Here's the math on Chromatic Orb. It uses a known math problem called the birthday problem used to calculate the probability that at least 2 from a set of a certain size will be the same.
The probability that at least 2 out of (n)d8 will be the same number:
And then on top of that, at most levels there is roughly an 88% chance to hit with advantage, which a sorcerer would have using Innate Sorcery. Or 65% chance without, if you're a Wizard instead.
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Yeah, I wanted to create actual comparisons between two spells, not just the probabilities, so people can compare exactly what the DPR differences are. I can break it down now and calculate Halfling Luck, Heroic Insp, etc.
Same but with Advantage. Chromatic orb single-target damage doesn't jump much, but it improved exponentially where multiple targets are available. With Innate Sorcery, this spell is a must-have crowd-control spell.
1d8 Firebolt
4.62 Average Damage per Cast
5.50 Average Damage per Target Hit
2d8 Firebolt
9.23 Average Damage per Cast
11.00 Average Damage per Target Hit
3d8 Firebolt
13.87 Average Damage per Cast
16.50 Average Damage per Target Hit
4d8 Firebolt
18.47 Average Damage per Cast
22.00 Average Damage per Target Hit
Level 1 Chromatic Orb:
17.03 Average Damage per Cast
15.07 Average Damage per Target Hit
Level 2 Chromatic Orb:
30.75 Average Damage per Cast
20.09 Average Damage per Target Hit
Level 3 Chromatic Orb:
52.51 Average Damage per Cast
25.11 Average Damage per Target Hit
Level 4 Chromatic Orb:
82.52 Average Damage per Cast
30.15 Average Damage per Target Hit
Level 5 Chromatic Orb:
115.58 Average Damage per Cast
35.15 Average Damage per Target Hit
Level 6 Chromatic Orb:
148.11 Average Damage per Cast
40.18 Average Damage per Target Hit
Level 7 Chromatic Orb:
178.20 Average Damage per Cast
45.20 Average Damage per Target Hit
Level 8 Chromatic Orb:
208.85 Average Damage per Cast
50.23 Average Damage per Target Hit
Level 9 Chromatic Orb:
239.75 Average Damage per Cast
55.25 Average Damage per Target Hit
As per: Stats
Using AC of 20, and Attack Bonus of 11 (Crit range is 20), no advantage, assuming enough targets exist for it to jump.
1,000,000 iterations, so it should be very accurate
Firebolt for Comparison:
1d8 Firebolt
2d8 Firebolt
3d8 Firebolt
4d8 Firebolt
Level 1 Chromatic Orb:
Level 2 Chromatic Orb:
Level 3 Chromatic Orb:
Level 4 Chromatic Orb:
Level 5 Chromatic Orb:
Level 6 Chromatic Orb:
Level 7 Chromatic Orb:
Level 8 Chromatic Orb:
Level 9 Chromatic Orb:
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ModeratorHere's the math on Chromatic Orb. It uses a known math problem called the birthday problem used to calculate the probability that at least 2 from a set of a certain size will be the same.
The probability that at least 2 out of (n)d8 will be the same number:
Chromatic Orb
Level 1, 2 targets, 3d8, 1-(8!/(8-3)!)/(8^3) = 34.4% chance to bounce
Level 2, 3 targets, 4d8, 1-(8!/(8-4)!)/(8^4) = 59%
Level 3, 4 targets, 5d8, 1-(8!/(8-5)!)/(8^5) = 79.5%
Level 4, 5 targets, 6d8, 1-(8!/(8-6)!)/(8^6) = 92.3%
Level 5, 6 targets, 7d8, 1-(8!/(8-7)!)/(8^7) = 98.1%
Level 6, 7 targets, 8d8, 1-(8!/(8-8)!)/(8^8) = 99.8%
Level 7, 8 targets, 9d8, at 100%
Level 8, 9 targets, 10d8, at 100%
Level 9, 10 targets, 11d8, at 100%
And then on top of that, at most levels there is roughly an 88% chance to hit with advantage, which a sorcerer would have using Innate Sorcery. Or 65% chance without, if you're a Wizard instead.
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Yeah, I wanted to create actual comparisons between two spells, not just the probabilities, so people can compare exactly what the DPR differences are. I can break it down now and calculate Halfling Luck, Heroic Insp, etc.
Same but with Advantage. Chromatic orb single-target damage doesn't jump much, but it improved exponentially where multiple targets are available. With Innate Sorcery, this spell is a must-have crowd-control spell.
1d8 Firebolt
2d8 Firebolt
3d8 Firebolt
4d8 Firebolt
Level 1 Chromatic Orb:
Level 2 Chromatic Orb:
Level 3 Chromatic Orb:
Level 4 Chromatic Orb:
Level 5 Chromatic Orb:
Level 6 Chromatic Orb:
Level 7 Chromatic Orb:
Level 8 Chromatic Orb:
Level 9 Chromatic Orb: