There are four players, \(p_1\) to \(p_4\). These players
play doubles tennis matches with the following results:
|
match |
score |
|
\(\lbrace p_1,p_2\rbrace\) vs \(\lbrace p_3,p_4\rbrace\) |
9-2 |
|
\(\lbrace p_1,p_3\rbrace\) vs \(\lbrace p_2,p_4\rbrace\) |
4-4 |
|
\(\lbrace p_1,p_4\rbrace\) vs \(\lbrace p_2,p_3\rbrace\) |
6-7 |
|
\(\lbrace p_1\rbrace\) vs \(\lbrace p_3\rbrace\) |
10-14 |
|
\(\lbrace p_2\rbrace\) vs \(\lbrace p_3\rbrace\) |
12-14 |
|
\(\lbrace p_1\rbrace\) vs \(\lbrace p_4\rbrace\) |
10-14 |
|
\(\lbrace p_2\rbrace\) vs \(\lbrace p_4\rbrace\) |
11-10 |
|
\(\lbrace p_3\rbrace\) vs \(\lbrace p_4\rbrace\) |
13-13 |
It is suspected that \(p_1\) and \(p_2\) have some form of
team cohesion and play better when paired than when either solo or with
other players. As the scores show, each player and, apart from p1-p2,
each doubles partnership, is of approximately the same strength.
Dataset tennis gives the appropriate likelihood function for the
players' strengths; and dataset tennis_ghost gives the
appropriate likelihood function if the extra strength due to team
cohesion of \(\lbrace p_1,p_2\rbrace\) is represented by a
ghost player.
These objects can be generated by running script
inst/tennis.Rmd, which includes some further discussion and
technical documentation and creates file tennis.rda which
resides in the data/ directory.