Illogical Truth - Multiple Attacks?

[Yunru]

Firebolt, or Eldritch Blast? In a complete white room, which would you expect to deal more consistent damage? 4d10 with one attack, or four attacks for 1d10 each?

The correct answer is...

[sblock]Firebolt, somehow. At least, according to AnyDice: https://anydice.com/program/12ce9
What's illogical is that it seems counter to the fact that the more times you do something, the closer you approach doing the average damage.
Which seems to play out on the tables, the means are the same, but Eldritch Blast has less deviation. But when it comes to damage, Eldritch Blast has a 50% chance of doing 13.2 or more as expected, and then Firebolt has a 50% chance of doing 17 or more. What?[/sblock]

Can anyone explain why that is?

 

[doctorbadwolf]

I assume you double checked your inputs for human error somewhere?

 

[Yunru]

Yuup. Not alot to check with "output d{0,0,1,1,1}*4d10 named "Firebolt""

 

[Blue]

Yuup. Not alot to check with "output d{0,0,1,1,1}*4d10 named "Firebolt""

Let me make sure I follow: Are you using that to emulate a 60% chance to hit?

 

[Yunru]

Let me make sure I follow: Are you using that to emulate a 60% chance to hit?

Yup.

 

[Blue]

EB has a greater chance of doing some damage, but a lesser chance of doing the highest damages.

Think like this - to do 0 damage happens 40% of the time with Firebolt, but only 2.56% of the time with EB. Right there there's a lot fo tiem when FB will give you a result of 0. So when FB does give you a result, it's a higher result then the EB.

Firebolt doesn't give you more consistent damage at all, that characterization is false. EB will consistently give you something. Firebolt will be inconsistant - miss more, but have a higher result when it hits.

Looking at individual damage results, through 19 points of damage EB is more likely to give you that result. Once you get past that, the chance that a single FB will hit and damage is greater then enough EBs will hit to do more damage.

 

[bganon]

I wouldn't call Firebolt "more consistent" - it has a 40% chance of doing zero damage. Factoring in the attack roll like that makes the results look a little weird.

 

[Yunru]

But Eldritch Blast doesn't even meet it's mean at 50%, and that's when the mean's been adjusted for the 60% hit rate

 

[Yardiff]

Most characters casting EB are Warlocks. So each blast gets stat bonus to damage?

 

[FrogReaver]

Firebolt, or Eldritch Blast? In a complete white room, which would you expect to deal more consistent damage? 4d10 with one attack, or four attacks for 1d10 each?

The correct answer is...

[sblock]Firebolt, somehow. At least, according to AnyDice: https://anydice.com/program/12ce9
What's illogical is that it seems counter to the fact that the more times you do something, the closer you approach doing the average damage.
Which seems to play out on the tables, the means are the same, but Eldritch Blast has less deviation. But when it comes to damage, Eldritch Blast has a 50% chance of doing 13.2 or more as expected, and then Firebolt has a 50% chance of doing 17 or more. What?[/sblock]

Can anyone explain why that is?

In this example Firebolt only does damage 60% of the time. Eldritch blast at least does damage 97.44% of the time.

Firebolt does 4d10 damage 60% of the time. Eldritch blast only does 4d10 damage 12.96% of the time.

Eldritch blast is more consistent at doing damage. Firebolt typically does higher damage when it hits. Both of these are expected results IMO.