WordPress URLs for 1 taxonomy on 2 different custom post types

aeromaxx-parse-request.php

<?php
/** 
 * Answering: http://lists.automattic.com/pipermail/wp-hackers/2012-August/044119.html
 * By: Mike Schinkel - http://about.me/mikeschinkel
 */ 
add_action( 'parse_request', 'aeromaxx_parse_request' );
function aeromaxx_parse_request( $wp ) {
  if ( preg_match( '#^/(draw-results|ball-statistics)/game/([^/]+)/#', $_SERVER['REQUEST_URI'], $matches ) ) {
    $wp->query_vars = array(
      'post_type' => $matches[1], // Assumes your post types are registered with same name as your URL slugs
      'game' => $matches[2],      // Assumes your taxonomy is registered as 'game'
    );
  }
}