Implements the Stephenson 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 second parameter controlling player deviation across time, a bonus parameter, and a neighbourhood parameter.
steph(x, status = NULL, init = c(2200,300), gamma = 0, cval = 10,
hval = 10, bval = 0, lambda = 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, 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 two
giving the initial rating and initial deviation respectively.
If different initializations for different players are
required, this can be done using status. The initial
deviation cannot be greater than rdmax.
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 c parameter, which controls the increase in the
player deviations across time. Must be a single non-negative number.
Note that both cval and hval increase player
deviations, so if hval is not zero then cval should
typically be lower than the corresponding parameter in
glicko.
The h parameter, which also controls the increase in the player deviations across time. Must be a single non-negative number.
The bonus parameter, which gives a per game bonus to each player on the basis that players who play more often may improve irrespective of whether they win or lose. A single non-negative number. Note that this will create ratings inflation (i.e. ratings will increase over time).
The neighbourhood parameter, which shrinks player ratings towards their opponents. A single non-negative number.
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.
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 c parameter.
The h parameter.
The bonus parameter.
The neighbourhood parameter.
The character string "Stephenson".
The Stephenson rating system is a method for evaluating the skill of players. It was developed by Alec Stephenson in 2012 as a variant of his winning entry in a competition to find the most useful practical chess rating system, organized by Jeff Sonas on Kaggle, a platform for data prediction competitions. The precise details are given in the file doc/ChessRatings.pdf.
This implementation is written so that Glicko is obtained as a
special case upon setting all of the parameters hval,
bval and lambda to zero. Default values are roughly
optimized for the chess data analyzed in the file
doc/ChessRatings.pdf, using the binomial deviance criterion.
Glickman, M.E. (1999) Parameter estimation in large dynamic paired comparison experiments. J. R. Stat. Soc. Ser. C: Applied Statistics, 48(3), 377-394.
Glickman, M.E. (2001) Dynamic paired comparison models with stochastic variances. Journal of Applied Statistics, 28, 673-689.
# NOT RUN {
afl <- aflodds[,c(2,3,4,7)]
robj <- steph(afl)
robj
robj <- steph(afl[afl$Week==1,])
for(i in 2:max(afl$Week)) robj <- steph(afl[afl$Week==i,], robj$ratings)
robj
# }
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