Implements the Elo based rating system for for multi-player games where the result is a placing or a score. This includes zero-sum games such as poker and mahjong. The default arguments used here are those used by Tenhou for riichi mahjong.
elom(x, nn = 4, exact = TRUE, base = c(30,10,-10,-30), status = NULL,
init = 1500, kfac = kriichi, history = FALSE, sort = TRUE, …,
placing = FALSE)A data frame containing 2nn+1 variables, where
nn is the number of players in a single game: (col 1)
a numeric vector denoting the time period in which the game
took place, (cols 2 to nn+1) numeric or character
identifiers for each of the nn players, (cols nn+2
to 2nn+1) the result of the game expressed as a number,
typically a score for each player (e.g. the number of remaining
chips in poker). Negative numbers are allowed.
Alternatively, the result can be a placing (e.g. 1 for
first place, 2 for second place), in which case the placing
argument MUST be set to TRUE. Placings must be integers: in the
event of a tie, multiple players can be given the same placing.
Number of players in a single game. If the number of players
varies, then this argument should be set to the maximum number of
players in any game, and the exact argument should be set to
FALSE. Unused player identifiers in x must then
be set to the missing value NA. The game score for NA
player identifiers is ignored and therefore can also be set to
NA.
If TRUE (the default), then every game always has
exactly nn players. If TRUE, then x cannot have
missing values.
The base values used for the rating. Can be a numeric
vector of length equal to nn, a numeric matrix with nrow(x)
rows and nn columns, or a vectorized function of
the game score. If a numeric vector, then the person with the highest
score gets base[1], the person with the second highest score
gets base[2], and so on. In the event of a tie on the game score,
tied players are given the largest available base value. For
games with less than nn players, see Details. If base is
a matrix, then the ith row is used for the ith game in x. If
base is a vectorized function, then each player gets
the result of the function applied to the game score. In Riichi
mahjong, where players start with 25000 points, a typical example
might be function(x) (x-25000)/250.
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, 1st, 2nd,
3rd and so on, and finally Lag, which
are all 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.
The K factor parameter. Can be a single number or
a vectorized function of two arguments, the first being the
ratings and the second being the number of games played. See
kriichi for an example.
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.
If the results are given as placings (e.g. 1 for
first place, 2 for second place) then this argument MUST be set
to TRUE, otherwise the placings will be interpreted
as game scores.
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 number of players for a single game.
The K factor or K factor function.
The character string "EloM".
For multi-player games there is no player one advantage parameter (e.g. a home advantage in football or a white advantage in chess).
If the sum of the vector base is not zero, or
if base is a function which is not zero when evaluated
at the starting chip/points value, then you may observe
unusual behaviour and/or substantial ratings inflation/deflation.
The two-player Elo system is based on game outcomes in the interval
[0,1] and therefore uses a different scaling. As a result, the K
factors here should be smaller. The default (as used by Tenhou)
is a K factor of 0.2 for players that have played a large number of
games (see kriichi).
If the number of players varies and base is a vector (of length
nn), then if the game has less than nn players, the vector
is reduced by successively removing the centre value (for odd lengths)
or by averaging both centre values (for even lengths). For example, if
the x data frame contains both four-player and three-player
mahjong games, then under the default values the three-player base
vector becomes c(30,0,-30), which is consistent with the vector
that Tenhou uses for three-player mahjong.
A numeric matrix can be used to allocate different base vectors to
different games. For example, in Riichi mahjong, games can be Tonpuusen
(East round only) or Hanchan (East and South rounds), and you may wish
to allocate different base vectors to each type.
Elo, Arpad (1978) The Rating of Chessplayers, Past and Present. Arco. ISBN 0-668-04721-6.
# NOT RUN {
robj <- elom(riichi)
robj
ut <- unique(riichi$Time)
robj <- elom(riichi[riichi$Time == ut[1],])
for(i in 2:length(ut)) {
robj <- elom(riichi[riichi$Time == ut[i],], status = robj$ratings)
}
robj
# }
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