I'd wager about zero, with a zero per cent rate of success.
Obviously having technical founders can have many benefits, including:
a.) Can create technical product yourself, spend less on coders initially (e.g. Zuckerburg)
b.) Some products may need complicated code even for a POC (whereas sites like Twitter, less so. Any mediocre dev could make a badly written Twitter clone)
c.) Easier to think of technical ideas. For example I doubt a non-technical person would think of creating BitCoin. On a smaller level, could fail to think of feature-sized ideas within a company.
I think that, if Twitter didn't exist and I decided to create it, lack of coding skill wouldn't be a problem, as long as I had funding for coders to replace the technical founder's early role. Don't get me wrong, I'm not claiming I could do what Twitter have done, but I don't think that the things I'd have done worse would be because of technical ability, the same as if I was hired as a lawyer my failings wouldn't be for tech/code reasons.
Edit:
As an example data point, the company I work for is a digital publishing company, creating and managing content websites. Founded by people from hardware distribution industry, and successful - yet I would argue that our core business type is similar to Reddit, in that success/failure comes more from business decisions than "wow, you coded a better website than other people!" (Reddit being better than Digg, for example, is much more than "Reddit is coded better".)
Well, let's be fair here - he did implement their idea, at least the important part of it, the bit without which Facebook probably would have been a flop (the early elite school exclusivity, which was a major selling point especially at the first few schools, since there was nothing else particularly special about the site itself).
He just decided to keep it for himself rather than hand it over when it was ready.
I'm not sure about Twitter, but I think so too in that case.
So maybe it IS important.
Despite your opinion that it they are unnecessary, is it a coincidence that all the startups you name had technical founders? Obviously your chances of success are not zero without a technical cofounder, but empirically a technical cofounder does seem to be a common factor.
Of course, in most of those cases I would assume that the person/s providing the money would have a lot less input into the final product than a non-technical founder would have in a company, so perhaps they're better compared to a VC than a founder?
I imagine a conversation with Mozart went something like this:
"Mozart, I want a libretto."
"What should be in it?"
"It should be about birds."
"Okay, I'll get on it."
The corresponding conversation in our world would be:
"Jack, I want a piece of software."
"What should it do?"
"It should be like a blog but every post limited to 140 characters."
"Okay, I'll get on it."
It is Mozart and Jack who end up making 99% of the design decisions. What I'm saying that once the guy hiring the creator gets so involved that a good portion of the decisions are his/hers then that's a very inefficient way to compose a piece of music or a piece of software, and you're better off doing the composing yourself. Of course in many cases marketing is more important than the technical side, but this is no different. In a startup with just a couple of people the contribution comes from the guy doing the marketing, not a guy deciding the rough marketing strategy. In a big company the influence reverses because the business decisions have a lot of leverage simply because they affect what a large number of employees are going to do. Simply put, the question you're asking is "Could twitter be done by me getting YC (and later VC) money and then hiring a programmer and a marketer?". The right question is "Why would the YC give the money to me instead of the programmer and the marketer?". Note that a perfectly valid answer for a lot of startups could be "I have connections and experience in the field" (especially for e.g. medical or payments startups), but the answer needs to be something.
Didn't the airbnb founder(s) have little/no coding experience?