Inspiration & Hero Points Math

[Ovinomancer]

If the inspiration is a limited resource, and I know the DC/AC targets, than I'd rather have the d6, since I can choose to deploy it in a situation when I have a 5/6 or 6/6 chance of the bonus shifting the failure to a success.

I'd want the d20 option for when I screw up a save really bad, and the d6 option isn't going to save me.

Don't take this wrong, but you haven't thought that through. The odds that you miss by 1 or 2 is just 10% of all rolls. So the near guarantee that the +d6 turns that into success had to be moderated by the chances of it happening to begin with. So, 5% chance of 100% conversion (missed by one) only adds a 5% increase in overall odds. The +d20 works far more reliably than the +d6, with only when you need to roll 17+ on the die changing over. Again, for proficient tasks, you will rarely actually need to roll 17+.

+d6 favors the non-proficient on hard tasks. In just about every other situation, the +d20 is the better choice (even for thr non-proficent at need rolls less than 17).

The bit about liking the +d6 is mostly confirmation bias for those minority of cases where do miss by 1 or 2. It's ignoring the other cases.

 

[iserith]

Don't take this wrong, but you haven't thought that through. The odds that you miss by 1 or 2 is just 10% of all rolls. So the near guarantee that the +d6 turns that into success had to be moderated by the chances of it happening to begin with. So, 5% chance of 100% conversion (missed by one) only adds a 5% increase in overall odds. The +d20 works far more reliably than the +d6, with only when you need to roll 17+ on the die changing over. Again, for proficient tasks, you will rarely actually need to roll 17+.

+d6 favors the non-proficient on hard tasks. In just about every other situation, the +d20 is the better choice (even for thr non-proficent at need rolls less than 17).

The bit about liking the +d6 is mostly confirmation bias for those minority of cases where do miss by 1 or 2. It's ignoring the other cases.

Your analysis is really interesting.

What do you think about [MENTION=6776133]Bawylie[/MENTION]'s more, say, experiential analysis in terms of how it feels at the table? I realize there's no accounting for taste, but I'm interested in your take on that given that you would be sitting at the table fully knowing the underlying maths.

 

[Laurefindel]

As others have said, inspiration gives the equivalent of a +5 bonus when the target number is around 10 or 11. When the number you need is in the higher range ( like 17-20), advantage becomes a lot less reliable. Also, advantage doesn’t allow you to get over 20 on a 20-sided die like hero point. Generally, inspiration is best to counter disadvantage and (almost) guarrantee a success on a roll you already have good chances of succeeding, while hero points better help you succeed difficult rolls.

Again as it has been noted, any type of meta plot point is usually stronger when used after you know what result you came up with. But even if you allow inspiration-as-reroll, hero-point are usually superior for a high DC roll.

 

[Ovinomancer]

Your analysis is really interesting.

What do you think about [MENTION=6776133]Bawylie[/MENTION]'s more, say, experiential analysis in terms of how it feels at the table? I realize there's no accounting for taste, but I'm interested in your take on that given that you would be sitting at the table fully knowing the underlying maths.

Confirmation bias, really. You get a few moments of those "miss by 1-2" where the +d6 saves the day and it feels great. You discount the other times where you missed by more and it wasn't worth it.

The other way it feels better is that is more efficient -- you're only using it when it has a high probability of helping.

However, if you're considering +d20 after the roll like the +d6, then its almost always going to be better to take the the +d20. If comparing traditional advantage (before the roll) to after the roll +d6, then the efficiency argument gains lots more weight.

 

[Ovinomancer]

As others have said, inspiration gives the equivalent of a +5 bonus when the target number is around 10 or 11. When the number you need is in the higher range ( like 17-20), advantage becomes a lot less reliable. Also, advantage doesn’t allow you to get over 20 on a 20-sided die like hero point. Generally, inspiration is best to counter disadvantage and (almost) guarrantee a success on a roll you already have good chances of succeeding, while hero points better help you succeed difficult rolls.

Again as it has been noted, any type of meta plot point is usually stronger when used after you know what result you came up with. But even if you allow inspiration-as-reroll, hero-point are usually superior for a high DC roll.

