Это не проверено, просто идея ...
$_POST['sports'] = array('basketball', 'baseball', 'football', 'soccer');
$sql = sprintf("SELECT * FROM sports WHERE sport.name IN (%s)", implode( ',', array_fill(1,count($_POST['sports']), '?') ) );
// SELECT * FROM sports WHERE sport.name IN (?,?,?,?)
$st = $dbh->prepare($sql);
// bind all values
foreach( $_POST['sports'] as $i => $sport) {
$st->bindValue( ++$i, $sport );
}
$st->execute();