Implements the Glicko-2 rating system for estimating the relative skill level of players in two-player games such as chess. It extends the Glicko method by including a volatility parameter for each player, representing the degree of expected fluctuation in the rating. Volatility is therefore a measure of consistency of performance.
glicko2(x, status = NULL, init = c(2200,300,0.15), gamma = 0,
tau = 1.2, history = FALSE, sort = TRUE, rdmax = 350, …)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,
Deviation, Volatility, and optionally Games,
Win, Draw, Loss and Lag, which are
set to zero if not given.
The rating vector at which to initialize a new player
not appearing in status. Must be a vector of length three
giving the initial rating, initial deviation and initial volatility
respectively. If different initializations for different players are
required, this can be done using status. The initial
deviation cannot be greater than rdmax. The initial
volatility cannot be greater than rdmax divided by
400/log(10).
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 tau parameter, which controls the change in the player volatility across time. Smaller values prevent the volatility measures from changing by large amounts. Must be a single number. Mark Glickman suggests a value between 0.3 and 1.2. A non-positive value can be specified, in which case the volatilities are never updated.
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.
The maximum value allowed for the rating deviation.
The maximum value allowed for the volatility is rdmax
divided by 400/log(10).
Not used.
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 tau parameter.
The character string "Glicko-2".
The Glicko-2 rating system is a method for evaluating the skill
of players. It is more complex than Glicko because it includes a
volatility for each player. It requires a single parameter
optimization for each player within each time period. We use the
R function optimize in preference to the root-finding
approaches suggested in Glickman (2001) and Glickman (2013).
Default values are roughly optimized for the chess data analyzed
in the file doc/ChessRatings.pdf, using the binomial deviance
criterion. 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.
Glickman, M.E. (2001) Dynamic paired comparison models with stochastic variances. Journal of Applied Statistics, 28, 673-689.
Glickman, M.E. (2013) Example of the Glicko-2 system.
# NOT RUN {
initstate <- data.frame(Player=1:4, Rating = c(1500,1400,1550,1700),
Deviation = c(200,30,100,300), Volatility = 0.06)
games <- data.frame(Week = 1, Payer1 = 1, Player2 = 2:4, Score = c(1,0,0))
robj <- glicko2(games, status = initstate, tau = 0.5, sort = FALSE)
print(robj, cols = 1:4, digits = 6)
afl <- aflodds[,c(2,3,4,7)]
robj <- glicko2(afl)
robj
robj <- glicko2(afl[afl$Week==1,])
for(i in 2:max(afl$Week)) robj <- glicko2(afl[afl$Week==i,], robj$ratings)
robj
# }
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