Hitpoint Mechanic Analysis

[Chris_Nightwing]

I shan't quote the rule, but the way in which Constitution interacts with rolling hitpoints appears very interesting on paper, but gave me immediate concern that it may not function that well in practice. So I ran the numbers.

For each possible positive Con modifier (+1 to +5) and for each likely HD (d4-6-8-10-12), I calculated the probability distribution of eventual HP (gained through hit dice only). I then grouped these by Con modifier and plotted them over each other (first row of graphs). I also plotted reverse distributions (if you have X HP, how likely is it that you have a given HD compared to the other HD) to assess those (second row).

Then I did the same, but grouping by HD.
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Now, what can I say? Well, this rule has the effect of both increasing your average HP and narrowing the distribution of HP as your Con bonus increases. This becomes really noticeable when the d4 line disappears (it becomes a fixed value: maximum). In general though, a bigger HD makes it more likely that you have more HP for a given Con bonus.

Increasing your Con bonus has a more extreme effect if you have a lower HD. The best HD, d12, has broad bands of probability for different Con bonuses, ie: it's mostly down to luck. This is obvious.

To assess the question of whether it's better to be a low HD, high Con character or a high HD, low Con character, I plotted everything all at once.
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Now here we need to apply a bit of common sense, and suggest that low HD characters won't reach 20 Con. This still leaves d6(+4) better off than plain old d8(0/+1) and d4(+4) better than d6(+3), but beyond that point the HD becomes overall dominant (at least in terms of averages).

If they have reconfigured HD to d6-8-10, this rule will not make Con score all that dominant, and whilst it bothers me that +1 Con mod does nothing (here), I would be happy to play by this rule. If you were to dish out average HP (Con mod has no effect), Con would still be relevant to healing and resistance.

One more thing: I will find time to model a different, but similar rule, which is that you add your Con bonus to your HD roll, but it maxes out at the relevant maximum roll. This would make +1 Con mod relevant and make a high HD more important (says my gut instinct).

 

[The Shadow]

Great work! I'm intrigued by your idea at the bottom, though I'm a little worried about the effect of low constitution.

 

[KidSnide]

Excellent work.

I'm not sure about the details, but I like that they kept the aspect of 4e where con doesn't dominate your total hit points, but has a major impact in how many times you can keep going after having been beaten bloody (before needing to rest).

-KS

 

[Chris_Nightwing]

Yeah, so turns out that makes things much worse. Both d4 and d6 saturate in the given range of Con modifiers. Distributions are more spread out, but much more overlapping. An increase in HD is about the same as a Con mod 2 higher, but the Con mod increase narrows your distribution.

So with both mechanics, distributions shift upwards more by HD increase than Con increase, but over the Con mod range available, this second mechanic causes more narrowing and higher shifts overall.

 

[Jack Daniel]

I posted about this on the Wizards boards yesterday.

I'm curious to see what your analysis will look like regarding modifying the die for CON, but giving the die a ceiling equal to its size. I've often considered implementing a rule like that in other D&D editions. but my intuition tells me that it would throw HP distributions way out of whack.

Another possibility, less elegant but more evenly distributed (says my gut) is to leave the CON mod as the minimum possible roll, but vary the maximum benefit by hit die type, i.e. if you're rolling d4s, your minimum is 1, regardless of CON; if you're rolling d6s, you can have a minimum 2 if your CON is mod is at least +2; if you're rolling d8s, you have minimum 2 if your CON mod is +2 at minimum 3 if your CON mod is +3 or better; all the way up to d12, where your minimum roll can actually reach 5 for a CON mod of +5.

 

[KesselZero]

I love this post. Assuming I understand all your work correctly, I actually like this system. I like that a low-HD PC can make up for it with a high Con-- that feels right to me, and fits with the primacy that 5e is giving to ability scores. If you want your wizard to be tough, give him lots of Con and negate your lousy dice. Makes sense to me! It even makes sense that a high-Con wizard (getting at least 3 or 4 HP per level at 16 or 18 Con) could theoretically outpace a low-Con fighter (Con below 14 = no help with your HP) who rolls badly (though not one who rolls average, since he'd be getting 6.5 HP/level on average). It seems right that your character creation choices should have meaningful impact-- and that your fighter probably shouldn't dump Con.

