I think that the answer to the OP depends on a lot of things. First, of course, is the nature of the crime. Is it better to let a shoplifter go free, rather than send an innocent to jail? Sure. Shoplifting isn’t that bad a crime. Murder or rape are different. So let’s say that we’re talking a murder here. First of all, I think that, generally speaking, it is better to let one murderer go free than to jail one innocent. In some cases, that may vary. Consider the OJ case. Everyone “knows” OJ was guilty. I’m pretty sure he did it, too. So let’s pretend he did do it, and got off. Is he really likely to kill again? Probably not. The first time, not to justify it, was a fluke - a crime of passion. He’s not going around murdering people and stealing their jewels, or anything. The worst thing that’s happened as a result of his not going to prison is that Anna Nicole and her beau are left sans justice. Tragic, yes, but not fatally so (no pun intended). If OJ had gone to prison, and he was innocent, though, then we would have subjected an innocent man to years of psychological and likely physical punishment for no reason. Certainly, it would be better to err on the side of his being innocent here.
Now what about someone who’s a serial killer? They killed before, they’re probably going to kill again. If you let the guilty go in this case, there’s a good chance others will die - maybe lots of others. In this case, it may be a good idea to err on the side of a guilty verdict.
Now what about the oft-cited claim “It’s worse to jail an innocent than to let 100/1000/1 million/whatever men go free”? I think it’s bull. If you let 100 murderers go free, and they kill 100 more people, is that really worse than jailing someone innocent? Is it worse than executing someone innocent? Sorry, I don’t think so. Ask the families of the 100 victims - I’m sure they’ll disagree, as well. What about the damage done to the public’s view of the justice system if we punish the innocent? Well, that’s a good point. But I don’t think the public being skeptical of the justice system because it occasionally jails innocents is any better than skepticism due to the justice system repeatedly letting the guilty get off. You can argue “relative justice” if you’d like, but that’s a pretty nebulous concept.
As far as actual studies about the deterence value of punishment, I don’t know about punishment in general, but last year a trio of researchers at Emory university conducted a study on the deterence value of capital punishment in particular. It concluded that each person executed saved between 8 and 28 lives, with a best estimate of about 18 per execution. Ian Murray summarizes the report here:
Jeff