Implements the Elo rating system for estimating the relative skill level of players in two-player games such as chess, implementing a version similar to that employed by the FIDE.
fide(x, status = NULL, init = 2200, gamma = 0, kfac = kfide,
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 Lag and Elite, which are set
to zero if not given, and Opponent, which is set
to the player rating 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.
The K factor parameter. Can be a single number or
a vectorized function of three arguments, the first being the
ratings, the second being the number of games played, and the
third being a binary indicator for whether or not a player
has ever achieved a rating above 2400. See kfide,
kgames and krating for examples.
The function kfide is used by default.
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, Elite, which
is a binary indicator for whether or not a player has ever
reached 2400, and Opponent, which gives the average
rating of all opponents. The Lag variable 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. The Elite variable is required due to the
K factor dependency in the FIDE implementation. The
Opponent variable is not currently used in the
updating algorithm.
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 uses default arguments that are consistent
with the implementation of FIDE for rating chess players.
It does not employ the initialization used by FIDE. For the
chess data analyzed in the file doc/ChessRatings.pdf, prediction
performance is poor because the default values of the K factors
are too low. This can be altered using the kv argument
which is passed to the function kfide.
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 <- fide(afl)
robj
robj <- fide(afl[afl$Week==1,])
for(i in 2:max(afl$Week)) robj <- fide(afl[afl$Week==i,], robj$ratings)
robj
# }
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