Am I missing something fundamental here?

 

[Ainamacar]

This is a really interesting thread, so I did the same analysis as [MENTION=882]Chris_Nightwing[/MENTION] for some other potential hit point systems. In particular, these values are the hit points that derive from rolling only.

1) The playtest method. Due to the nature of this method, the probability tends to be concentrated at the minimum allowed value for the roll.
2) The "multiroll" method. In this method you reroll each hit die until you get a value greater than or equal to Con modifier. Note that this means the probability of each of the allowed values occurs with equal probability. For example, a d6 and a Con mod of 3 would mean that 3, 4, 5, and 6 each have a 1/4 chance of being picked.
3) The [MENTION=694]Jack Daniel[/MENTION] method 1. That is, one adds Con mod to the roll, but the result is capped at the largest value of the die. This concentrates the probability at the largest hit value of the hit die. For example, a d6 with Con mod of 3 would result in 4 and 5 each with a 1/6 chance, and a 2/3 chance of a 6.

These are grouped by modifier and by hit die. I've kept the same color-coding and scaling as the original images, so hopefully comparisons will be easy.

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These are actually 3 really useful edge cases because the probability is concentrated at the minimum allowed value, distributed equally, or concentrated toward the value of the HD. Clearly the playtest method is the one which will result in the lowest hp totals and keeps the total range hp between classes the tightest, but it also means that high hd classes get less benefit proportionally, although these will generally still have higher hp totals.

 

[Jack Daniel]

Well, here's something that I didn't notice and didn't take into my considerations: according to the playtest document, you do modify hit dice for Con normally when rolling them to heal during short rests. That kind of changes my whole perception of this issue. The method as written in the playtest does indeed keep HP tight and relatively on the low side, but that might not be such a bad thing after all.

KesselZero makes a good point: it's kind of interesting to see Con weighting HP to the low end of the hit die roll, and making more of an impact on the small-HD classes.

Think of it another way: if, instead of rolling the hit die for new HP at each level, you're just taking the low (i.e. rounded-down) average result (as it does on the playtest character sheets, viz. 2 for d4, 3 for d6, etc.), then what you're effectively doing is taking the higher of two numbers, either half your hit die or your Con mod.

The actual hit die + Con mod then comes into play when you roll your hit dice during short rests, so a fighter with a good Con is still benefiting more (by usually healing better) than a wizard or rogue with the same Con.

 

[ggroy]

One more thing: I will find time to model a different, but similar rule, which is that you add your Con bonus to your HD roll, but it maxes out at the relevant maximum roll. This would make +1 Con mod relevant and make a high HD more important (says my gut instinct).

The answer to this without the "maxes out at the relevant maximum roll" part, is easy to write down.

It will be a distribution with:

mean = n * [average(hit dice) + con bonus]

standard deviation = sqrt [n*var(hit dice)]

(sqrt is the square root)

where

average(hit dice) = 2.5 for a d4
average(hit dice) = 3.5 for a d6
average(hit dice) = 4.5 for a d8
average(hit dice) = 5.5 for a d10
average(hit dice) = 6.5 for a d12

var(hit dice) = 15/12 for a d4
var(hit dice) = 35/12 for a d6
var(hit dice) = 63/12 for a d8
var(hit dice) = 99/12 for a d10
var(hit dice) = 143/12 for a d12

average(dN) = (N+1)/2, var(dN) = (N^2 -1)/12.

 

[Chris_Nightwing]

This is a really interesting thread, so I did the same analysis as [MENTION=882]Chris_Nightwing[/MENTION] for some other potential hit point systems. In particular, these values are the hit points that derive from rolling only.although these will generally still have higher hp totals.

I didn't think of the second system - that also sounds good on paper. Unfortunately my scripts are at work, but I'll take a look on Monday. The real test is how the overlay of all curves looks. For the playtest method, it's difficult for a Con mod to compensate for a low HD; you still don't get that many hit points if you're using a d4. For the third method, I was surprised to see that whilst the spread increased, the overlap was worse and a good Con mod could defeat a higher HD. The middle method.. I'm not sure!