Inspiration & Hero Points Math

[Ovinomancer]

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

You're getting me back for mistaking you for Lanefan, aren't you.

 

[Ovinomancer]

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.

Totes valid. You can't math aesthetics.

 

[Laurefindel]

You're getting me back for mistaking you for Lanefan, aren't you.

hum, no? I meant no offense, I apologize if I did offend you.

I do agree that the advantage = +5 is an oversimplification and a potentially gross statistical error, but it does have statistical meaning.

 

[Ovinomancer]

hum, no? I meant no offense, I apologize if I did offend you.

I do agree that the advantage = +5 is an oversimplification and a potentially gross statistical error, but it does have statistical meaning.

Heh, no, I was commenting because my rant was about comparing advantage to ANY plus, not just +5, and you responded with a post saying, yea, it's more like a +1 in other places. :grrr:

I'd like it better if we stopped referring to advantage in +x numbers at all. It's the wrong way to discuss a probability density function and it causing misunderstandings.

On the larger issue, I made a math error in my earlier posts. I naively added the 17.5% d6 chance to the chance to succeed on the d20 rather than first multiplying the difference by the initial failure chance first. This changes this a little bit, as the floor is needing to roll an 18+ rather than a 17+ before the d6 beats out the second d20. Here are the PDFs for no re-roll, d20 re-roll, and d6 ad

 

[Mercule]

Well, prior to Ovinomancer's post, I was going to say the two were probably about even,other than the potential for +d6 giving a chance for results above 20.

My gut still says something's a bit off with that graph, but I haven't gone through the math, myself. Basically, advantage is roughly equal to a +5 bonus at a DC 11, tapering to an effective +1 (or marginally less) at either end. The d6 should be a consistent +3.5 across the entire spectrum. I guess the net effect is that, at the low end, advantage has the potential to completely offset a horrible roll, whereas +d6 doesn't -- regardless of "equivalent" bonuses. So, that's probably where the actual math disproves my gut.

I guess that means the decision between the two (disadvantage and hero points) comes down to whether you'd rather insulate the PCs from the occasional cursed die (advantage) or give them the opportunity to play outside their weight class if the dice smile (hero points).

Personally, I think the hero points sounds a bit more fun, myself. I wouldn't object to either style and would be fully aware that it might not play out as fun as it sounds.

 

[Ovinomancer]

Well, prior to Ovinomancer's post, I was going to say the two were probably about even,other than the potential for +d6 giving a chance for results above 20.

My gut still says something's a bit off with that graph, but I haven't gone through the math, myself. Basically, advantage is roughly equal to a +5 bonus at a DC 11, tapering to an effective +1 (or marginally less) at either end. The d6 should be a consistent +3.5 across the entire spectrum. I guess the net effect is that, at the low end, advantage has the potential to completely offset a horrible roll, whereas +d6 doesn't -- regardless of "equivalent" bonuses. So, that's probably where the actual math disproves my gut.

I guess that means the decision between the two (disadvantage and hero points) comes down to whether you'd rather insulate the PCs from the occasional cursed die (advantage) or give them the opportunity to play outside their weight class if the dice smile (hero points).

Personally, I think the hero points sounds a bit more fun, myself. I wouldn't object to either style and would be fully aware that it might not play out as fun as it sounds.

Yeah, but this is the problem of thinking in terms of +'s instead of looking at the probability density function. The reason that +d6 isn't a flat +3.5 (or 17.5%) increase is because the chances of failing the roll to start changes. The chart is for what happens if you use the extra die on a fail. This is why the +d6 isn't flat and instead increases until it hits almost the 17.5% bump at needing a 20. You still have a 5% chance of not needing the die, and that means you'll only realize 95% of the +d6 bump even on a 20. Needing a 21 would be the full bump because you will always fail that roll.

 

[Oofta]

Yeah, but this is the problem of thinking in terms of +'s instead of looking at the probability density function. The reason that +d6 isn't a flat +3.5 (or 17.5%) increase is because the chances of failing the roll to start changes. The chart is for what happens if you use the extra die on a fail. This is why the +d6 isn't flat and instead increases until it hits almost the 17.5% bump at needing a 20. You still have a 5% chance of not needing the die, and that means you'll only realize 95% of the +d6 bump even on a 20. Needing a 21 would be the full bump because you will always fail that roll.

It seems like the math (and odds) change pretty significantly by having the roll after the fact and knowing the DC.

I'd still probably go with the second D20, even if it's not logical simply because it would be more fun.YMMV but I'd rather turn a catastrophic failure into a win. Besides, in my experience the numbers I need to roll do cluster around that central point or lower and rarely approach the high end of the curve.

 

[Ovinomancer]

It seems like the math (and odds) change pretty significantly by having the roll after the fact and knowing the DC.

I'd still probably go with the second D20, even if it's not logical simply because it would be more fun.YMMV but I'd rather turn a catastrophic failure into a win. Besides, in my experience the numbers I need to roll do cluster around that central point or lower and rarely approach the high end of the curve.

Okay, for the +d6 it depends on the question asked. I'm asking the "roll at least X" question, and that didn't change because the +d6 is irrelevant if you've rolled high enough on the d20 to begin with. If, instead, you want the PDF of d20+d6, then it'll look different. The "past the post" nature of D&D means the former is the question we should care about. If you're using escalating success thresholds, the latter may be more important to you.

 

[Oofta]

Okay, for the +d6 it depends on the question asked. I'm asking the "roll at least X" question, and that didn't change because the +d6 is irrelevant if you've rolled high enough on the d20 to begin with. If, instead, you want the PDF of d20+d6, then it'll look different. The "past the post" nature of D&D means the former is the question we should care about. If you're using escalating success thresholds, the latter may be more important to you.

I appreciate the attempt to help, but I admit it. Totally lost me. What I'm not clear on is the benefit at the numbers I normally need. I rarely need to roll a 20 to succeed, and even if I do I'm probably going to fail anyway. I understand if I do need that 20 I'm better with a d6.

But most of my targets cluster more around the middle. I'd have to do a little research for it but if I assume for a moment that I need to roll between an 7 and 14 to succeed what's my best option?

P.S. Apologies for the fuzziness of the language. I enjoy logic puzzles, but statistical analysis has never been a strong suit.

 

[Ovinomancer]

I appreciate the attempt to help, but I admit it. Totally lost me. What I'm not clear on is the benefit at the numbers I normally need. I rarely need to roll a 20 to succeed, and even if I do I'm probably going to fail anyway. I understand if I do need that 20 I'm better with a d6.

But most of my targets cluster more around the middle. I'd have to do a little research for it but if I assume for a moment that I need to roll between an 7 and 14 to succeed what's my best option?

P.S. Apologies for the fuzziness of the language. I enjoy logic puzzles, but statistical analysis has never been a strong suit.

d20 is your friend for that range.

To try to explain why it doesn't matter to the math if you roll with or roll after the d20, let's look at a specific example: You need to roll a 10 on the die to succeed at a given task. So, let's say you roll a d20 and a d6 at the same time. You have a 55% chance of rolling a 10 or better on the d20. This is a success without the d6, so the roll on the d6 is irrelevant -- it just doesn't matter. So, then the only times the d6 matters are when the d20 doesn't roll 10+. This is the exactly same criteria that would apply if you chose to roll after the d20 instead of with. Rolling the dice together doesn't change the math because the extra die only ever matters if the first d20 fails. This works the same for the +d20 case as well -- the second d20 only matters if the first fails.

THAT's why the numbers don't change if your roll with or after -- only the efficiency of use as you aren't burning the extra roll on successes or those cases where it won't matter anyway (fail by more than 6 for the d6).