An example from experience: Use Math, there should always be a clear winner.
My primary D&D group is composed of mostly Math degrees (or related). As such when we have questions on whos spell to use we simply run a (generally) quick calculation to determine whos is better to use. For example...
- The important factors are the DC (chance of success) and the damage (we will use average [with some notes for min/max]).
- Using your examples we have a DC15 @ 3D8 damage, DC14 @ 4D8 damage, and DC13 @ 3D8 damage.
- Assuming no modifiers for the defensive DC roll, chance to hit for those three abilities is 70%, 65% and 60%. (note DC15 effectively means roll a 14 or lower and do damage - thus (1-14/20) meaning 70% chance to fail)
- The average damage for those three rolls is 13.5, 18, and 13.5.
Some simple calculations
DC15@3D8 = 0.70 × 13.50 = 09.45 [Min: 0, Max: 18]
DC14@4D8 = 0.65 × 18.00 = 11.70 [Min: 0, Max: 24]
DC13@3D8 = 0.60 × 13.50 = 08.10 [Min: 0, Max: 18]
In this situation, the clear winner is DC14, followed by DC15, finally DC13.
The only thing I might argue for is that "potent" likely refers to stronger in terms of game mechanics (e.g. Higher Spell Level, higher DC, higher damage). However as far as I could find this is not clarified anywhere in RAW so it is up to the DM to decide.
One concern that has been brought up is that doing calculations on the fly could be a challenging/time consuming concern for most groups. With that in mind this can be simplified somewhat by making note of some specific constraints:
- You have to be comparing the same type of dice (e.g. a D4 will not compare to a D12).
- You have to adjust based on the creatures bonus (e.g. if the save is +3, then use -3 when calculating the save).
Here is the quick reference table I made to help show this.
Link for both details and simple table: https://docs.google.com/spreadsheets/d/19VOp_rGHEQ4r7aDMlbW4mTnXiDK_YyZmtjUnWuCa870/edit?usp=sharing
This table depicts the number of DC steps up you would have to make in order to make a lower/higher number of dice viable.
# Dice
DC 1 2 3 4 5 6 7 8 9
20 20 10 7 5 4 2 1 1 0
19 19 10 6 5 4 2 1 1 0
18 18 9 6 5 4 2 1 1 0
17 17 9 6 4 3 2 1 1 0
16 16 8 5 4 3 2 1 1 0
15 15 8 5 4 3 2 1 1 0
14 14 7 5 4 3 2 1 1 0
13 13 7 4 3 3 1 1 1 0
12 12 6 4 3 2 1 1 1 0
11 11 6 4 3 2 1 1 1 0
10 10 5 3 3 2 1 1 1 0
9 9 5 3 2 2 1 1 1 0
8 8 4 3 2 2 1 1 0 0
7 7 4 2 2 1 1 1 0 0
6 6 3 2 2 1 1 0 0 0
5 5 3 2 1 1 1 0 0 0
4 4 2 1 1 1 0 0 0 0
3 3 2 1 1 1 0 0 0 0
2 2 1 1 1 0 0 0 0 0
1 1 1 0 0 0 0 0 0 0