Are those 500,000 searches EXACT? & if you meant competition = medium in the google keyword tool, it means the no.of advertisers not the seo competition in ranking your site.
Broad match keyword tennis shoes Ads may show on searches for buy tennis shoes best shoes for tennis tennis shoe laces running shoes tennis sneakers -------------------------------------------------------------------------------------------------------------- Like tennis shoes has 246 000 searches (US,english) which doesn't mean that tennis shoes are searched that much. That is number of searched variations like listed above. Real search amount for tennis shoes (exact) is 22 200. Read more here: http://support.google.com/adwords/bin/answer.py?hl=en&answer=2497836&from=6100&rd=1 Always look exact when doing keyword research!