Jan 172014
 

I had this theory that hit points grew at a greater-than-linear rate. I based my theory on the way that CON items add a greater amount of hit points at each level; I assumed that an increasing rate of increase would show up as a geometric progression of some sort.

Which would be bad for a game like DDO. A geometric power curve would be incredibly difficult to manage at higher levels.

With that in mind I broke down everything that adds to the hit points of my Barbarian Knicker Tan and plotted them out.

I learned two things:

  • My theory is wrong
  • Knicker is leaving hit points on the table

Hit Point Curve
Click to enlarge

A surprisingly smooth curve. There is a bump when Green Steel first becomes available, and another at level 25 that is due to the fact that Knicker’s hit points lag behind the curve. I plotted this based on the assumption of a continuous progression of tomes, CON boost items, and hit point items but Knicker has only a +2 CON tome, only 30 points in false life, and no Vitality. She has only a +7 CON item but should have +8 at her level.

So the level 25 “jump” is actually a “dip” and illustrates the hit points that Knicker is leaving on the table.

But why does this matter?

Other than giving me another opportunity to have fun with graphs, it serves a purpose. A geometric progression would be bad. Level 20 and 22 characters (for example) have to coexist in the same quests. The level 22 character should perform better than the level 20, but not unapproachably better.

Otherwise quests have to be scaled to a specific level rather than a range of levels, and the whole party grouping mechanic falls apart.

Bad. Very bad. But also something we don’t have to worry about, Turbine has our backs on this. In fact, it wouldn’t surprise me if graphs much like this one exist in Turbine too; the progression is too smooth to be a coincidence. It looks like the result of careful planning.

Of course, Knicker is only one character. To be thorough, I should be doing the same thing for all my characters, and not just hit points but also spell points and any other power metrics I can devise. But for now, one will have to do, these things take awhile.

Not that I ever mind the time I spend having fun with graphs.

๐Ÿ™‚ ๐Ÿ˜€ ๐Ÿ™‚

  12 Responses to “Hit Point Growth Curve Is Amazingly Linear”

Comments (12)
  1. That’s really weird, as my Guild leader has a Barb that is over 1100 hp at level 27 or 28.

  2. HP isn’t everything – though in sauce form it goes well with chips (fries for you colonials) ๐Ÿ™‚ I saw a guy in a pug with over 2k during a run last week… wasn’t doing especially well at killing & frankly I was having an easier time healing the guy with 650 or so who was destroying all those who got in his way.

  3. Somewhere inside of me is a math geek wanting desperately to mention that of course the graph will be (more or less) linear in growth as all the different stacking bonuses are still just applying (increasing) “offsets” to the already linear base HP equation, and not applying any exponents or other non-linear functions.

    …but I will endeavor to keep him quiet. Boy, that guy can be a really annoying, sometimes.

    ๐Ÿ˜‰

    Of course, PnP is a little different because you don’t automatically get ‘full’ die HP, but must roll the appropriate die, so your increase is not “fixed”, but variale. But even though a “rolled” graph may look more “geometic”, it’s still, at the heart, a basically linear graph, especially if you plot it out alongside the theoretical maximum HP graph (which is effectively what DDO give us).

    Math is fun!

    ๐Ÿ˜‰

    • I am not a math-o-mancer, but I think CON growth is exponential meaning anything that CON modifies is too?

      I am treating CON item bonus as a function of level per level: ( 1/2 level ) * level. CON tome bonus: ( ( level – 2 ) / 4 ) * level.

      Although the true bonuses are the INT() of these formulae, they are exponential formulae, yes?

  4. I don’t believe so (but I’ve been wrong once or twice before – hehehe). I think you’re overthinking the CON bonus. All a tome does is increase the “base” con stat (at certain levels of character progression); other CON bonuses, just โ€œtemporarilyโ€ add to the base stat (โ€œtemporaryโ€ in the fact if you remove the item, you remove your CON boost). What happens with HP, though, is just a retroactive increase/decrease based on the (current) CON bonus/penalty and character level.

    The basic equation remains the same: {[(hit die size) + (CON bonus)] * (character level)} + 25HP

    {The +25HP is the heroic durability granted at level 1; there are additional durability bonuses of +5 at class levels 5, 10, and 15 that are added statically}. The above does not take into account any static bonuses (except the first heroic durability feat) such as “false life” or “vitality”; but those can just be tacked on at the end anyway.

    You can check this with Ron’s Character Planner: create a toon with a CON of 10 (don’t need to adjust any other stat for this) and then jump to L20 and see what the HP are. Now go in and add a tome increase of +4 (to the CON stat [this is NOT the HP bonus] – you can do +5 to CON, but the HP bonus doesn’t change) and see what the new HP are. Now, go create another toon (of the same class) with a CON of 14, jump to L20 and see what the HP are – it will match the previous toon’s HP.

    Also – It looks like you might be confusing “CON stat point value increase” with “character level”. That is, assuming I’m reading your (1/2 level) * level correctly. CON gives ยฑ1 HP per character level for every 2-points ยฑ 10 points in CON. So if I have a base CON = 10 and I put on a +2 CON item, I now get an additional 1HP/character level.

    I hope that’s less confusing than I think it is…

    Anyway, just remember that any CON HP bonuses/penalties are always “retroactively” adjusted to the current value of CON whenever CON changes, by whatever means (which I guess are pretty much just tomes or items…).

    ๐Ÿ˜‰

    {BTW – I don’t know why, but whenever I try to reply to a reply, it doesn’t want to work for me, like it does ‘every one else’. Probably just me and my old, outdated web browser…} {Also, I hope everyone realizes that my first reply was just poking a little fun – not trying to be mean or condecending or anything like that. I’m an engineer – if you know any engineers, then that should be all the explanation I need.}

    ๐Ÿ˜‰

    • No worries mate!

      Still curious about: CON bonus multiplies by level, as you illustrate. But the maximum CON bonus also multiplies by level. The rate of increase itself increases. Isn’t that textbook exponential progression?

      I need to check this when I get home.

    • Engineer, eh? Good man.

      I wonder if that’s why no one understands my humour…

  5. I think I see what you’re saying. If it multiples upon itself, then yes, that would be an exponential progression; but if it only adds on itself…

    Probably another term used than “exponential”, but I have no idea what it would be, off hand.

    maybe I should have paied more attention in those math classes.

    ๐Ÿ˜‰

  6. You are correct, sir. I’m sitting here thinking of HP as a function of one variable (level), but it is actually a fuction of 2 variables (level and CON bonus); and since CON bonus is multiplied by level (“x times y”), this would make it a “non-linear” function (though not necessarily a geometrically or exponentially progressing one – defintiely not an exponentially progressing one, as there are no exponents).

    However, for any given CON bonus value, the equation for HP is linear, with respect to level. And by changing the CON bonus, you do change the slope of the equation, which is illustrated by your graphs. All of the static bonuses (“false life”, “Vitality”, etc.) change the offset, but not the slope (which creates parallel lines).

    The basic equation for calculating HP is correct, though. And it’s probably easier to just use that to (re)calcuate HP based on current CON bonus (even after it’s changed) than trying to come up with an equation for “how” CON bonus affects HP (and I did try that by integrating the basic HP equation with respect to CON bonus, but my integration-fu appears to be weak from lack of use…).

    Sometimes, I’m just an idiot (and I’m not afraid to admit it). Cheers!
    ๐Ÿ˜‰

  7. Well, goodness knows that the HP for monsters is geometric or exponential, so why not us?

  8. I’m not sure if it made any sense whether it would make it a better system ๐Ÿ˜‰

What do you think?

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