Implements the Elo rating system for estimating the relative skill level of players in two-player games such as chess.
elo(x, status = NULL, init = 2200, gamma = 0, kfac = 27,
history = FALSE, sort = TRUE, …)A data frame containing four variables: (1) a numeric vector denoting the time period in which the game took place (2) a numeric or character identifier for player one (3) a numeric or character identifier for player two and (4) the result of the game expressed as a number, typically equal to one for a player one win, zero for a player two win and one half for a draw.
A data frame with the current status of the
system. If not NULL, this needs to be a data frame
in the form of the ratings component of the returned
list, containing variables named Player, Rating,
and optionally Games, Win, Draw,
Loss and Lag, which are set to zero if not given.
The rating at which to initialize a new player not
appearing in status. Must be a single number. If
different initializations for different players are required,
this can be done using status.
A player one advantage parameter; either a single
value or a numeric vector equal to the number of rows in
x. Positive values favour player one, while negative
values favour player two. This could represent the advantage
of playing at home, or the advantage of playing white for chess.
Note that this is not passed to predict.rating,
which has its own gamma parameter.
If TRUE returns the entire history for each
period in the component history of the returned list.
If TRUE sort the results by rating (highest
to lowest). If FALSE sort the results by player.
Passed to the function kfac.
A list object of class "rating" with the following
components
A data frame of the results at the end of the
final time period. The variables are self explanatory except
for Lag, which represents the number of time periods
since the player last played a game. This is equal to zero
for players who played in the latest time period, and is
also zero for players who have not yet played any games.
A three dimensional array, or NULL if
history is FALSE. The row dimension is the
players, the column dimension is the time periods.
The third dimension gives different parameters.
The player one advantage parameter.
The K factor or K factor function.
The character string "Elo".
The Elo rating system is a simple method for evaluating the skill
of players. It has been used since around 1960 and is still
employed in various settings. Although the basic form uses only
the ratings, additional complexity is commonly introduced
by adding a player one advantage parameter and by using different
K factors. A player one advantage parameter has been added to the
original definition in the reference. A player one advantage
parameter is also used for prediction purposes in
predict.rating.
This implementation has a simple initialization, and allows the
K factor to depend on both the ratings and the number of games
played. Default values are roughly optimized the chess data
analyzed in the file doc/ChessRatings.pdf, using the binomial
deviance criterion and considering only constant K factors.
See the function fide for a different
implementation.
Elo, Arpad (1978) The Rating of Chessplayers, Past and Present. Arco. ISBN 0-668-04721-6.
# NOT RUN {
afl <- aflodds[,c(2,3,4,7)]
robj <- elo(afl)
robj
robj <- elo(afl[afl$Week==1,])
for(i in 2:max(afl$Week)) robj <- elo(afl[afl$Week==i,], robj$ratings)
robj
# }
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