The goal of footBayes is to propose a complete workflow to:
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Fit the most well-known football models, including the double Poisson, bivariate Poisson, Skellam, and Student‑t distributions. It supports both maximum likelihood estimation (MLE) and Bayesian inference. For Bayesian methods, it incorporates several techniques: MCMC sampling with Hamiltonian Monte Carlo, variational inference using either the Pathfinder algorithm or Automatic Differentiation Variational Inference (ADVI), and the Laplace approximation.
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Visualize the teams' abilities, the model checks, the rank-league reconstruction;
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Predict out-of-sample matches.
Starting with version 2.0.0, footBayes package requires installing the R package cmdstanr (not available on CRAN) and the command-line interface to Stan: CmdStan.
For a step-by-step installation, please follow the instructions provided in Getting started with CmdStanR.
You can install the released version of footBayes from CRAN with:
install.packages("footBayes", type = "source")Please note that it is important to set type = "source". Otherwise,
the ‘CmdStan’ models in the package may not be compiled during
installation.
Alternatively to CRAN, you can install the development version from GitHub with:
# install.packages("devtools")
devtools::install_github("leoegidi/footBayes")In what follows, a quick example to fit a Bayesian double Poisson model for the Italian Serie A (seasons 2000-2001, 2001-2002, 2002-2003), visualize the estimated teams’ abilities, and predict the last four match days for the season 2002-2003:
library(footBayes)
library(dplyr)# Dataset for Italian Serie A
data("italy")
italy <- as_tibble(italy)
italy_2000_2002 <- italy %>%
dplyr::select(Season, home, visitor, hgoal, vgoal) %>%
filter(Season == "2000" | Season == "2001" | Season == "2002")
colnames(italy_2000_2002) <- c("periods",
"home_team",
"away_team",
"home_goals",
"away_goals")
# Double poisson fit (predict last 4 match-days)
fit1 <- stan_foot(data = italy_2000_2002,
model = "double_pois",
predict = 36,
iter_sampling = 200,
chains = 2) The results (i.e., attack and defense effects) can be investigated using
print(fit1, pars = c("att", "def"))To visually investigate the attack and defense effects, we
can use the foot_abilities function
foot_abilities(fit1, italy_2000_2002) # teams abilitiesTo check the adequacy of the Bayesian model the function pp_foot provides posterior predictive plots
pp_foot(fit1, italy_2000_2002) # pp checksFurthermore, the function foot_rank shows the final rank table and the plot with the predicted points
foot_rank(fit1, italy_2000_2002) # rank league reconstructionIn order to analyze the possible outcomes of the predicted matches, the function foot_prob provides a table containing the home win, draw and away win probabilities for the out-of-sample matches
foot_prob(fit1, italy_2000_2002) # out-of-sample posterior pred. probabilitiesFor more and more technical details and references, see the vignette!