When should the cop come forward?

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I was cop in a large game at MTGS. A discussion came up (Day 5, I think) about whether the cop should reveal himself or not and clear some townies (assuming the cop was still alive). We weren't sure if the doc was still alive, either, since roles weren't revealed upon death.

If the cop (assume sane) hasn't found any scum, at what point is it worth it to come forward as the cop? How many living townies must the cop be able to clear? Should I have come forward even if I could only have cleared 2 people (with 16 still alive)?

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At that point, I had only had 4 results. One had died, the other two townies were alive, and the fourth was a blocked result (but that person was outed as a scum during the day anyway). So I only had two living results. I thought about coming forward because my two live targets were at one point attacking each other, and it might have helped to settle the matter. But then there was a mod-related incident that resulted in one of the two withdrawing from the game, leaving me with only one live result. I decided not to come forward, and I got killed during the night.

But anyway, that's all beside the point. I feel the same way you do, that 2 out of 16 doesn't seem to be enough, especially if those two aren't in danger of being lynched soon.

With some extra information, though, I realize I probably should've come forward. In terms of it being the endgame, we figured there were about 4 mafia left out of 16 players. We already knew 1 (he was outed and had given up), so he was the definite lynch for that day. We also had two other confirmed townies by their roles, so that leaves 3 out of 13 people for the remaining scum. I suppose if I had come forward and cleared two people plus myself, that would have given us 3 out of 10. That's actually not so bad, I guess.

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So is there a general rule of thumb that should be followed? Say, if you can clear 1/3 of the remaining people? 1/4? Or should you keep hoping that you won't be killed so you can get another investigation?

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Well, of course it depends on a number of things, but I was hoping to get somewhat of a "baseline" figure, assuming a normal game (randomly lynching "non-confirmed" people, nightkilling "confirmed" people starting with the cop). I think mith has the same idea in mind. This would give you a general idea of when it's worth it to come forward, and then you can adjust it accordingly to your circumstances.