Illogical Truth - Multiple Attacks?

[FrogReaver]

Average damage, against a single target, is exactly the same: 22 (average of 4d10) x chance to hit. (Plus crit damage, but that also will come out the same.) Fire bolt is swingier but the average is identical. I don't know whether the error is in your inputs or a bug on the site, but there is definitely an error.

In practice, EB is superior because a) you will waste less damage on blow-through with multiple targets, and b) you will encounter fewer resistant/immune monsters.

His results are accurate.

 

[Yunru]

That they are. The mean is exactly the same sitting at exactly 13.2 as it should, it's just the point at which they have a 50% to do that much damage isn't the mean, which I didn't expect.

 

[FrogReaver]

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

Let me give a simple example:

Suppose there are 2 distributions defined below
d1 = {3, 3, 3, 3, 6, 6}
d2 = {0, 0, 6, 6, 6, 6}

The Mean on both distributions is 4. With d1 you only have a 33% getting a result equal to the Mean or above. With d2 you have a 66% chance of getting a result equal to the mean or above. In other words, what you are demonstrating with the EB and firebolt example is a perfectly natural occurrence that has numerous other examples.

The only issue is the commonly mistaken assumption that rolling some number or higher 50% of the time has anything to do with the Mean. It doesn't. Rolling some number or higher 50% of the time would be the Median, not the Mean.

Now the Median is a great indicator of central tendency, maybe even better than the Mean is in many circumstances, but it's not the Mean. Expecting the Median to be the same as the Mean is actually extremely rare. It would actually be extraordinary if the mean and median were the same in either the firebolt or the eb example.

 

[FrogReaver]

That they are. The mean is exactly the same sitting at exactly 13.2 as it should, it's just the point at which they have a 50% to do that much damage isn't the mean, which I didn't expect.

Erased Post due to foot in mouth syndrome...

 

[doctorbadwolf]

Oh. I don't generally let my players redeclare . . . Although I just remembered now that they also tend to tell me the results of all their attack rolls first, then roll all the damage together, so there's no way to know which attack actually felled the fellow.

If all the damage is rolled together, I guess I can see that. You could just start with the highest result, and let any remaining dice when enough has been done to kill it roll over to another target.

For me, I’d rather err on the side of allowing stuff like declaring a new target, or at least reminding the player they can target each beam individually if they want to.

 

[Satyrn]

If all the damage is rolled together, I guess I can see that. You could just start with the highest result, and let any remaining dice when enough has been done to kill it roll over to another target.

For me, I’d rather err on the side of allowing stuff like declaring a new target, or at least reminding the player they can target each beam individually if they want to.

I prefer to roll and resolve one attack at a time. There's more reasons than the foe dropping before the last attack, too. For example, if the warlock's Eldritch Blast* can slag the target, the slagged condition is easier for me to handle one attack at a time (each time an attack inflicts the slagged condition the damage dealt by future attacks is increased).


*This isn't really the best example since I haven't actually written up an invocation or anything to make a slagging Eldritch Blast (it's going on my to-do list right now) but the same applies to a fighter wielding a Maliwan slag-rifle.