Measuring Doubt

The batsmen is supposed to get the benefit of the doubt. But what does that mean? Does the umpire (in his mind) has to be a 100% sure? Is it preponderance of doubt? Is it better than 50% doubt?

I am sure umpires give out, in real situations, when they might still have some doubt. If they were going for really 100% doubt free decisions then we would see a vast majority of "difficult" outs not being given. I don't think that is the case.
It would be interesting to do a study over the last five years (Since data is relatively clean and available and applies to current umpires) to see when matched with technology (where technology had a better resolution) how many outs were not given and how many not outs were given. Then use the formula

Percent Threshold Level of Doubt Acceptable to Umpire = [(outs not given)/(outs not given + not outs given out)] * 100

This can be done for each umpire and for the whole umpiring community as a whole.

If an umpire never gives a "not out" as out but has outs not given then his threshold level of acceptable doubt is 100%. He is damn sure that it is out before he gives it.

If an umpire gives a "not out" as out and outs not given about the same number of time then his threshold level of acceptable doubt is 50%. He can go either way on a difficult case.

If an umpire has "not outs" as outs but has not given outs that should have been then he is trigger (finger?) happy with no threshold.

For most umpires the number should fall somewhere between 50 and 100 percent for them to give benefit of doubt more to the batsmen.

For a perfect umpire both quantities are zero and the threshold is undefined (0/0) but then he does not need it.