# How to compare hit % and damage between 1 attack vs 4 attacks with disadvantage?

Quite a few scenarios here, wish my AnyDice fu were up to par—if it's too much, no need to cover all of them, just the most representative, so I can figure out the rest. For the given character parameters:

Character level: 17+
Spell Attack Modifier: 11
Proficiency: 6
Charisma Modifier: 5
Target Armor Class: 21

How could I compare on AnyDice:

1. Probability of hitting with Shocking Grasp vs probability of hitting at least once with 4 Eldritch Blast beams (with disadvantage)?
2. Average damage in both cases (EB with Agonizing Blast).
3. Probability of hitting with Shocking Grasp (with advantage) vs probability of hitting at least once with 4 Eldritch Blast beams (with disadvantage)?
4. Average damage in both cases (EB with Agonizing Blast)?
5. Tricky one: Probability of hitting with Shocking Grasp (with advantage) vs probability of hitting with 4 Eldritch Blast beams (with disadvantage until one hits, then the remaining ones without disadvantage—i.e., assuming Repelling Blast)?
6. Average damage in both, assuming the target has Hex (extra 1d6 per hit).

Thanks!

• If you're gonna math it up that way, you might also consider that Shocking Grasp allows you to run away and possibly not take damage the next turn. The opposite end is taking damage that can down you, kill you, or break concentration on Hex. I'm sure you know that things aren't black and white with damage, but maybe some one else doesnt. Dec 10, 2015 at 18:15
• @PremierBromanov - Given the Context of part (5), the intent may be to compare that component of Shocking Grasp to the push effect of Repelling Blast, while performing a cost analysis on the damage done. Average damage of Shocking Grasp, with Hex, is 17.8. Average damage of Eldritch Blast and Hex, initially at disadvantage but with Repelling Blast , is 22.05. Each results in allowing the Warlock to runaway. Dec 10, 2015 at 18:58

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*1d61d6+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:

1. 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.

2. 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.

3. 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).

4. Same as 2, but with advantage.

5. 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!

6. I'll leave this one up to you, just add 1d6 to the damage variables at the top and re-run the program.

• On 5: Given the context of the question, order of events does matter. If the first, second, or third Eldritch Blast hits, the statistics change for each subsequent attack. With repelling blast, the Eldritch Blast no longer has disadvantage, and has a flatter probability. Their are 16 total branch event chains of what could happen? Dec 10, 2015 at 15:54
• Additionally: If their are 4 beams of Eldritch blast, the character is at least level 17. With a spell attack bonus of 11 = profieciency + Charisma mod, where proficiency = 6, Charisma mod = 5. At lvl 17, Shocking grasp does 4d8. Dec 10, 2015 at 16:08
• Heya, thanks for this—it's awesome! However, both comments above are correct: Shocking grasp does 4d8, and EB is 1d10+5 (I corrected both when I noticed them, but you should correct them in your answer, so others don't get confused). And 5 is not the same as 3—if pH(n) is the probability of hitting with the nth beam (and pHd(n) the probability to hit with disadvantage), then the probability to hit on 5 would be: pHd(1) * pH(2) * … * pH(4) + [1-pHd(1)] * pHd(2) * pH(3) * … + [1 - pHd(1)] … In short, have to add the 16 permutations for hitting with Disad on nth attack, then without Dis on 4-n. Dec 10, 2015 at 18:34
• I have misunderstood 5 as "try 4 times or until you hit". Let me see if I can come up with something in AnyDice. Dec 10, 2015 at 19:17
• @DrunkCynic fixed both the damage values and solved #5 in Anydice now. Dec 10, 2015 at 20:32

Disclaimer: I don't know how to make anydice ignore a roll of 1 on a D20. While not especially pertinent, because 1+11 <21, it bugs me.

Assumptions I've made: at least level 17, and Charisma modifier is 5.

1. Probability of Hitting with Shocking grasp versus hitting with at least one of four Eldritch Blasts. http://anydice.com/program/7317 . As a corollary, here is an evaluation of the chances of hitting with a number of Eldritch Blasts: http://anydice.com/program/7318

2. Average Damage of Shocking Grasp versus Eldritch Blast (with Agonizing): http://anydice.com/program/731a

3. Probability of Hitting with Shocking grasp with advantage versus hitting with at least one of four Eldritch Blasts with disadvantage. http://anydice.com/program/731b

4. Average Damage of Shocking Grasp with advantage versus Eldritch Blast (with Agonizing): http://anydice.com/program/731c

5. Probability of hitting with Shocking grasp, with advantage, remains unchanged from (3). For the four Eldrtich Blasts, order is important: there are 16 permutations, 11 unique. With disadvantage, there is a 30.25% chance an will hit, while attacks without disadvantage have a 55% chance to hit.

Making tables on SE is hard.

1. The expected damage of Shocking Grasp, with advantage, is relatively unchanged from 4. Just add 3.5 for Hex. The expected damage of an Eldritch Blast, with a Charisma modifier of 5, and Hex on the target, is 14 = 5.5+5+3.5. Refer to the image in (5) for the expected damage on the Eldritch Blast, Averaging 22.
• Caveat: depending on your table, rolling a 1 on d20 for an Eldritch Blast may matter. The DM may rule that a fail for the attack overall, increasing the probability that the attack fails entirely (MMMM). Dec 10, 2015 at 18:51

No anydice needed, just basic probability.

1. 55% chance to hit with sg. Chance of missing with 1 eb(d) is 1-.55x.55=.6975. So chance of missing with all is .6975^4=.2367. Hitting with at least 1 is therefore .7633.

2. Can't tell without knowing caster level but assuming 17+, expected damage from sg is 4x4.5=18x.55=9.9, for eb(d) it is 4x.3075x5.5=6.765 (you don't give a Cha mod but just add it to the 5.5).

3. sb(a) 1-.45x.45=.7975. eb(d) as above.

4. sb(a) .7975x18=14.355. eb(d) as above.

5. Not tricky at all. sb(a) is as 3. eb(d) is as 1; stopping after the first hit means you hit with at least 1!

6. sb(a) as 3. eb(d) .7633x5.5=4.2.

• Note that 5 is incorrect—since the question states "assuming Repelling Blast," the gist is that after hitting with the nth EB, you can push the target away (thereby not having disadvantage for the remaining 4-nth beams). Dec 11, 2015 at 20:39