data(doubles)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 doubles_noghost gives the appropriate likelihood function
for the players' strengths; and dataset doubles 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.