R/e.single.R

In EloRating: Animal Dominance Hierarchies by Elo Rating

#' Elo ratings for a single interaction
#'
#' calculate/update Elo ratings for a single dyadic interaction
#'
#' @param ELO1old,ELO2old numeric, Elo rating of the first and second individual
#' @param outcome \code{1} = first individual wins and second looses\cr
#' \code{2} = second individual wins and first looses\cr
#' \code{0} = interaction ends in a draw/tie (no winner and no looser)
#' @param k numeric, \emph{k} factor, by default \code{k = 100}
#' @param normprob logical (by default \code{TRUE}). Should a normal curve be assumed for calculating the winning/losing probablities, or a logistic curve. See \code{\link{winprob}} for details
#'
#' @return integer vector of length 2 with updated ratings of first and second individual after the interaction
#'
#' @references
#' \insertRef{elo1978}{EloRating}
#'
#' \insertRef{albers2001}{EloRating}
#'
#' @importFrom stats pnorm
#'
#' @author Christof Neumann
#'
#' @examples
#' e.single(ELO1old = 1200, ELO2old = 1000, outcome = 1, k = 100)
#' # same as before
#' e.single(ELO1old = 1000, ELO2old = 1200, outcome = 2, k = 100)
#' # an undecided interaction
#' e.single(ELO1old = 1200, ELO2old = 1000, outcome = 0, k = 100)
#' # if rating differences are too big, no change occurs
#' # if higher-rated individual wins
#' e.single(ELO1old = 2000, ELO2old = 1000, outcome = 1, k = 100)
#' # same as before but lower-rated individual wins and
#' # therefore wins maximum number of points possible (i.e. k)
#' e.single(ELO1old = 2000, ELO2old = 1000, outcome = 2, k = 100)
#'
#' @export

e.single <- function(ELO1old, ELO2old, outcome, k = 100, normprob = TRUE) {

  # outcome must be one of the following:
  # "1" = first individual wins and second looses
  # "2" = second individual wins and first looses
  # "0" = interaction ends in a draw/tie (no winner and no looser)

  # normprob:
  # should winning probability calculated from normal curve or logistic curve?

  # calculates the difference between the two ratings
  ELO_diff <- ELO1old - ELO2old

  if (normprob) {
    # z score based on fixed SD=200 (see Elo 1978)
    z_score <- ELO_diff / (200 * sqrt(2))
    # calculates the winning probabilty
    p_win <- pnorm(z_score)
  } else {
    # winning probability based on logistic approach
    p_win <- 1 - 1 / (1 + 10 ^ ( ELO_diff / 400 ))
  }

  # product of winning probabilty and k-factor
  kp <- k * p_win

  # the actual updating calculations
  if (outcome == 1) {
    ELO1new <- ELO1old - kp + k
    ELO2new <- ELO2old + kp - k
  }
  if (outcome == 2) {
    ELO1new <- ELO1old - kp
    ELO2new <- ELO2old + kp
  }
  if (outcome == 0) {
    ELO1new <- ELO1old - kp + 0.5 * k
    ELO2new <- ELO2old + kp - 0.5 * k
  }
  # returning the updated ratings
  # ratings are rounded to integers
  return(round(c(ELO1new, ELO2new), 0))
}