I really dislike the "advantage is worth +X" comparisons because they're pretty much wrong and distort understand of what's actually happening with the probabilities. It's like saying apples are bananas because they're both fruit. That the PDFs look the same at "need to roll 10+ on d20" between advantage and d20+5" doesn't mean they're the same. I've seen too many people take the +5 as literal truth and go of the rails with it.

Sorry, Lan, this isn't aimed at you at all, your post was just convenient rant fodder.

 

[iserith]

Confirmation bias, really. You get a few moments of those "miss by 1-2" where the +d6 saves the day and it feels great. You discount the other times where you missed by more and it wasn't worth it.

The other way it feels better is that is more efficient -- you're only using it when it has a high probability of helping.

However, if you're considering +d20 after the roll like the +d6, then its almost always going to be better to take the the +d20. If comparing traditional advantage (before the roll) to after the roll +d6, then the efficiency argument gains lots more weight.

That makes sense. In my case, the players only know the traditional advantage method, so that must be why they think +1d6 after the roll is better. It's not so much the bonus as it is the efficiency.

They'll still get to earn Inspiration as I've been running it (up to 4 times per session per player), but now it will be more efficient for them to apply it. And instead of applying to their own rolls, it can only be applied to other players' rolls. So this should be interesting.

 

[Satyrn]

Sorry, Lan, this isn't aimed at you at all, your post was just convenient rant fodder.

I've mistaken [MENTION=67296]Laurefindel[/MENTION] for Lanefan before. Does this mean I'm not alone in doing so?

 

[Laurefindel]

I really dislike the "advantage is worth +X" comparisons because they're pretty much wrong and distort understand of what's actually happening with the probabilities.

no offense taken. The +5 equivalent only comes from the fact that at DC 11, advantage give you a 25% chance of failure, which is the equivalent of a DC 16 on a d20. Thus the +5 equivalence.

the point I was trying to make in my post was that this +5 equivalence is only true around a target number of 11. The more you move away from that TN, the less of a +5 bonus equivalence it becomes. At TN 20, chances of failure become 0.9025 (lets say 90%), which is the equivalent of a +1 bonus (going from TN 20 to 19-20).

[edited for chances of success vs chances of failure -up]

’findel

 

[guachi]

I think I'd be more likely to remember to use my Inspiration if it were a d6. I could put the Inspiration d6 in front of me and I'd notice it.

Yes, I can also put an Inspiration d20 in front of me but we roll d20 so often I'd probably grab it absentmindedly to use for some other d20 roll.

Inspiration suffers from two major problems in games I've played - can't remember to grant it. Can't remember to use it. I like the idea of "claiming Inspiration" to overcome the first problem. And if a d6 sitting in front of me helps me overcome the second I'm less inclined to care about the math. An Inspiration die not spent isn't very useful.

 

[iserith]

I think I'd be more likely to remember to use my Inspiration if it were a d6. I could put the Inspiration d6 in front of me and I'd notice it.

Yes, I can also put an Inspiration d20 in front of me but we roll d20 so often I'd probably grab it absentmindedly to use for some other d20 roll.

Inspiration suffers from two major problems in games I've played - can't remember to grant it. Can't remember to use it. I like the idea of "claiming Inspiration" to overcome the first problem. And if a d6 sitting in front of me helps me overcome the second I'm less inclined to care about the math. An Inspiration die not spent isn't very useful.

The way it usually plays out in my game is that the players claim Inspiration, then immediately spend it. That tends to be with the personal characteristics that are easy to portray. They set themselves up for some kind of awesome attack or what they imagine might be a risky maneuver that will call for an ability check, do the portrayal, claim the Inspiration, then spend it right away when I call for attack rolls or ability checks. This makes it a bit easier to not forget about it.

They bank it as well from time to time. That's often when there's just a perfect opportunity for the characteristic to be portrayed in the given situation that might not come up again later in the game. So they portray, claim, and bank. That gets recorded with a little pip on the character sheet. It could be overlooked or forgotten about, but I think they've gotten so used to having Inspiration as a resource, it's gotten to be like hit points or spell slots - important enough to keep in the front of one's mind.