I took Trent Green in the 4th round of my 12-team league and I plan on giving him about four more weeks worth of starts.
Here is a good strategy that encourages patience:
Flip your draft and use that order to determine how long of a leash you should give each player. I took Andre Davis in the 15th (final) round of my draft. Flipping things, I planned on giving him one week to prove himself before I even considered cutting him. My 14th pick has two weeks, 13th pick three weeks, 12th four weeks and so on. Although it is hard to always strictly adhere to this strategy (especially with positional needs), it is something to consider.
So, Trent Green has the first twelve weeks of the season to prove his worth to me. Depending on the strength of your backup QB, you should give Green about six weeks of starts before you start considering sending him to your bench. Thus, he is about ¼ of the way to earning a seat on my bench.
Thank you Tiki!