Modern law seems to (generally) fall under two headings, proof beyond reasonable doubt (criminal) or the preponderance of the evidence (civil).
Basically, these are statements of probability. But they’re not actually categorized as such. The “preponderance of evidence” doesn’t mean that your odds of guilt are better than even. It means that the odds of guilt are high enough for the jury to feel comfortable letting the judge sentence you. Proof beyond a reasonable doubt, similarly, more or less means the same thing, it’s just pointed out that the penalties are higher and hence the probability of guilt needs to be higher.
But, going into sentencing, there is no correlation to the strength of the evidence. A murder serves a murderers sentence, regardless of whether there’s two unreliable witnesses saying he did it or whether there’s videotape of him commiting the act, his fingerprints on the murder weapon, clear motive, and so on. Yes, perhaps the judge can give lighter or graver sentences based on his view of the strength of the evidence, but that’s not real scientific is it? And of course, there is no way to say, “Okay you probably did it, but not enough so that we feel comfortable giving you the minimum sentence.” It’s very binary.
But so that you know that a person was killed in a room. You know that suspect A was in that room. You can estimate that it is unlikely for there to have been more than five people who could have gone into that room when the murder took place. So, the odds of his guilt is 1 in 5. Is that enough to do anything at all? No, probably not. But now say that he has a motive. What are the odds that anyone else would have a motive for killing the victim? As a fairly likeable person, let’s guess that it’s 1 in 20. Overall, there’s only 1 chance in 100 that anyone else could be our murderer. Personally, I would say that’s worth something in the way of sentencing, even if it’s only community service.
But then say that we have a second case where there’s videotape of the crime being performed. What are the odds that someone else would have blackmailed the suspect into this act? Well say that it’s 1 in 10,000. How many people would have a motive? 1 in 20, which he did. How many people would know that the victim would be in that place at that time? Up to 5 people might have known, of which our guy is one. Here we’re looking at odds of 1 in 1,000,000. Is there really enough ambiguity in that to be worth fearing the death penalty?
So let’s say that instead of juries deciding guilt or innocence, their job is simply to look at each item of evidence and decide how likely it makes it that the person is the guilty party. If it’s less than X at the end, then the person goes free. Otherwise, it’s used as a multiplier on the sentencing.