Your main point seems to be that the majority of time SB will not see use because if they are likely to fail the save they probably failed it on the first roll which means that SB will not get used and if they are likely to pass the save then they are likely to pass it again on any reroll. Hence SB is wasted learned/prepared spell in that regard because it is unlikely to come up. (Please correct me on this if I'm wrong)
As a counterpoint I would say that having SB as a prepared/learned spell is a very minor cost (especially at later levels) especially with the variety of other uses that are available for it. In addition the times that it does come up with a reroll having a dramatic effect on the game are likely to be times that have an outsized effect. The times where it will likely come into play are going to be boss battles where it makes it more likely that instead of an epic confrontation with a villain the party ends up with 2 rounds of beating the pinata because the wizard paralyzed/hypnotized/banished the big bad.
The first part does effectively articulate my point.
I would disagree with the second, having it prepared/learned is a high cost. It is a very high cost for a non-wizard, but even for a wizard at high cost, especially at high level. For example, a 15-level wizard has 34 spells in his book (assuming he did not scribe any). 22 of these spells are 3rd level or higher, and he can prepare at most 20. That means you are giving up a 3rd level or higher spell to prepare SB when you are 15th level. At 10th level you are giving up a 2nd or higher level spell.
If you get ready to use it every time you cast a spell, the times when it will likely come into play are going to be random. It might be when the boss makes his save against your most powerful spell but it is more likely that it will be when you cast a lower level spell in an earlier fight because you have more lower level spots and these will generate more SB enemy save opportunities.
If you only plan and prepare to use it during the boss battles, or when there is a large payoff then you will rarely use it. It will be very rare that it will come into play at all if you "save" it for saves in the boss battles.
25% is the MOST it will be effective and that is if every enemy needs a DC 11 to save. If the DC is lower or higher than 11, it will be less than 25% (often much less). So in actual play it will be closer to 20% effective. A 10th level wizard only has 11 spell slots a day above 1st level, and only two 5th level slots.
I would also argue it is not a low cost in terms of slot when compared to other 1st level spells, abilities and cantrips that apply similar statistical debuffs usually to multiple rolls, and potentially against multiple foes. Bane for example is WAY more powerful in terms of using a spell slot to lower saves, mind sliver is less powerful but is unlimited use. This smaller "payoff" is offset both by the fact SB is a reaction, making it less costly than an action and easier to chain with a spell and by the fact you can use it for a wider array of things than either of these.
It is a normal reroll that works like any other reroll in the game. Here is the text form the spell:One thing to clarity, SB is not a “reroll” in the truist sense, it is a new roll that can replace the original result.
this is important when considering advantage/disadvantage, SB doesn’t care about those conditions, the new roll is unaffected. For example, many high cr monsters have magic resistance, to make up for relatively low saves. SB gets an extra boost here, as the new roll won’t have advantage and so SB has a much higher chance of being effective.
You magically distract the triggering creature and turn its momentary uncertainty into encouragement for another creature. The triggering creature must reroll the d20 and use the lower roll.
This is no different than any of the other abilities that cause a reroll.
The way it is applied is also identical to the example given in the PHB which the new roll "replaces" the original result of a save, attack or ability check. In cases of advantage/disadvantage, you do not throw away both dice on the reroll, you reroll one of the two dice and replace that one dice.
To use the example above, if the enemy rolls a 20 and an 18 with advantage, and you cast SB he would reroll the 20. If he rolled a 4, the 4 would replace the 20, he would then have a 4 and an 18 and 18 would be the number used on the save, attack or ability check.
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