How does "beyond a reasonable doubt" translate into a probability?

I don’t think it translates well into probabilities. It’s a threshold, on or off, is there doubt or not.
“Beyond reasonable doubt” in the legal case means that if there is a doubt then don’t convict because the consequences are dire.

Each juror has to decide that. There is no formula.

I have wondered about this myself. Is every doubt “reasonable” or are some not? I guess if I ever ended up on a jury (and historically I tend to be excused as unacceptable for some reason or other) I would be considering a preponderance of the evidence – I don’t think I could hang a conviction on a single piece of 90% evidence.

I believe that @MollyMcGuire is essentially correct in that in legal cases, and that the notion of reasonable doubt is something left to each juror to decide.

But then how many times does a verdict hinge on evidence for which the probability can be calculated? This can be done for DNA testing, but I’m not aware of it being applied to other forms of evidence. Any such calculation must rest on assumptions that the opposing lawyer can attack. Take the O.J. Simpson trial. Simpson’s defense team countered DNA evidence by exposing blunders in the samples’ chain-of-custody and (apparently) creating “reasonable doubt” in the minds of the jury over whether members of the LAPD had tampered in order to frame him.

I wonder if the likelihood of other explanations of what happened play into it.

Fifty-fifty.

It would depend on other evidence, as well, for me.

@Lightlyseared It is absolutely not 50–50.

In civil (not criminal) cases, it effectively is. If I sue you and the jury thinks there is more than a 50% chance I am right, they are supposed to find for me. If its 50% or less, they should not find for me.

In criminal cases, its supposed to be a much higher burden.

@LostInParadise “That at first seems to be pretty good, but 90% chance of match means a one in ten chance that someone chosen at random would be a match.”

That’s not true. If the police/prosecutor use a higher threshold (at least usually) then more often than not, you will have a less than 10% chance of being wrong when you say guilty. As far as I know, the police are usually almost 100% sure for most crimes (since they are usually easy to solve). It should only be rare that the police go with someone who they think its only 90% likely to be guilty. But it may make sense to have the jury use this threshold for those situations when it does happen.

But, there is no formula. What there is instead, in the US, is the common law. Through a huge number of cases decided by judges (on appeal, summary judgment, etc…) we have enough cases that we can use as analogies to decide. This comes in when the judge gives instructions to the jury.

In the end, though, its up to the jury to decide. My guess would be they are usually very very certain when they convict, but I don’t know.

Here is the response from a college friend who is a prosecutor:

Impossible to imagine that there isn’t some other evidence in the case that does or does not corroborate the dna results. If corroborative evidence exists, then “guilty.” If not, “not guilty” in both situations as I’m not convicting without anything that removes the human factor in handling the evidence or a technician who may hsve an axe to grind.

Thanks @Pied_Pfeffer . I am wondering though how we should evaluate eyewitness accounts. We tend to put a lot of stock in them, but they are less than 100% reliable. Illinois abolished the death penalty due to proven inaccuracies in the judicial system.

Eyewitness accounts run the full gamut, don’t they? They range from completely outrageous to dead-on, and yet they can be right or wrong. Even a person admitting to committing a crime can later be proven to be innocent. It takes good and ethical detectives, lawyers, juries and judges to come to the right conclusions.

Eyewitness accounts can often break open a case. That’s why hotlines are set up. They sometimes work, even though a lot of false leads need to be researched. I’m currently watching a series of true crime stories, and several of the cases would have ended up in cold case storage if it hadn’t been for the efforts of the investigative team following up on leads from eyewitnesses that called in.