Individual pairwise trials, teams or individuals

A consistent suite of functions that give likelihood functions for a single pairwise trial between specified sets of competitors; supercedes trial().

pick(winners, allplayers)
pass(losers,  allplayers)
beats(winners, losers)
loses(losers, winners)
trial(winners, players, val=1)

Arguments

winners

Players on the winning team

losers

Players on the losing team

allplayers

All players, winning and losing

players, val

Inputs to (soon to be deprecated) function trial()

Details

Consider a competition between two disjoint sets of players, \(A=\left\lbrace a_1,\ldots, a_n\right\rbrace\) and \(B=\left\lbrace b_1,\ldots, b_m\right\rbrace\).

If \(A\) wins the likelihood function will be \(\frac{a_1+\ldots+a_n}{a_1+\ldots+a_n+b_1+\ldots+b_m}\) and if \(B\) wins the likelihood function will be \(\frac{b_1+\ldots+b_m}{a_1+\ldots+a_n+b_1+\ldots+b_m}\).

We can represent a win for \(A\) with either pick(A, c(A,B)) or beats(A,B); or pass(B, c(A,B)) or loses(B,A)

Function trial() will be deprecated soon. It is an inefficient synonym for pick().

The trial() function is used in inst/kka.Rmd (but will shortly be changed).

Author

Robin K. S. Hankin

Examples

pick(letters[1:2], letters[1:5])   # field abcde; ab beats cde
#> log( (a + b) * (a + b + c + d + e)^-1)
pass(letters[1:2], letters[1:5])   # field abcde; ab loses to cde
#> log((a + b + c + d + e)^-1 * (c + d + e))

beats(letters[1:2], letters[3:5])  # field abcde; ab beats cde
#> log( (a + b) * (a + b + c + d + e)^-1)
loses(letters[1:2], letters[3:5])  # field abcde; ab loses to cde
#> log((a + b + c + d + e)^-1 * (c + d + e))

monster <- "home"
players <- letters[1:4]

H <- hyper2()
H <- H + pick(c("a", "b", monster), c(players, monster))
H <- H + pick(c("a", "d", monster), c(players, monster))
H <- H + pick(c("a",      monster), c(players, monster))
H <- H + pass(c("c", "d", monster), c(players, monster))

## above see how pick() / pass() is better.

monster <- "cheating"

## Now new players e and f join the chat:
H <- H + beats(c("a", "e"), c("b", "c"))
H <- H + beats(c("a", "c", monster), c("b", "d"))
H <- H + beats(c("e", "f"), c("a", "b", monster))
H <- H + loses(c("a", "f", monster), c("d", "e"))
## above, see beats/loses are more convenient than pick/pass


H
#> log( (a + b) * (a + b + c + cheating + d)^-1 * (a + b + c + d +
#> home)^-4 * (a + b + c + e)^-1 * (a + b + cheating + e + f)^-1 * (a + b
#> + home) * (a + c + cheating) * (a + cheating + d + e + f)^-1 * (a + d +
#> home) * (a + e) * (a + home) * (d + e) * (e + f))