派生字段中的CakePHP分页条件

i would like to paginate a list of games, where the sport is a chosen sport. the relatition is as followed: Game BelongsTo Competition BelongsTo Team BelongsTo sport What i would like to do is show all games where the teams sport_id = 1. The following doesn't work:

        $this->paginate = array('limit' => 30, 'page' => 1, 
    'conditions' => array('Competition.Team.sport_id' => '1'),
        'contain' => array('Competition', 'Competition.Team',
        'Gamefield', 'Changingroom', 'ChangingroomAway', 'Gametype'),
    'order'=>array('game_date'=>'asc'),         
    );  

Can anyone help me with this one?

I've found my solution:

    var $paginate=array(
    'Game'=>
    array(
        'joins'=>array(
            array('table'=>'competitions',
                  'alias'=>'Competition2',
                  'type'=>'left',
                  'conditions'=>array('Game.competition_id=Competition2.competition_id')
                  ),
            array('table'=>'teams',
                  'alias'=>'Team2',
                  'type'=>'left',
                  'conditions'=>array('Competition2.team_id=Team2.team_id')
                  ),
            ),
        'order'=>array('game_date'=>'asc'),
        'contains'=>array('Competition2'=>array('Team2'))
                    ));
function index() {
    $datum = date('Y-m-d H:m');
    $this->Game->recursive = 0;
    $scope=array('OR' => array(array('Team2.sport_id' => 2), array('Team2.sport_id' =>3)), 'Game.game_date >' => $datum);
//       Configure::write('debug',2);
    $this->set('games', $this->paginate(null,$scope));
}

Thanks to TehThreag for helping me

Containable doesn't create any joins unless the relation would have been joined anyways, despite using Containable.

This means that for habtm, if you want a join you have to do as Michael did and specify them. Also, doing a couple of joins should be faster with logical indexes than doing a habtm with Containable anyways, as the results from a contain for the same data as above would require an in ( id1,id2,...id# ) condition and a number of queries from there to fetch the individual related records.

The joins solution gets the data back in one db query.