How do I create a single WordPress page that will use PHP to include different HTML files based on a vaule in the URL?

Assuming you already set permalinks for your WordPress site, add this to your page.php:

 <?php 
    include("http://www.mysite.edu/_sports/static/".$post->post_name.".html); 
 ?>

$post->post_name would be the slug of your page.

If you’re in a page with the slug volleyball-box-score, with the code above, you would get include("http://www.mysite.edu/_sports/static/volleyball-box-score.html);. If you’re in a page with the slug other-page, you would get include("http://www.mysite.edu/_sports/static/other-page.html);. Etc.