rank.teams: Team Ranks Via Poission Regression

Description

Creates ranks using a dataframe of match records. This, along with print.fbRanks and predict.fbRanks, are the main functions in the package. Use vignette("Basic_team_ranking",package="fbRanks") at the command line to open a vignette that walks through a basic ranking using a data.frame or comma-delimited text file.

Usage

rank.teams(scores=NULL, teams=NULL,  family="poisson", fun="glm", max.date="2100-6-1", min.date="1900-5-1", date.format="%Y-%m-%d", time.weight.eta=0, add=NULL, silent=FALSE, ...)

Arguments

scores

A data frame of match results. Must have columns "date", "home.team", "home.score", "away.team", "away.score". Missing scores must be denoted NaN. Extra columns to be used for filtering in print results or as explanatory variables can be included, e.g. surface or attack.adv.

teams

A data frame with the team data. Must have columns "name" and "alt.name.x", where x can be anything, e.g. 1. Extra columns to be used for filtering in print results or as explanatory variables can be included, e.g. age. None of the column names in the teams data frame are allowed to be the same as names in the scores data frame.

family

Passed to glm or glmer. If you are using speedglm, use the glm notation for family, e.g. "poisson", rather than the equivalent speedglm notation, e.g. poisson(log).

fun

"glm", "glmnet", or "speedglm"

max.date

Latest match date to use when fitting the model.

min.date

Earliest match date to use when fitting the model.

date.format

The date formate for max.date, min.date and dates in the scores dataframe.

add

Vector of explanatory variables to add to the model. Must be a character vector that corresponds to names of columns in scores or teams dataframes.

time.weight.eta

How much time weighting to include. 0 is no weighting. 0.1 would weight the most recent games quite strongly.

silent

Suppresses printing.

...

Other filters to apply when ranking. These must match column names in either teams or scores. For example, if teams has a column named 'country' with values 'UK','Canada' and 'Germany', you can pass in country="UK" to only rank using the matches for UK teams.

Value

fit: A list with the glm fit for each cluster.
graph: A list with some information about the graph describing the interconnectedness of the teams from the igraph package. The elements are graph (output from graph.edgelist), membership (output from cluster), csize (output from cluster), no (output from cluster), names (output from get.vertex.attribute).
scores: The scores dataframe with all team names replaced with display names.
teams: The teams data.frame.
max.date: The most recent match used in model fit.
min.date: The oldest match used in model fit.
time.weight.eta: The time weighting used.
date.format: The date format to use when displaying output using the fbRanks object.

Details

The function uses Dixon and Coles time-weighted poisson model to estimate attack and defense strengths using the glm function. Extra explanatory variables (factors or continuous) can be added to the model. The output is a print out of the attack+defense strengths (in total column) and the exp(attack) and exp(defense) strengths in separate columns. Take the ratio of team A's attack strength to the team B's defense strength to get the expected goals scored by team A in a match between A and B.

The 2 raised to the difference in total strengths of two teams is the relative scoring rate of team A to team B. Thus if the difference in total strength is 1 (team A - team B = 1) then team A scores 2^1 times faster than team B (in a match up between the two) and expected to score 2 goals for every 1 of team B. If the diffence is 3, then team A is expected to score 2^3 = 8 goals for every 1 of team B.

The model can be fit with three different glm functions: glm(), speedglm(), and glmnet() using the fun argument. speedglm() requires the speedglm package. It is considerably faster than glm() and returns identical coefficient values. glmnet() requires the glmnet package. It uses a different algorithm and does not return exactly the same values as glm(). lambda=0 is passed to the glmnet() (in the rank.teams code) to force it to return the OLS values, yet for the poisson family there are some small differences. However, it is exceedingly fast and uses little RAM. It is required for ranking large datasets with 1000s of teams because glm() and speedglm() have extreme RAM requirements for models with 1000s of teams and take excessive amounts of time to fit. In addition, testing suggests that glmnet() coefficients are more robust (closer to true values) for these large models.

References

Dixon and Coles (1997) Modeling Association Football Scores and Inefficiencies in the Football Betting Market, Applied Statistics, Volume 46, Issue 2, 265-280

Examples

Run this code

#load the example data set
data(B00data)

#rank teams in the RCL D1 league using just the league data
x=rank.teams(scores=B00.scores, teams=B00.teams, venue="RCL D1")

#repeat with surface (turf, grass) as an explanatory variable
ranks2=rank.teams(scores=B00.scores, teams=B00.teams, venue="RCL D1", add=c("surface","adv"))

#Slightly fewer goals per game are scored on turf
coef(ranks2)$coef.list$cluster.1$surface.f

#Slightly more goals per game are scored at home
coef(ranks2)$coef.list$cluster.1$adv.f

#get the ranks based on summer data
# x=rank.teams(scores=B00.scores, teams=B00.teams, 
#              min.date="2012-5-1", max.date="2012-9-8", silent=TRUE)

# See the vignette Basic Team Ranking for more examples

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