(I'd hope it would be close to 0, but I wouldn't be surprised if it was much higher.)
It's also virtually always social skill related... if you weren't up to the task technically, you wouldn't have been asked to interview. The in person interview is normally to decide "do I want to see this person 40+ hours a week for the next 5 years" rather than "can they do the job."
Lots of exceptions obviously but mostly true across the board.
There are a lot of flaws in the way interviews are done in our industry that make it more subjective than it should be, but I still wouldn't consider the latter set of problems to be social skill related.
That's why we have discussions like this: https://blog.codinghorror.com/why-cant-programmers-program/.
If validating their technical qualifications is not the point of the interview, are you really only interviewing candidates to see if people like their social skills? That sounds legally shady for most cases, and honestly for extreme cases where there's a valid concern that IS the kind of thing I'd expect to be filtered out by an introductory call with a manager or something.
The phone screen should cover lots of technical areas with deep follow up questions and examples.
I work in a specific niche (not coding) and can tell you that I bat .1000 on technical fit... cultural fit cannot be assessed until you meet the person and they meet the team, or at a minimum, hiring manager.
Otherwise we miss interviewing people who can do the job, and in my experience, some of the most interesting people; but this means, one may sometimes be interviewing people that cannot do the job.
Since these are human-mediated processes, there is no accurate single-stage filter, and anyone claiming to operate an unbiased hiring process is either a fool or a liar. A hiring funnel (and really, any decision process) that recognises the inevitability of biases, and is phased accordingly, leads to more optimal outcomes.
I'm not saying no human should be involved. I'm saying an excellent human should screen candidates in a phone (or Teams or Zoom or whatever) interview before they are invited to sit across from you at your desk or in a conference room.
If you find yourself sitting across from someone who cannot technically do the job, your step one has failed (and should never fail).
If you don't hire someone because their in-person interview didn't go well, it is social skill (or cultural fit) related.
If that's not the case, reference step one to see that you have an error in who you are inviting for in-person interviews (or your phone screener should not be the person phone screening).
"If you find yourself sitting across from someone who cannot technically do the job, your step one has failed (and should never fail)."
The suggestion that any screening test must be infallible is simply nonsense, since simultaneous perfect specificity and sensitivity is impossible, and contradicts numerous findings in decision-theoretic research, and I therefore simply and absolutely disagree. All processes fail, and in particular, because individual process steps fail; it merely remains to determine whether you're biased for showing interesting people the door, or inviting them in to take a closer look. This is also the essence of a screening test in, say, medicine, that are necessarily biased to be sensitive over specific, since a false rejection of a patient may be health threatening; more specific (and generally more expensive) testing follows. Or perhaps in sales, where a lead attracts ever more attention as it moves through the qualification funnel.
As I say, these are general consequences of decision theory, a branch of mathematics to which hiring has no magical exemption.
Ergo, anyone claiming their screening is infallible is either a fool or a liar. Sadly, many recruiters are both, which partially explains why so many HR departments are essentially a mediocrity police that create barriers to accessing the entire talent pool. These are not to be trusted (and must, therefore, be bypassed at the earliest opportunity) when in comes to building teams of heterogeneous and interesting people with complementary skills and diverse perspectives, which is to say, any high-performance team, or at least every high-performing team I've been privileged to encounter in the last forty years.
Incidentally, my experience at AWS was the opposite. The talent acquisition team there, at least that assisting my own business unit, was very much on the ball when it came to pulling in candidates from left-field.
When we meet after an interview round "meh" is a much more common collective reaction than "run away now."
And in my experience, if you fail the technical portion of an interview, most companies will tell you. Meaning, if you ask and they don't bring up technical skills, it's probably not the technical skills.
When I was young I interviewed at Microsoft and was rejected. I asked the recruiter for feedback. She talked me through some of the feedback from the interviewers and gave me advice for the future. It was really helpful.
I like that one. I've done interviews where the answer should be at most a summary sentence, and 2-3 supporting points. I know the candidate knows the answer, it's a warmup question! Then what do I get? Word salad. A gigantic run-on sentence where the candidate talks and talks and talks and this, and that, and also, and furthermore... lasting 5 minutes or until I politely interrupt with, "OK let's move on to the next question."
It is better to keep quiet about negative feedback in the lawsuit-heavy culture we inhabit.