Football_SBM

This repository contains the data and code associated with the paper:
"F. Basini, V. Tsouli, I. Ntzoufras, N. Friel, Assessing competitive balance in the English Premier League for over forty seasons using a stochastic block model, Journal of the Royal Statistical Society Series A: Statistics in Society, 2023".

Repository structure:

• README.md - you're reading it
• /Data_Premier - contains the tables of results (match grids) of the Premier League championship from season 1978/79 to 2019/20 in csv format. e.g. Result_Premier_0102.csv for season 2001/02.
  • Note on the data: each csv file contains the results table where entries of the main diagonal are blank and the entry of match results is written as | 4~3 | for a match won 4 to 3 by row team against col team, where row team is playing home.
• LABEL_CORRECTION_AND_ANALYSIS.R - code to apply the label switching algorithm (collpcm) and carry out post-hoc analysis of the chain.
• SBM_FUNCTIONS.R - contains all functions used in the MCMC algorithm. e.g. get_loglik returns the collapsed loglikelihood.
• READ_TABLE_RESULTS.R - code to load the result table and extract the relational pattern y.
• MCMC_main.R - the heart (:heartpulse:) of the whole code which calls the other source files and runs the MCMC algorithm.
• /Inference_results - now empty, folders for each season analysed will be created inside this folder once the code is run, e.g. [/Inference_results/mcmc_Premier_Season_0102] for season 2001/02.
• OVER_TIME_ANALYSIS.R - script to run the analysis for all the season in the data folder and to produce the analysis of top block probability over time and the associated plots.

Usage

• Clone repository.

To analyse one season at a time

---

• Open MCMC_main.R in RStudio and set Football_SBM as your working directory.
• Uncomment line 29 and set season to the season you want to analyse using the last two digits of each year, e.g. "1819" for 2018/19. (Provided that it is between 1978/79 and 2019/20)

season = "1819"

• Run it all. Waiting time: about 4 minutes

---

To analyse all seasons altogether

---

• Open OVER_TIME_ANALYSIS.R in RStudio and set Football_SBM as your working directory.
• Run it all. Waiting time: about 2 and a half hours

---

Results

In the associated folder /Inference_results/mcmc_Premier_Season_*season* that will be created, the following items will be available:

File name and description	Output
FinalTable_Premier_Season_*season*_*iter*k_seed_*seed*.txt is the final league table for the season, in latex format.
Heatmap_Season_*season*.pdf the match grid of the season with results categorised by colour.
Heatmap_Estimated_Season_*season*.pdf the permuted match grid of the season, from *a posteriori* analysis, with teams listed according to the most likely block membership, results categorised by colour. This file is saved only when the MAP for K is larger than 1.
Ktrue_NF_Premier_Season_*season*_*iter*k_seed_*seed*.pdf is the jittered traceplot of K as plotted in Nobile and Fearnside (2007).
For each value of K (number of clusters) predicted:
Summary_table_Premier_Season_season_iterk_seed.txt is the table of posterior allocations of the teams in the league, in latex table format.
StackedPlot_Premier_Season_*season*_*iter*k_seed_*seed*.pdf is the stacked plot of posterior allocations of the teams in the league ordered by the final ranking to the associated Summary_table.
Also: WS_Premier_Season_*season*_*iter*k_seed_*seed*.RData the whole workspace is saved at the end of the analysis.

In addition, if you are using OVER_TIME_ANALYSIS.R, there will be one futher directory mcmc_Premier_OVER_TIME_ANALYSIS, which will contain:

• mcmc_Premier_OVER_TIME.RData the workspace regarding the over time analysis.
• Posterior_K_table_OVER_TIME.txt the table with posterior probability of K over each season.

* Size_top_block_table.txt the table with size of the estimated top block over each season. * TopBlock_Size_barplot.pdf the barplot showing the value of the size of the estimated top block over each season.

* TopBlock_prob_datapoints_JITTERED.pdf the plot of the probability of being in the top block for all teams in the league and over all seasons.

* \Over_time_Teams folder containing the probability of belonging to the top block over each season but focusing on one team at a time (see Fig. 8 of the paper). Below we provide an example for Manchester City:

Dependencies:

All packages used are available on CRAN.

• Data wrangling:

install.packages("plyr")
install.packages("stringi")
install.packages("seqinr")

• Plotting:

install.packages("RColorBrewer")
install.packages("lattice")

• Printing tables in Latex format:

install.packages("xtable")

• Algorithm to adjust for label switching:

install.packages("collpcm")

Jason Wyse and Caitriona Ryan (2019). collpcm: Collapsed Latent Position Cluster Model for Social Networks. R package version 1.1. https://CRAN.R-project.org/package=collpcm