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Is upcasting the chromatic orb spell (PHB, p. 221) for fire damage at 2nd level ever better than casting scorching ray (PHB, p. 273)?

I am mainly asking this since both are attack roll based fire spells

Is there a point where 4d8 (average of 20) damage would be better than 3 attacks of 2d6 (average 8) damage each?

Ways I would like to test it:

  • attacks made with +5 to hit and another set with +7 to hit.

  • attacks made at disadvantage

  • attacks made at advantage

  • attack made at advantage with Elven Accuracy feat.

  • against 3 enemies: one AC 12 , one AC 16, one AC 20.

My reason for this is that I am making a spread sheet comparing spells that have similar functions, and the comparison my players want to see first is these two.

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    \$\begingroup\$ Related questions that might help you answer it yourself: How do I calculate the chance to hit a given AC? and How do you calculate average damage for DPR comparisons?. It is not nearly as complex as some other statistical models, and I'm sure with some practice you could get the hang of it. If you can't figure it out from just these Q&As, the fellows in RPG.SE General Chat are very technically literate and could likely help you out. \$\endgroup\$ – David Coffron Feb 1 at 23:08
  • \$\begingroup\$ Ask for @Xirema. \$\endgroup\$ – GreySage Feb 1 at 23:33
  • \$\begingroup\$ Not to sound obvious, but Chromatic Orb isn't a fire spell - it's a fire/cold/lightning/thunder/acid spell. \$\endgroup\$ – Miniman Feb 1 at 23:44
  • \$\begingroup\$ Average value of 4d8 is 18, and average value of 2d6 is 7. \$\endgroup\$ – Tim Feb 2 at 9:53
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Scorching ray is always more damaging if you have the same chance to hit

I could tell you even before running the numbers that this would be the case. As long as both spells are on equal playing ground (both have adv/dis, etc.), the higher average damage will always win out. This is because even though scorching ray is split among 3 attacks, the average damage will stay the same. The difference between scorching ray and chromatic orb's damage is only going to be the deviation (the likelihood that the result is close to the average) in the damages:

enter image description here

Notice that the scorching ray damage is slightly more likely to hit near the average (since there are more dice involved). As you can see, I had to correct the scorching ray by 3 points for them to line up (to show the different deviations) meaning scorching ray will deal 3 more damage than chromatic orb if they all hit. Since each ray has an independent chance of hitting, the damage output approximates to the same.

The numbers

Linked here, you can find a spreadsheet with all of the calculations you requested (feel free to download a copy if you want to check out the formulas I used). Essentially it only involves figuring out the chance that the character hits and multiplying the average damage by that chance. Since the scorching rays are independent, you can simply multiply this adjusted damage by 3.

In summary, scorching ray will always be more damaging if the chance to hit is the same throughout.

The case for chromatic orb

There is one instance where chromatic orb deal more average damage, and that is when only the first attack will have advantage (such as if you used true strike). The modified damage in this instance is in the spreadsheet linked in the previous section to show how this changes the numbers. In this case, the greater damage that is applicable to an advantage attack does more than the extra average damage of scorching ray. However, as your normal chance to hit increases, this advantage to chromatic orb decreases and scorching ray catches up.

Versatility of chromatic orb

Chromatic orb still has a comparative advantage over scorching ray and that is its versatility. Fire is one of the most resisted damage types in the game, so if you are dealing with a monster with such a resistance, scorching ray falls off hard, but chromatic orb can select a different option. This lets you go around resistances and target vulnerabilities, greatly increasing utility (perhaps at the cost of raw damage).

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  • \$\begingroup\$ Thanks it's a big help!! Its interesting to see that a 2nd level chromatic orb can be better in certain scenarios ^.^ this will make for some fun team work between the level 3 sorc and either the cleric or the mastermind rogue I DM for since guiding bolt and help action are first attack. ^.^ \$\endgroup\$ – Deceptecium Feb 2 at 0:21
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    \$\begingroup\$ "As you can see, I had to correct the scorching ray by 3 points for them to line up meaning scorching ray will deal 3 more damage than chromatic orb if they all hit." Answer would be improved by elaborating why you did this. What's important about making them "line up" and what does that mean? \$\endgroup\$ – Bloodcinder Feb 2 at 2:11
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    \$\begingroup\$ I would suggest first having an image where the distributions are not artificially lined up. I was confused for a while, as it seems that the average damages are the same, looking at the picture, which contradicts basic arithmetic. Or at least add a big fat warning above the graph that the averages there do not reflect reality. \$\endgroup\$ – Thanuir Feb 2 at 7:35
  • \$\begingroup\$ If you take critical hits into account, it might be that it is more likely to get an isntance of high damage with chromatic orb (where only crit is necessary) when compared to scorching ray, where really outstanding damage would require several hits. Maybe worth an examination. \$\endgroup\$ – Thanuir Feb 2 at 7:40
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The instances where chromatic orb is better are few and far between.

To start, if there are no misses, scorching ray deals an average of 21 (6 * 3.5) points fire damage, and chromatic orb deals 18 (3 * 4.5) points of fire damage.

When there is a 50% chance of hitting (assuming the same modifier to hit), you divide both damage totals by 2, so chromatic orb would deal an average of 9 damage, and scorching ray would be 10.5. If there is a 1 in 20 chance you hit, you will hit 3 times more often (actually slightly more, as you can hit multiple hits, but it is very unlikely), but deal a third of the damage, so it cancels out.

There is a point, however, when chromatic orb is more useful. Scorching ray tends to be much more consistent, as you take multiple attacks, and chromatic orb tends to be either nothing or a lot of damage. So, when you need to deal a lot of damage, chromatic orb is better due to its "high risk, high reward" policy.

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  • \$\begingroup\$ Maybe more specific / clear to say "when less than big damage is truly useless", i.e. when the only useful thing is to do more than X damage on your turn. As other comments mentioned, both can crit, but a chromatic orb crit doubles all the damage for the whole spell, not just one ray. \$\endgroup\$ – Peter Cordes Feb 2 at 8:15

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