>The whole point is the quantified output. If you just ask an LLM to type out its confidence "manually", it'll make up some nonsense. The logprob numbers are more reliable.

The whole point of my argument is that neither is good, but from a technical perspective logprobs is probably the worst unless you train a model on specific outputs. In which case you'd throw out the generality again, so when I think about it more, it's actually the worst overall. In my experiments, having the model simply assign "high" or "low" probability in a structured output generally performs best. You can try numbers, but you will never get anything close to what you could expect from traditional ML. And most certainly not from logprobs.