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I'm preparing a clockwork soul sorcerer/lore bard for a high level one shot (17 lore/ 3 clockwork soul). The combination seems very versatile for a support character. One area of overlap between them is being able to use reactions to affect the results of opponent's roll.

Both Restore Order and Cutting Words can be used as a reaction if the target has advantage, but statistically which is more effective at lowering the final result of the roll? This is a higher level bard so they use a d12, but I'm also curious how differently the results look when lower a bardic inspiration die is used.

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Cutting Words is almost always better, just by the numbers.

This table gives the probability of meeting a given DC with a straight roll compared to advantage minus a Bardic Inspiration die:

DC Straight Roll Advantage-d12 Advantage-d10 Advantage-d8 Advantage-d6
10 0.55 0.39875 0.47375 0.54375 0.60875
11 0.5 0.31875 0.39875 0.47375 0.54375
12 0.45 0.23375 0.31875 0.39875 0.47375
13 0.4 0.14375 0.23375 0.31875 0.39875
14 0.35 0.04875 0.14375 0.23375 0.31875
15 0.3 0 0.04875 0.14375 0.23375
16 0.25 0 0 0.04875 0.14375
17 0.2 0 0 0 0.04875
18 0.15 0 0 0 0
19 0.1 0 0 0 0
20 0.05 0 0 0 0

As you can see, Cutting Words with d10 and d12 is always better, and the d6 and d8 can be better for higher DCs.

For some intuition here, we can consider that advantage is at most equal to +5 to the roll, for DCs around 10 or 11:

DC Advantage +5 +d12 +d10 +d8 +d6
10 0.7975 0.8 0.875 0.825 0.775 0.725
11 0.75 0.75 0.825 0.775 0.725 0.675
12 0.6975 0.7 0.775 0.725 0.675 0.625
13 0.64 0.65 0.725 0.675 0.625 0.575
14 0.5775 0.6 0.675 0.625 0.575 0.525
15 0.51 0.55 0.625 0.575 0.525 0.475
16 0.4375 0.5 0.575 0.525 0.475 0.425
17 0.36 0.45 0.525 0.475 0.425 0.375
18 0.2775 0.4 0.475 0.425 0.375 0.325
19 0.19 0.35 0.425 0.375 0.325 0.275
20 0.0975 0.3 0.375 0.325 0.275 0.225

As you can see, for lower DCs, advantage is roughly equivalent to +5 to the roll. For higher DCs, +5 to the roll is a much more potent effect. Thus, in every case, Cutting Words, which averages -6.5 with the d12, is going to be much more potent than canceling advantage.

Cutting Words can be used after you know the result.

Restore Balance says:

When a creature you can see within 60 feet of you is about to roll a d20 with advantage or disadvantage, you can use your reaction to prevent the roll from being affected by advantage and disadvantage.

However, Cutting Words says:

You can choose to use this feature after the creature makes its roll

With Cutting Words, you can wait till you know the roll result to decide if you want to use it.

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    \$\begingroup\$ Cutting Words is even better than your analysis shows. Restore Balance is used before the dice are rolled, but Cutting Words is used after the initial roll is made but before its success is determined. There is thus an asymmetry of the information available. To use Restore Balance, you will never know whether it is actually needed or not, and thus often it will be wasted on rolls that were going to fail anyway. Cutting words, on the other hand, can be much more targeted, because it will typically be used when you have a much better idea of whether it is both needed and can make a difference. \$\endgroup\$
    – Kirt
    Jan 2 at 21:16

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