Gygax never explained what the ratio is so what you have posted is irrelevant.
Despite your attempted dismissivness, it's relevant. You start from the premise that there is a ratio, and then try to figure out roughly what it might be. But you cannot even start, until you post what the comment was to begin with. It's highly relevant.
Also, what HP represents is also irrelevant because where damage on a miss fails is not only believability, but also consistency.
It's also quite consistent, and therefore relevant. People keep pretending the "it's magic" answer to spells doing damage on a miss is somehow a powerful argument. It's not, particularly concerning the topic of "is this a consistent mechanic". It's consistent in D&D that some things do damage even on a miss. Spells do it, and sometimes non-magical things do as well when looking at things like poison gas, and this kind of ability. Now that doesn't mean you have to agree, but it does mean it's relevant to the discussion to raise those issues. Just dismissing it out of hand as not relevant because you disagree is, at best, non-productive and rude.
We don't need to continue bringing up Gygax.
I don't recall anyone saying you needed to do anything. But, it's helpful in that a lot of people are bringing up the historical context of the issue - the reason it "feels" wrong, or "seems" not-believable or not consistent, is because of the history of the concept. So, citing the history of the concept that supports hit points as being something other than simply physical damage is relevant and useful, at least for some people even if it is not helpful for you.
Every pro-damage on a miss user has yet to give us a logic consistent reason as to why it's a good mechanic for a game that is based on imagination.
People have given you lots of logical consistent reasons. They've said you are so strong that even glancing contact does damage (and that in a game where the goal is to simplify the system you assume a glancing blow for every 6-second exchange of attacks instead of adding touch-AC to the game which increases complexity). They've said the sweep of the arm with such weapons is so great that any swing at a target makes at least glancing contact. They've said your training is such that you will always at least make glancing contact with anything you're aiming at that is next to you. They've said there is some element of your power that makes contact even if you miss, or which reduces your luck or puts you in poor positioning to take a blow that was not the primary blow. They've said they're ability to wear you down is such that simply dodging your series of attacks does damage. They've said the die roll simply represents a symbolic number for a series of attacks made during that 6 second period, and the strength damage represents a hit in that series of blows which was not the primary attempted attack but a secondary one. Some have even tied it to magic.
Now you don't like those reasons, but not liking them is not the same as them being illogical or inconsistent.
They have also not given us a reason for why it makes sense that you can kill creatures with a miss which in turn equals a success.
Spells do this. Some poisons do this. The game allows for killing very low hit-point things on a miss in several aspects. This simply expands the realm of things that can kill low-hit-point creatures on a miss to include a single martial ability, due to power or training or weapon or swing or strength or any of the explanations given. Again, you don't like the explanations given - but please stop saying that your dislike of them equates with them not existing or them having no sense of logic or consistency to them.
I think the problem here is the devs think a miss means you were unsuccessful in using your full potential. They have completely changed the meaning of the words hit and miss.
I miss you with a poison gas cylinder I just threw at you. Though you take no hit points damage, you die. Or, you take hit point damage anyway, and you die. This is a concept that has a long history in this game. Sometimes, a miss can still kill things. Because sometimes the attack roll was simply to determine how much hit point damage you potentially take and not whether you are going to take damage, or how big an area the death spreads, or what precise area the death spreads in. Sometimes, you're doomed the moment they try to aim at you.