volleyball {hyperdirichlet} | R Documentation

## Results from the NOCS volleyball league

### Description

Results from the NOCS volleyball league. Object `volleyball_results` is a matrix in which each column corresponds to a player and each row corresponds to a volleyball set; `vb` is the corresponding likelihood function in the form of a hyperdirichlet distribution.

Object `vb_synthetic` is a hyperdirichlet object corresponding to a synthetic dataset obtained from 4000 simulated volleyball sets.

### Usage

    data(volleyball)

### Details

A volleyball set is a Bernoulli trial between two disjoint subsets of the players. The two subsets are denoted (after the game) as the “winners” and the “losers”: these are denoted by `1` and `0` respectively.

Thus the first line reads of `volleyball_results` reads:

     p1  p2  p3  p4  p5  p6  p7  p8  p9
     1    0  NA   1   0   0  NA   1  NA

showing that the teams were `p1`, `p4` and `p8` against `p2`, `p5` and `p6`; players `p3`, `p7` and `p9` did not play.

Dataset `vb_synthetic` is the likelihood function of 4000 simulated trials in which the skills are distributed according to Zipf's law: `1/(1:9)/sum(1/(1:9))`.

These datasets illustrate the fact that such Bernoulli trials are only weakly informative. The synthetic dataset involves 4000 observations because this was about the minimum number for which one could estimate the probabilities reasonably reliably. Even then, the lowest probabilities are poorly identified.

### Source

Volleyball games at NOCS, 2006-2008

### Examples

    data(volleyball)
    maximum_likelihood(vb , start_p = c(0.407, 0.091, 0.432, 1.73e-05,
    2.24e-08, 1.9e-05, 1.8e-07, 0.03, 0.039) , control=list(maxit=100))

    zipf <- 1/seq_len(9)
    maximum_likelihood(vb_synthetic , start_p=zipf, control=list(maxit=100))

[Package hyperdirichlet version 1.3-8 Index]