Isn't the biggest delta what we are looking for? Where does imposing disadvantage on incoming attacks have the biggest effect? Where do I not lose the most HPs? Not HPs in proportion to what I could have lost, total HPs lost.
No, and that's been my point. You're caught up on "big delta must mean best" but it just means big delta. It's like saying that you've saved more money because you bought a $100 item for 50% off than if you didn't buy it at all. The biggest delta there is the 50% off versus none off, but you didn't save any money at all in the first case, and $100 in the second. The biggest effect is the second one.
I think that I wasn't clear on this. I would apply disadvantage to the @11+ because I think this would do more damage to me. Implying that I feel that disadvantage @11+ is more effective that disadvantage @20.
Why would you imply what you feel? Why not just say it? Sorry, weird pet peeve quirk. Carry on.
Again, I think you misunderstand the question? The question was not about you, but about which target you'd rather attack -- @11 with disadvantage or @20 with disadvantage. You answered this question the first time (I thought) but now it seems you're trying to answer a different question? Given @11 with or without disadvantage is an easier target than @20 without (much less with), I'm pointing out that @11 with disadvantage cannot be that large of a benefit because it's the obviously better choice of whom to attack.
To further this question, would you rather attack a foe where you need an 11 with disadvantage or a 12 with disadvantage? Why? I think that the answer here will be pointing in the direction I'm going. (To answer my own hypothetical, it should be obvious that attacking the 11 is preferable to the 12 because of the higher hit chance.)
ummm no, if I reduce one hit of 10 damage to not being hit* I have not taken 10 damage I have not saved 100HP, just 10.
Sigh. My wife feels the same way. She says she's saved me money because she bought whatever on sale. I point out that you've saved nothing because you actually spent money. The same applies here. If I take 10 damage, I've spent 10 hitpoints. If I take no damage, I don't save 10 hitpoints, I've saved all of my hitpoints because I haven't spent any at all -- I still have every one of them. Similarly, if I spend all of my hitpoints, I haven't saved any (obviously). If I spend half of them,
I also haven't saved any -- I've
spent half of them.
In the eg you give,
@11+ I will be dead at the end of combat I have lost 100 HP
@11+ DIS I will survive 20 rounds of combat with 50 HP at the end - not quite enough to go for another round
@20 I will survive the combat with 90 HP - plenty of HP left to carry on fighting
@20 DIS I will survive the combat with 100HP - plenty of HP left to carry on fighting
So in both cases of @20 I come out of the combat almost without a scratch.
In the first casae of @11+ I'm in no shape to carry on - I'm dead
In the second case of @11+ I could, with a bit of luck or a healing potion, go another round
Sure. Now go 40 rounds. Which is better now? 60 rounds. 100 rounds. There's only one choice that has the possibility to last 100 rounds, and it's not 11.
Yes, I'm still losing 50HP, but I'm not losing the other 50 as well, I still have 50HP to carry on doing stuff. Losing 10 HPs leaves me with 90 HPs to do stuff. Not losing 10 HPs is certainly better than losing them, but not as nice as not losing 50. I would not be doing anything different if I have 90/100 HP compared to the action I would take if I had 100/100HP. I would be doing things very differently if I had 1/100 HP.
How many resources do you use to correct the 50 hitpoints spent vs the none spent? You spend far more resources to keep an 11 up than a 20 -- the overall cost is much, much higher. But you still say it's better despite admitting that you're down half your hitpoints and have to spend healing potions vs not having to do that at all because you got a bigger discount at the damage shop?
Weird.
Think of it this way, if they both attacked you, without disadvantage, you'll die
If you impose disadvantage only on the @20, you die - the 11+ still does 100 damage.
If you impose disadvantage on the @11+ you will walk away with 40 HP
So which of those three have the biggest change to the outcome?
Wait, what? I'm confused. Are you trying to propose a situation where 2 creatures are attacking you simultaneously where one needs an 11 to hit you and the other needs a 20? And you're saying that since the 20 will rarely hit you anyway, the biggest reduction in incoming damage is to disadvantage the 11? Sure, totally agree. This is that tactical thing that I was talking about where a specific situation leads to a choice that makes sense within that situation. This isn't an underlying feature of the biggest effect of disadvantage, though, it's the specific tactical situation you're proposing -- 2 opponents, one inept and one fearsome. This also touches on the other point I was making about situational choices -- you cannot choose the 11 or the 20 only. If you could, you'd clearly choose the 20 by itself. So, in that sense, the biggest effect is still at 20 as it reduces your total incoming damage to nearly zero -- no resources used on your part. But, since you cannot choose, you have to weigh the entirety of the situation, and, indeed, in this situation you'll get the best use out of disadvantaging the fearsome opponent vs the inept one.
Turn this around, though, and ask if you have two party members, one hit on an 11 and one hit on a 20, and you can pick one to stand in the door and hold off a big monster or horde from the rest of you, which will you pick? Clearly the 20 and not the 11. Situation matters. But, as far as largest mathematical effect, it remains with the 20 as it reduces incoming hits by a factor of almost 200 versus a factor of 2 at 11. End point.