icehockey {BradleyTerry2}

College Hockey Men's Division I 2009-10 results

Description

Game results from American College Hockey Men's Division I composite schedule 2009-2010.

Usage

icehockey

Format

A data frame with 1083 observations on the following 6 variables.

date

a numeric vector

visitor

a factor with 58 levels ⁠Alaska Anchorage⁠ ... Yale

v_goals

a numeric vector

opponent

a factor with 58 levels ⁠Alaska Anchorage⁠ ... Yale

o_goals

a numeric vector

conference

a factor with levels AH, CC, CH, EC, HE, NC, WC

result

a numeric vector: 1 if visitor won, 0.5 for a draw and 0 if visitor lost

home.ice

a logical vector: 1 if opponent on home ice, 0 if game on neutral ground

Details

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 (https://www.collegehockeynews.com/info/?d=pwcrpi). Some have argued that Bradley-Terry rankings would be fairer (https://www.collegehockeynews.com/info/?d=krach).

Source

http://www.collegehockeystats.net/0910/schedules/men.

References

Schlobotnik, J. Build your own rankings: http://www.elynah.com/tbrw/2010/rankings.diy.shtml.

College Hockey News https://www.collegehockeynews.com/.

Selections for 2010 NCAA tournament: https://www.espn.com/college-sports/news/story?id=5012918.

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"))