If you can sleep easy at night not worrying about servers, staff members, advertisers, software code, and page load speeds... You DO NOT have a big board.

That or you have a lot of money and have one heck of a team..
I would quantify a big board on total posts, age and especially current online members and/or connections to the server(s). I'd also go with the Big-Boards pre-req. of 500k posts for starters but a site would then need at least 1k new posts a day... And at least 50 new members.. Just my opinion of course..
Oh, and definitely be using a dedicated server(s).