ordertable2supp function

Translate order tables to support functions

Wikipedia gives a nice summary in table form of Formula 1 racing results on pages like https://en.wikipedia.org/wiki/2017_Formula_One_World_Championship

(at World Drivers' Championship standings) but the data format is commonly used for many sports [see ordertable.Rd] and function ordertable2supp() translates such tables into a hyper2

support function and also a order table.

Both functions interpret zero to mean Did not finish (wikipedia usually signifies DNF as a blank).

ordertable2supp(x, noscore, incomplete=TRUE)
ordervec2supp(d)

Arguments

• x: Data frame, see details

• d: A named numeric vector giving order; zero entries are interpreted as that competitor coming last (due to, e.g., not finishing)

• incomplete: Boolean, with FALSE meaning to insist that each rank $1,2,...,n$ is present [zero entries mean did not place irregardless]. The default TRUE allows for gaps. This is useful if we are considering the first few lines of an ordertable because there might be missing ranks.

• noscore: Character vector giving the abbreviations for a non-finishing status such as did not finish

  or disqualified . A missing argument is interpreted as c("Ret", "WD", "DNS", "DSQ", "DNP", "NC")

Details

Function ordertable2supp() is intended for use on order tables such as found at https://en.wikipedia.org/wiki/2019_Moto3_season. This is a common format, used for Formula 1, motoGP, and other racing sports. Prepared text versions are available in the package in the inst/ directory, for example inst/motoGP_2019.txt. Use read.table() to create a data frame which can be interpreted by ordertable2supp().

Function ordervec2supp() takes an order vector d and returns the corresponding Plackett-Luce loglikelihood function as a hyper2 object. It requires a named vector; names of the elements are interpreted as names of the players. Use argument pnames to supply the players' names (see the examples).

> x <- c(b=2,c=3,a=1,d=4,e=5) # a: 1st, b: 2nd, c: 3rd etc
> ordervec2supp(x)
log( a * (a + b + c + d + e)^-1 * (a + b + d + e)^-1 * b * (b + d +
e)^-1 * c * (d + e)^-1 * e)

Zero entries mean did not finish :

> ordervec2supp(c(b=1,a=0,c=2))  # b: 1st, a: DNF, c: second
log((a + b + c)^-1 * (a + c)^-1 * b * c)

Note carefully the difference between ordervec2supp() and rankvec_likelihood(), which takes a character vector:

>  names(sort(x))
[1] "a" "b" "c" "d" "e"
> rankvec_likelihood(names(sort(x)))
log( a * (a + b + c + d + e)^-1 * b * (b + c + d + e)^-1 * c * (c + d +
e)^-1 * d * (d + e)^-1)
> rankvec_likelihood(names(sort(x))) == ordervec2supp(x)
[1] TRUE
>

Function order_obs() was used in the integer-indexed paradigm but is obsolete in the name paradigm. A short vignette applying ordervec2supp() and ordertable2supp() to the salad

dataset of the list("prefmod") package [and further analysed in the list("PlackettLuce") package] is presented at inst/salad.Rmd.

Returns

Returns a hyper2 object

Author(s)

Robin K. S. Hankin

See Also

ordertable,ordertable2supp3

Examples

ordertable2supp(soling_table)

# competitors a-f, racing at two venues:
x <- data.frame(
    venue1=c(1:5,"Ret"),venue2=c("Ret",4,"Ret",1,3,2),
    row.names=letters[1:6])

## First consider all competitors; incomplete=FALSE checks that all
## finishing competitors have ranks 1-n in some order for some n:

ordertable2supp(x,incomplete=FALSE)

## Now consider just a-d; must use default incomplete=TRUE as at venue2
## the second and third ranked competitors are not present in x[1:4,]:

ordertable2supp(x[1:4,])   

## Function ordervec2supp() is lower-level, used for order vectors:

a1 <- c(a=2,b=3,c=1,d=5,e=4) # a: 2nd, b: 3rd, c: 1st, d: 5th, e: 4th
a2 <- c(a=1,b=0,c=0,d=2,e=3) # a: 2nd, b: DNF, c: DNF, d: 2nd, e: 3rd
a3 <- c(a=1,b=3,c=2)         # a: 1st, b: 3rd, c: 2nd. NB only a,b,c competed
a4 <- c(a=1,b=3,c=2,d=0,e=0) # a: 1st, b: 3rd, c: 2nd, d,e: DNF

## results of ordervec2supp() may be added with "+" [if the observations
## are independent]:

H1 <- ordervec2supp(a1) + ordervec2supp(a2) + ordervec2supp(a3)
H2 <- ordervec2supp(a1) + ordervec2supp(a2) + ordervec2supp(a4)

## Thus H1 and H2 are identical except for the third race.  In H1, 'd'
## and 'e' did not compete, but in H2, 'd' and 'e' did not finish (and
## notionally came last):

pmax(H1)
pmax(H2)   # d,e not finishing affects their estimated strength