plotProportions {BradleyTerry2}  R Documentation 
Plot Proportions of Tied Matches and Nontied Matches Won
Description
Plot proportions of tied matches and nontied 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.
Usage
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,
...
)
Arguments
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 BradleyTerry model). 
home.adv 
if applicable, the fitted home advantage parameter from a generalized Davidson model (or a BradleyTerry 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 xaxis. 
ylab 
the label to use for the yaxis. 
legend 
text to use for the legend. 
col 
a vector specifying colours to use for the proportion of nontied matches won and the proportion of tied matches. 
... 
further arguments passed to plot. 
Details
If home.adv
is specified, the results are reordered 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 midpoint of the bin. Then the bins are recomputed omitting the tied games and the proportion of nontied matches won by the first player is found and plotted against the new midpoint.
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 BradleyTerry model.
Value
A list of data frames:
win 
a data frame comprising

tie 
(when ties are present) a data frame comprising 
Note
This function is designed for single match outcomes, therefore data aggregated over player pairs will need to be expanded.
Author(s)
Heather Turner
See Also
Examples
#### A BradleyTerry example using icehockey data
## Fit the standard BradleyTerry 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("20089", "201213"))
## 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)
}
}