D&D 5E On Die Averages and Hit Points in 5e

[Cadence]

Aggregating total damage over a career isn't a thing. It means nothing. Damage only matters against individual opponents, any any overflow is waisted. The numbers for GWF mean they make absolutely no difference in a fight.

True that they get no benefit from protection with two handed weapons but they can at least switch to a shield and get some bonus. GWF gives no measurable benefit in an individual fight.

Wasn't the original post about 0.5 hp points that matter only once per day (or full healing)? Two hits and on average this 0.3 takes that out and and a bit more, right?

Small but positive is really different than nothing. One of the two pillars of math (analysis) is built on it, and theoretical probability spends most of its time showing something actually is zero. Rounding error or negligible? Sure.

 

[OptionalRule]

Wasn't the original post about 0.5 hp points that matter only once per day (or full healing)? Two hits and on average this 0.3 takes that out and and a bit more, right?

Small but positive is really different than nothing. One of the two pillars of math (analysis) is built on it, and theoretical probability spends most of its time showing something actually is zero. Rounding error or negligible? Sure.

I'm not tracking you, the original post is about dice averages and how that gets into HP totals, healing and per day is never mentioned.

Also, this isn't about mathematical debates, it's about how a misunderstanding of the effect is leading to bad house rules (or rules in the case of GWF), or at emotionally weighting rules that make no discernable difference. I'm using math to show why, but it's not an exercise in mathematical theory. The GWF post used simulated rolls over a mathematical model specifically to keep from arguing about the model.

 

[Cadence]

I'm not tracking you, the original post is about dice averages and how that gets into HP totals, healing and per day is never mentioned.

Yes. And the amount it is different is 0.5 per level. Your dismissal of the 0.3 added expected value in combat got into game mechanics. I was trying to show the 0.5 to hp was similar

Also, this isn't about mathematical debates, it's about how a misunderstanding of the effect is leading to bad house rules (or rules in the case of GWF), or at emotionally weighting rules that make no discernable difference. I'm using math to show why, but it's not an exercise in mathematical theory. The GWF post used simulated rolls over a mathematical model specifically to keep from arguing about the model.

Right, and the original post seemed fine for making that point. Definitions are important in math, though. And few are more important than epsilon > 0 being very different than 0.

 

[Ruin Explorer]

There's confusion on this?

Yeah I'm confused that there's confusion. I've known the average of a d8 is 4.5 (and so on) since, like, well I don't remember a time when I didn't. It wasn't RPGs that taught me that either, it was basic math.

As for the point re: players preferring rolling HP and feeling it's a gift and so on, that's not been my experience at all. Most of the groups I play in used fixed HP and even with the same players I'm not seeing any preference for rolling HP - in fact I've seen an active dislike from a lot of people. Perhaps because they realize 5 is higher than 4.5 (and so on).

 

[OptionalRule]

No it isn’t. If you roll normally without rerolling 1s you get:

d4: (1+2+3+4)/4=2.5
d6: (1+2+3+4+5+6)/6=3.5
d8: (1+2+3+4+5+6+7+8)/8=4.5
d10: (1+2+3+4+5+6+7+8+9+10)/10=5.5
d12: (1+2+3+4+5+6+7+8+9+10+11+12)/12=6.5

Not true. If you roll every time and don’t re-roll 1s, a 20th level character with, say, a d8 hit die, has an average of 90 hp. If you do reroll 1s, that character has an average of 100 hp. The same average as a character who takes the average-rounded-up value of 5 hp every time. That’s the point of the house rule. To eliminate the slight advantage of choosing to take the rounded-up average instead of rolling.

You're right of course. I don't know how to qualify what constitutes meaningful difference or weight the value of the rule and that's something for everyone to decide for themselves of course.

Instead I'll just put up the numbers. Simulating rollling hps for 10,000 characters at level 20 (with a 1d8 HD)

• Taking Avg HP gives them 103 hp
• Rolling normal (straight roll for hp) the average is 93 (93.63)
• Rolling and rerolling 1s once, the average is 101 (101.74)
• Rolling and rerolling 1s infinitely, the average is 103 (103.01)

To my mind none of these are a fix, as the best it can do it match average. But that assumes what people think they need to fix. Thank you for your thoughtful reply.

