import warnings
import numpy as np
from numpy.typing import NDArray
from scipy.optimize import minimize
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 .loss import compute_bivariate_poisson_loss
from .probabilities import compute_bivariate_poisson_probabilities
[docs]
class BivariatePoissonGoalModel(BaseGoalsModel):
"""
Karlis & Ntzoufras Bivariate Poisson for soccer, with:
X = W1 + W3
Y = W2 + W3
where W1, W2, W3 ~ independent Poisson(lambda1, lambda2, lambda3).
"""
[docs]
def __init__(
self,
goals_home: GoalInput,
goals_away: GoalInput,
teams_home: TeamInput,
teams_away: TeamInput,
weights: WeightInput = None,
):
"""
Initialises the BivariatePoissonGoalModel class.
Parameters
----------
goals_home : array_like
The number of goals scored by the home team
goals_away : array_like
The number of goals scored by the away team
teams_home : array_like
The names of the home teams
teams_away : array_like
The names of the away teams
weights : array_like, optional
The weights of the matches, by default None
"""
super().__init__(goals_home, goals_away, teams_home, teams_away, weights)
self._params = np.concatenate(
(
[0.0] * self.n_teams, # Attack
[0.0] * self.n_teams, # Defense
[0.1], # Home advantage
[0.0], # correlation_param => lambda3 = exp(0)=1
)
)
def __repr__(self) -> str:
lines = ["Module: Penaltyblog", "", "Model: Bivariate Poisson", ""]
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"Correlation: {round(self._params[-1], 3)}",
]
)
return "\n".join(lines)
def _loss_function(self, params: NDArray) -> float:
# 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]
correlation = params[-1]
return compute_bivariate_poisson_loss(
self.goals_home,
self.goals_away,
self.weights,
self.home_idx,
self.away_idx,
attack,
defence,
hfa,
correlation,
)
[docs]
def fit(self):
"""
Fits the Bivariate Poisson model to the data.
"""
options = {"maxiter": 1000, "disp": False}
constraints = [
{"type": "eq", "fun": lambda x: sum(x[: self.n_teams]) - self.n_teams}
]
bnds = [(-3, 3)] * (2 * self.n_teams) + [(-2, 2), (-3, 3)]
with warnings.catch_warnings():
warnings.filterwarnings("ignore")
self._res = minimize(
self._loss_function,
self._params,
constraints=constraints,
bounds=bnds,
options=options,
)
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 = 10
) -> 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 10
Returns
-------
FootballProbabilityGrid
A FootballProbabilityGrid object containing the probability of each scoreline
"""
if not self.fitted:
raise ValueError("Model is not yet fitted. 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]
correlation = 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_bivariate_poisson_probabilities(
float(home_attack),
float(away_attack),
float(home_defense),
float(away_defense),
float(home_advantage),
float(correlation),
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:
"""
Return the fitted parameters in a dictionary.
"""
if not self.fitted:
raise ValueError("Model is not yet fitted. Call `.fit()` first.")
# Construct dictionary
param_names = (
[f"attack_{t}" for t in self.teams]
+ [f"defense_{t}" for t in self.teams]
+ ["home_advantage", "correlation_log"]
)
vals = list(self._params)
result = dict(zip(param_names, vals))
# Also show lambda3 explicitly
result["lambda3"] = np.exp(result["correlation_log"])
return result
