The backstory: My site has a fantasy sportsbook where users can place "bets" on pretty much anything. Each game has a unique matchup page, where the odds are displayed and any conversation about the game takes place. Example here.
About 95% of the games are automatically graded, but I have to manually grade the rest. Therefore, as soon as every game starts I check to see if any users have made a pick on it, and if not I delete it because it reduces my workload.
The problem: About 15% of my search-driven traffic is queries for games that no longer exist, which makes sense because nobody bets on the super obscure games and these games are very easy to rank for. I am currently redirecting them to my 404 page but I'm worried that all of these hits are hurting my reputation with the big G.
Would it be better to noindex all of these pages at first and take the noindex away as soon as I'm positive that the game will stay?