 

[Charlaquin]

• Taking Avg HP gives them 103 hp
• Rolling normal (straight roll for hp) the average is 93 (93.63)
• Rolling and rerolling 1s once, the average is 101 (101.74)
• Rolling and rerolling 1s infinitely, the average is 103 (103.01)

This is precisely the intended outcome of the house rule - to make the average results of rolling for HP the same as the results of taking the rounded-up average.

To my mind none of these are a fix, as the best it can do it match average. But that assumes what people think they need to fix. Thank you for your thoughtful reply.

I’m not sure how matching the average could be seen as not being a fix when the issue being fixed is literally “the results of rolling don’t match the average.”

 

[NotAYakk]

Also, this isn't about mathematical debates, it's about how a misunderstanding of the effect is leading to bad house rules (or rules in the case of GWF), or at emotionally weighting rules that make no discernable difference. I'm using math to show why, but it's not an exercise in mathematical theory. The GWF post used simulated rolls over a mathematical model specifically to keep from arguing about the model.

So know what is equivalent to a mathematical proof? A computer program.

It just tends to be a lot less clear what exactly it is proving by generating its specific output.

Simulations, in particular, are proofs taking the rules of the simulation and saying the result of that is the output. If they have a random portion, then a given run is a proof that the result is one possible result, with a distribution described by the simulation.

Determining if the proof is any use then requires that you audit the computer program and its intended simulation and distribution. This is hard to do.

So yes it shuts down discussion of the mathematical model. Not by making it not a problem, but rather by a gish gallop strategy of making it ridiculiusly harder to reason about and describe.

It becomes a matter of faith in the code. Or a crapload of work to test it (computer programs have bugs very very often, both in design and implementation).

And if you don't understand the math and just spew computer simulation code, faith is probably the wrong response to your code.

 

[OptionalRule]

I’m not sure how matching the average could be seen as not being a fix when the issue being fixed is literally “the results of rolling don’t match the average.”

Because it depends on what you're trying to fix. If your fix is that you want rolled HP to be as good as average HP, then I have to question why you're rollling? To me, the fix to make something like the other thing is to use the other thing. In this case, if what you want is Average Hit Points, then use Average Hit Points.

Again, this isn't an exercise in math, this is an attempt to discuss the value and effect of rulings and house rules. The math is used here not to show there is a difference but to show what the effect is to have a discussion for the value and impact of a rule.

 

[NotAYakk]

I mention this later in the article when it comes to a house rule to reroll HP. Basically, replacing a 1 or 2 makes almost no difference with Great Weapon Fighter. There have been a number of articles about this, I wrote a thing about it awhile back too.

"a simulation" you used is not provided and clearly buggy.

It is buggy in implementation. Adding crits to 1d8 ... lowered your damage?

It is buggy in design. You talk about damage increase from crits without talking about accuracy and advantage; impact of crits varies significantly with that.

Your conclusions may be valid, but your simulation was junk in a very concrete way.

I agree that GWF sucks, but talking about "my simulation avoids math arguments" is not a great result.

OIC; maybe you are recording the average of each d8? So on a crit that is 2d8?

I am not sure. And the situation, mathematically, is simple enough that the simulation complexity at best adds a seperate validation of a simple math model. So if either disagrees, you spend effort finding out why.

Trusting the results of a that simulation without verification is a bad plan.

 

[OptionalRule]

"a simulation" you used is not provided and clearly buggy.

It is buggy in implementation. Adding crits to 1d8 ... lowered your damage?

It is buggy in design. You talk about damage increase from crits without talking about accuracy and advantage; impact of crits varies significantly with that.

Your conclusions may be valid, but your simulation was junk in a very concrete way.

I agree that GWF sucks, but talking about "my simulation avoids math arguments" is not a great result.

Without a doubt mistakes can happen, but this is just you floating in to act intellectual and insult people. So please drop the Math Paladin mantle.