plotProportions {BradleyTerry2} | R Documentation |
Plot proportions of tied matches and non-tied matches won by the first player, within matches binned by the relative player ability, as expressed by the probability that the first player wins, given the match is not a tie. Add fitted lines for each set of matches, as given by the generalized Davidson model.
plotProportions(win, tie = NULL, loss, player1, player2, abilities = NULL, home.adv = NULL, tie.max = NULL, tie.scale = NULL, tie.mode = NULL, at.home1 = NULL, at.home2 = NULL, data = NULL, subset = NULL, bin.size = 20, xlab = "P(player1 wins | not a tie)", ylab = "Proportion", legend = NULL, col = 1:2, ...)
win |
a logical vector: |
tie |
a logical vector: |
loss |
a logical vector: |
player1 |
an ID factor specifying the first player in
each contest, with the same set of levels as |
player2 |
an ID factor specifying the second player in
each contest, with the same set of levels as |
abilities |
the fitted abilities from a generalized Davidson model (or a Bradley-Terry model). |
home.adv |
if applicable, the fitted home advantage parameter from a generalized Davidson model (or a Bradley-Terry model). |
tie.max |
the fitted parameter from a generalized Davidson model corresponding to the maximum tie probability. |
tie.scale |
if applicable, the fitted parameter from a
generalized Davidson model corresponding to the
scale of dependence of the tie probability on the probability
that |
tie.mode |
if applicable, the fitted parameter from a
generalized Davidson model corresponding to the
location of maximum tie probability, in terms of the probability
that |
at.home1 |
a logical vector: |
at.home2 |
a logical vector: |
data |
an optional data frame providing variables required by the model, with one observation per match. |
subset |
an optional logical or numeric vector specifying a subset of observations to include in the plot. |
bin.size |
the approximate number of matches in each bin. |
xlab |
the label to use for the x-axis. |
ylab |
the label to use for the y-axis. |
legend |
text to use for the legend. |
col |
a vector specifying colours to use for the proportion of non-tied matches won and the proportion of tied matches. |
... |
further arguments passed to plot. |
If home.adv
is specified, the results are re-ordered if
necessary so that the home player comes first; any matches played on
neutral ground are omitted.
First the probability that the first player wins given that the match is not a tie is computed:
expit(home.adv + abilities[player1] - abilities[player2])
where home.adv
and abilities
are parameters from a
generalized Davidson model that have been estimated on the log scale.
The matches are then binned according to this probability, grouping together matches with similar relative ability between the first player and the second player. Within each bin, the proportion of tied matches is computed and these proportions are plotted against the mid-point of the bin. Then the bins are re-computed omitting the tied games and the proportion of non-tied matches won by the first player is found and plotted against the new mid-point.
Finally curves are added for the probability of a tie and the
conditional probability of win given the match is not a tie, under a
generalized Davidson model with parameters as specified by
tie.max
, tie.scale
and tie.mode
.
The function can also be used to plot the proportions of wins along with the fitted probability of a win under the Bradley-Terry model.
A list of data frames:
win |
a data frame comprising |
tie |
(when ties are present) a data frame comprising
|
This function is designed for single match outcomes, therefore data aggregated over player pairs will need to be expanded.
Heather Turner
#### A Bradley-Terry example using icehockey data ## Fit the standard Bradley-Terry model, ignoring home advantage standardBT <- BTm(outcome = result, player1 = visitor, player2 = opponent, id = "team", data = icehockey) ## 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) ## compare fit to observed proportion won ## exclude tied matches as not explicitly modelled here par(mfrow = c(1, 2)) plotProportions(win = result == 1, loss = result == 0, player1 = visitor, player2 = opponent, abilities = BTabilities(standardBT)[,1], data = icehockey, subset = result != 0.5, main = "Without home advantage") plotProportions(win = result == 1, loss = result == 0, player1 = visitor, player2 = opponent, home.adv = coef(levelBT)["home.ice"], at.home1 = 0, at.home2 = home.ice, abilities = BTabilities(levelBT)[,1], data = icehockey, subset = result != 0.5, main = "With home advantage") #### A generalized Davidson example using football data if (require(gnm)) { ## subset to first and last season for illustration football <- subset(football, season %in% c("2008-9", "2012-13")) ## convert to trinomial counts football.tri <- expandCategorical(football, "result", idvar = "match") ## add variable to indicate whether team playing at home football.tri$at.home <- !logical(nrow(football.tri)) ## fit Davidson model Dav <- gnm(count ~ GenDavidson(result == 1, result == 0, result == -1, home:season, away:season, home.adv = ~1, tie.max = ~1, at.home1 = at.home, at.home2 = !at.home) - 1, eliminate = match, family = poisson, data = football.tri) ## fit shifted & scaled Davidson model shifScalDav <- gnm(count ~ GenDavidson(result == 1, result == 0, result == -1, home:season, away:season, home.adv = ~1, tie.max = ~1, tie.scale = ~1, tie.mode = ~1, at.home1 = at.home, at.home2 = !at.home) - 1, eliminate = match, family = poisson, data = football.tri) ## diagnostic plots main <- c("Davidson", "Shifted & Scaled Davidson") mod <- list(Dav, shifScalDav) names(mod) <- main alpha <- names(coef(Dav)[-(1:2)]) ## use football.tri data so that at.home can be found, ## but restrict to actual match results par(mfrow = c(1,2)) for (i in 1:2) { coef <- parameters(mod[[i]]) plotProportions(result == 1, result == 0, result == -1, home:season, away:season, abilities = coef[alpha], home.adv = coef["home.adv"], tie.max = coef["tie.max"], tie.scale = coef["tie.scale"], tie.mode = coef["tie.mode"], at.home1 = at.home, at.home2 = !at.home, main = main[i], data = football.tri, subset = count == 1) } }