Each beam is a separate attack in this case. So
Different from Magic Missile. Because each is a separate attack, it's almost like treating it as a separate instance of the spell. It's a separate damage roll to so you add your CHA mod to each instance (magic missile is one damage roll per target).
Yes. Again, because they are separate attacks, each beam you target at an opponent, that hits, triggers a new concentration check.
You're exactly right on the comparison, this is a multi-attack spell, rather than multiple damage units like Magic Missile.
Assumptions
I'm going to be making the following assumptions, based on what you've already provided:
- 3rd level (since you get a crit on a 19 or 20)
- 16 Strength (no ASI to bump up to 18)
- Fighting a CR 3 creature (for base math)
- Average damage is 7.50 (4.50 from the die +3 Str mod)
- Average crit damage is 12.00 (4.50 per die +3 Str mod)
- Attack bonus is +5 (+2 prof, +3 Str mod)
- The enemy has AC 13 (per the DMG guidelines on page 274)
- DPR calculations are:
- Crit damage = Crit % x average crit hit damage
- Normal damage = Hit % x average hit damage
- hit % = 100 – [miss %] – [crit %]
Note that any flat modifier to the damage total won't change with a crit, since you only double the dice rolled, not the modifiers added.
Champion Fighter
Per the DMG page 274, a CR3 creature has an average AC 13, meaning you need to roll an 8 or higher.
With Advantage
AnyDice can tell us our miss chance and our crit chance. From there, we know our hit chance.
- A normal roll of 1d20 will have a 35% miss, 10.00% crit (1.20 DPR), and 55.00% normal hit (4.13 DPR) for a total DPR of 5.33
- A roll with advantage will have a 12.25% miss, 19.00% crit (2.28 DPR), and 68.75% normal hit (5.16 DPR) for a total DPR of 7.44
- A roll with your DMs +2 rule will have a 25.00% miss, 10.00% crit (1.20 DPR), and a 65.00% normal hit (4.88 DPR) for a total DPR of 6.08
With Disadvantage
AnyDice can tell us our miss chance and our crit chance. From there, we know our hit chance.
- A normal roll of 1d20 will have a 35% miss, 10.00% crit (1.20 DPR), and 55.00% normal hit (4.13 DPR) for a total DPR of 5.33 (unchanged)
- A roll with disadvantage will have a 42.25% miss, 1.00% crit (0.12 DPR), and 56.75% normal hit (4.26 DPR) for a total DPR of 4.38
- A roll with your DMs -2 rule will have a 45.00% miss, 10.00% crit (1.20 DPR), and a 45.00% normal hit (3.38 DPR) for a total DPR of 4.58
Rogue
How does this change affect other classes, specifically those who rely on bonus damage dice? I'm using a rogue for this example since sneak attack is easy enough to calculate, but a paladin falls under the same heading with their smite spells and the like.
We use the same percentages and base damage (assume Dex and a rapier) for our fighter, but we add sneak attack damage. That's 2d6 at level 3, so with advantage we add +2d6 (7) on a hit and +4d6 (14) on a crit. Attacks without advantage don't get sneak attack damage added in, so the disadvantage numbers from above carry over (I know you can get sneak attack damage without advantage, but we'll ignore that for simplicity).
With Advantage
- A normal roll of 1d20 will have a 35% miss, 5.00% crit (1.30 DPR), and 60.00% normal hit (8.70 DPR) for a total DPR of 10
- A roll with advantage will have a 12.25% miss, 9.75% crit (2.54 DPR), and 78.00% normal hit (11.31 DPR) for a total DPR of 13.85
- A roll with your DMs +2 rule will have a 25.00% miss, 5.00% crit (1.30 DPR), and a 70.00% normal hit (10.15 DPR) for a total DPR of 11.45
With Disadvantage
- A normal roll of 1d20 will have a 35% miss, 5.00% crit (1.30 DPR), and 60.00% normal hit (8.70 DPR) for a total DPR of 10
- A roll with disadvantage will have a 42.25% miss, 1.00% crit (0.12 DPR), and 56.75% normal hit (4.26 DPR) for a total DPR of 4.38 (identical to the fighter, as no advantage means no sneak attack)
- A roll with your DMs -2 rule will have a 45.00% miss, 5.00% crit (1.20 DPR), and a 50.00% normal hit (2.25 DPR) for a total DPR of 3.45
Conclusion
With your DMs proposed houserule, the expected DPR for any class is going to be decreased because of the fact that you're still only rolling 1 die, so the chance of a critical hit will not change. The biggest, well, advantage of rolling with advantage is it almost doubles your chance of a crit: 9.75% vs. 5.00% for a normal 20 crit and 19.00% vs. 10% for a champion fighter crit.
Indeed, that simple change reduces the overall expected damage output of the entire party, especially those classes that rely on burst damage in the form of more dice. As you gain in levels and get the extra attack feature, magic items/spells that add damage dice, and class features that change the damage dice done, the gap will only increase.
Best Answer
I have compiled all the necessary statistics into one AnyDice program. AB refers to your attack bonus, AC is your enemy's armor class.
AnyDice can also store dice sequences in variables. This does not "roll" and store a number, but every possible outcome is considered every time we use the variable. We'll use this to store the damage for Eldritch Blast (1d10+5) and shocking grasp (4d8) in EB and SG, respectively.
Calculating a basic chance to hit in AnyDice is just
1d20+AB>=AC. With (dis)advantage, you can use[lowest/highest 1 of 2d20]+AB>=AC. 1 means you hit, 0 means you miss. We'll use these often, so let's store them in ATT, DIS and ADV.To get the damage, you can multiply the result of the above with the damage calculation, e.g.
ATT*SG.The last thing to note is that in AnyDice
2*1d6≠1d6+1d6. I wrote a simple sum/multiply function that returns the latter:[sum DIS times 4] = DIS+DIS+DIS+DIS.That said, let's go through your points one by one:
Hitting with shocking grasp is just a simple attack, which comes out to 55%.
Hitting at least once with 4 attacks with disadvantage is just adding up 4 attacks with disadvantage, and then checking if the total result is at least 1, which comes out to 76.33%.
Your chance to hit with at least one of four EB at disadvantage is therefore (76.33/55-1)*100%=38.78% higher than with shocking grasp.
For average damage, the quickest way is to just multiply the chance to hit with the average damage of the attack. For a 2d8 shocking grasp, that is 55%/100% × 2 × 4.5 = 4.95. If you care about the statistics, multiply the damage term with the hit chance term.
For the EB calculation, you do this separately for every attack.
With advantage, the chance to hit with SG increases to 79.75% making it almost equal to the chance of hitting with EB (at least once).
Same as 2, but with advantage.
This one is indeed tricky. I put in another function to help. Passing DIS as a number (
D:n) allows us to do things depending on the value "rolled". The first line is the recursion limit. If the attack is a miss, we continue recursively. Otherwise, we register 1 (we just hit after all), and roll normally 4-N times.I also included the damage in this case, with its own function due to me hardcoding stuff. The average damage increases by around 33% compared to all-disadvantage!
I'll leave this one up to you, just add 1d6 to the damage variables at the top and re-run the program.