R/icehockey.R

In BradleyTerry2: Bradley-Terry Models

#' College Hockey Men's Division I 2009-10 results
#' 
#' Game results from American College Hockey Men's Division I composite
#' schedule 2009-2010.
#' 
#' The Division I ice hockey teams are arranged in six conferences: Atlantic
#' Hockey, Central Collegiate Hockey Association, College Hockey America, ECAC
#' Hockey, Hockey East and the Western Collegiate Hockey Association, all part
#' of the National Collegiate Athletic Association. The composite schedule
#' includes within conference games and between conference games.
#' 
#' The data set here contains only games from the regular season, the results
#' of which determine the teams that play in the NCAA national tournament.
#' There are six automatic bids that go to the conference tournament champions,
#' the remaining 10 teams are selected based upon ranking under the NCAA's
#' system of pairwise comparisons
#' (\url{https://www.collegehockeynews.com/info/?d=pwcrpi}). Some have argued
#' that Bradley-Terry rankings would be fairer
#' (\url{https://www.collegehockeynews.com/info/?d=krach}).
#' 
#' @name icehockey
#' @docType data
#' @format A data frame with 1083 observations on the following 6 variables.
#' \describe{ 
#' \item{date}{a numeric vector} 
#' \item{visitor}{a
#' factor with 58 levels `Alaska Anchorage` ... `Yale`}
#' \item{v_goals}{a numeric vector} 
#' \item{opponent}{a factor
#' with 58 levels `Alaska Anchorage` ... `Yale`}
#' \item{o_goals}{a numeric vector} 
#' \item{conference}{a factor
#' with levels `AH`, `CC`, `CH`, `EC`, `HE`,
#' `NC`, `WC`} 
#' \item{result}{a numeric vector: 1 if visitor
#' won, 0.5 for a draw and 0 if visitor lost} 
#' \item{home.ice}{a logical
#' vector: 1 if opponent on home ice, 0 if game on neutral ground} }
#' @references Schlobotnik, J. Build your own rankings:
#' \url{http://www.elynah.com/tbrw/2010/rankings.diy.shtml}.
#' 
#' College Hockey News \url{https://www.collegehockeynews.com/}.
#' 
#' Selections for 2010 NCAA tournament:
#' \url{https://www.espn.com/college-sports/news/story?id=5012918}.
#' @source \url{http://www.collegehockeystats.net/0910/schedules/men}.
#' @keywords datasets
#' @examples
#' 
#' ### Fit the standard Bradley-Terry model
#' standardBT <- BTm(outcome = result,
#'     player1 = visitor, player2 = opponent,
#'     id = "team", data = icehockey)
#' 
#' ## Bradley-Terry abilities
#' abilities <- exp(BTabilities(standardBT)[,1])
#' 
#' ## Compute round-robin winning probability and KRACH ratings
#' ## (scaled abilities such that KRACH = 100 for a team with
#' ## round-robin winning probability of 0.5)
#' rankings <- function(abilities){
#'     probwin <- abilities/outer(abilities, abilities, "+")
#'     diag(probwin) <- 0
#'     nteams <- ncol(probwin)
#'     RRWP <- rowSums(probwin)/(nteams - 1)
#'     low <- quantile(abilities, 0.45)
#'     high <- quantile(abilities, 0.55)
#'     middling <- uniroot(function(x) {sum(x/(x+abilities)) - 0.5*nteams},
#'                         lower = low, upper = high)$root
#'     KRACH <- abilities/middling*100
#'     cbind(KRACH, RRWP) 
#' }
#' 
#' ranks <- rankings(abilities)
#' ## matches those produced by Joe Schlobotnik's Build Your Own Rankings 
#' head(signif(ranks, 4)[order(ranks[,1], decreasing = TRUE),])
#' 
#' ## At one point the NCAA rankings gave more credit for wins on
#' ## neutral/opponent's ground. Home ice effects are easily
#' ## incorporated into the Bradley-Terry model, comparing teams
#' ## on a "level playing field"
#' levelBT <- BTm(result,
#'                data.frame(team = visitor, home.ice = 0),
#'                data.frame(team = opponent, home.ice = home.ice),
#'                ~ team + home.ice,
#'                id = "team", data = icehockey)
#' 
#' abilities <- exp(BTabilities(levelBT)[,1])
#' ranks2 <- rankings(abilities)
#' 
#' ## Look at movement between the two rankings
#' change <- factor(rank(ranks2[,1]) - rank(ranks[,1]))
#' barplot(xtabs(~change), xlab = "Change in Rank", ylab = "No. Teams")
#' 
#' ## Take out regional winners and look at top 10
#' regional <- c("RIT", "Alabama-Huntsville", "Michigan", "Cornell", "Boston College",
#'               "North Dakota")
#' 
#' ranks <- ranks[!rownames(ranks) %in% regional]
#' ranks2 <- ranks2[!rownames(ranks2) %in% regional]
#' 
#' ## compare the 10 at-large selections under both rankings
#' ## with those selected under NCAA rankings
#' cbind(names(sort(ranks, decr = TRUE)[1:10]),
#'       names(sort(ranks2, decr = TRUE)[1:10]),
#'       c("Miami", "Denver", "Wisconsin", "St. Cloud State",
#'         "Bemidji State", "Yale", "Northern Michigan", "New Hampshire",
#'         "Alsaka", "Vermont"))
#' 
#' 
"icehockey"