambda_away,
)
score_matrix.shape = (max_goals, max_goals)
return FootballProbabilityGrid(score_matrix, lambda_home, lambda_away)
[docs]
def get_params(self) -> ParamsOutput:
"""
Returns the model's fitted parameters as a dictionary
Returns
-------
dict
A dict containing the model's parameters
"""
if not self.fitted:
raise ValueError(
"Model's parameters have not been fit yet, please call the `fit()` function first"
)
assert self.n_params is not None
assert self._res is not None
params = dict(
zip(
["attack_" + team for team in self.teams]
+ ["defence_" + team for team in self.teams]
+ ["home_advantage", "rho"],
self._res["x"],
)
)
return params
@property
def params(self) -> dict:
"""
Property to retrieve the fitted model parameters.
Same as `get_params()`, but allows attribute-like access.
Returns
-------
dict
A dictionary containing attack, defense, home advantage, and correlation parameters.
Raises
------
ValueError
If the model has not been fitted yet.
"""
return self.get_params()
