Sure but that means it is still not usually relevant.Reducing the chance of a negative outcome from 20% to 4% may only be a "16% chance it actually made a difference", but it's also an 80% reduction in the rate of undesirable outcomes, and of the total 84% of situations in which it "didn't make a difference", you were not using it, and expended no resources, in 80% of those.
When an outcome is already rare, making it more rare does not usually matter.
If need a 3 to hit a Zombie then giving me a +1 to attack decreases my chance to miss by 50%, but it is not that relevant. Giving me a +6 to attack when I need a 13 to hit decreases my chance to miss by the same 50%, but it is MUCH MUCH more powerful.
So if your party forces 5 saves on enemies over the course of a battle, and each of those have an 80% chance the enemy fails, 32% of the time, they fail all of them. Great! You won! The other 68% of the time, one or more of those saves are succeeded, and you're in a situation where Silvery Barbs can come into play, and in the situations where it comes into play, 80% of the time it results in the save being failed instead.
But you are not considering stacked probability here and this is unrealistic for multiple reasons:
1. First off 5 saves on a high level spell is a lot. If you have a party of 5 14th level characters with 2 full casters they only have 4 spells of 6th level total, so using 5 of them in one battle is a bit unrealistic. Further if it is a truely powerful spell only the first failed save matters.
2. We are talking about powerful spells. If the enemy fails a single save against a spell of this magnitude you should win the battle. Your scenario is based on the idea that it matters to change the save, so failing the save means a win for the good guys. If you are using it to cause a failure for fireballs or dissonant whispers this is an entirely different discussion, but he has to make 5 saves for you to get a chance to use 5 SBs and hold true to those numbers..
That said even if you do this:
Chance enemy fails every single save and silvery barbs is irrelevant: 33%
Chance enemy saves at least once and silvery barbs does not change the outcome: 13%
Chance enemy saves at least once and silvery barbs changes the outcome: 54%
So in this highly unlikely scenario you have presented Silvery Barbs is still only effective half the time.
But like I said this is very unrealistic if we are talking about game cahnging spells. You only need to land one of them to win. In this case Silvery Barbs only has a 17% chance of chaging the outcome if the first landed spell wins (with 16 of that 17% coming on the very first spell cast).
Only if he actually gets to make 5 saves and enemy should not be getting 5 saves agaisnt a high level spell and still be in the fight.Thus, the chance it makes a difference in the outcome = 54%, for a cost of 1 spell slot.
That is the point.
Casting dominate monster 5 times so the numbers for silvery barbs look better is not a relevant test. One failure and the fight is over.
Shield is far more powerful in play than SB because the opportunity to use it and its effectiveness is higher. Also the enemy can not save against it. It works to increase your AC every time it is used and it usually effects more than one roll, especially at high level).Your 'math' seems to focus primarily on how unlikely it is to come up in isolated incidents. In a party of 6, for a given single target attack, one could say that Shield only 'makes any difference to the outcome' if they are targeted, hit, and hit by an amount where +5 AC would change the result. So you could 'calculate' the potential impact as 4%. But such 'calculations' would ignore how impactful it is in the situations where it Does come up, and I feel strongly that you're making the same mistake here.
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