Wednesday, 16 July 2014

Without Bothering to do the Math

Which you are welcome to do, if you want.

A troop of 800 orcs with a statistically average array of hit points attacks another group of orcs which is identical. Let us say that each orc in the melee has a 50% chance of hitting each round and each successful strike does an average of 4 hp damage each round.

The battle lasts 9 rounds.  At the end of the battle, how many orcs remain with 1 hp? How many remain with 8 hp? For the sake of clarity, these are 1st Edition Advanced Dungeons & Dragons orcs armed with spears.

Alexis argues that he knows the answer, and that if you do not agree with him, you are really, really fucking stupid.

Well, Alexis' numbers look okay to me, I suppose, if we assume that the orcs all form a line and whack at each other until the weakest fall. But, then, what happens if the weaker orcs on both sides cower in the rear while the alpha males duke it out?  Do we have any reason to imagine that weaker orcs are shirkers who hang near the rear? Only the source material, where Frodo and Sam are mistaken for orc shirkers in Mordor.

For all of that math to be relevant, it has to accurately model the variables of the scenario. Do you think that it does?

Okay, then, consider the possibilities of 1st level party consisting of a magic-user and 20 fighters. For fun, let's give them all maximum hit points per die, with no bonuses for Constitution. Which one of these fine PCs is going to die first? Should there ever be a 4 hp magic-user in a party? If we applied Alexis' math, and assumed that all 21 stood up toe-to-toe in a line with 21 equally NPCs, reason suggests that only the fighters remain. Of course, that's because PCs do not all stand up toe-to-toe in a line when fighting. Not if they want to live.

Likewise, I guess, we should consider thieves to be exceedingly rare in the campaign milieu. Monks, well, I can understand their rarity in a predominantly Western milieu, but they are another class that some players have managed to do quite well with despite their meagre hit points.

Wait! you say, that magic-user has spells! We must take that into account!

Sure. For one encounter. Then he is just a fighter without armour, with sub-optimal weapons and hit points.

There is nothing objectively "wrong" with Alexis' model, and you should use it if it feels "right" to you.  But if it does not feel "right" to you, there is no reason to agree with Rumson just because "he knows".


  1. I'm not sure why anyone would go through this trouble unless they were playing a wargame.

    1. Well, the other reason might be if they were crazy. Not that I'm suggesting anything.

    2. I don't think it is crazy to want to do this, if it is important to you. Demanding that everyone else do the same, though, is a bit off the sane path.

  2. Yeah, I don't buy Alexis's premises, so I don't buy his bits. I had been considering adding his blog back into my regular reading, but then this thing happened, and I remembered why I removed him from my reader in the first place.

    1. Exactly; it's still working from a false premise that says HP is a heritable trait that models the actual health (not just likelihood-to-die in the upcoming encounter) of a creature. If you don't accept the premise that HP is some kind of objective measurement of genetic fitness, nothing else follows.

    2. There is a real problem in thinking that "the math" demonstrates X to be true, where the math itself does not answer the objection to X. No one is arguing that, in a battle where everyone lines up toe-to-toe that low hit point creatures (all else being equal) are not in all likelihood going to die first. They are arguing that, despite this bit of obviousness (which really should not require proof), low hit-point creatures can easily exist in the game in the proportions that the rules suggest that they do.

      In his comments, Alexis says, "I don't want health to be realistic. I want there to be a verisimilitude to the game I'm playing. Hit points being what they are, this is how they manifest when attacks land."

      But what hit points do within the construct of the game rules, and what hit points represent within the fictive milieu, need not be as Alexis suggests. 1 hp means, "you hit him and he dies". Unless you do 1 hp damage, there is no difference between that 1 hp and whatever other damage you may have done. Whether you did 1 hp, 5 hp, or 6 hp, the result is "you hit him and he dies". 4 hp against a foe doing 1d8 damage means "50% of the time it takes more than one swing to fell him". Nothing more, nothing less. That also means that 5 times out of 8, Mr. Four Hit Points is effectively identical to Mr. One Hit Point. The purpose of this is verisimilitude, not realism. Realism is trying to determine hit points precisely by mass and training.

      Alexis also says, in the comments, "The point of the original post was that, given the likelihood of 1HD/1hp creatures dying in combat, there ought to be way less of them within the construct of the game's world."

      But, again, this doesn't follow, because even if you accept his general ideas about the meaning of Hit Dice and hit points, you would also have to accept that the average orc (or what-have-you) population is being slaughtered at a rate higher than it can be replenished. Because the replenishing orcs are not going to all be the most powerful - they will be young and untried. Again, the standard spread favours verisimilitude. It also assumes that the weaker tribe members are as prone to combat as the stronger tribe members, which we know is not the case in any species or culture that has ever existed. The weak avoid combat when they can, unless the odds are very much in their favour due to other circumstances.

      Finally, if we took Alexis' argument at face value, what of humans? The average sedentary human has 1-2 hp, 1-4 is common for farm workers, and 1-8 only for professionally trained soldiers. This being the case, why are there humans in the game milieu at all? Among those humans, how has any magic-user survived 1st level? Etc., etc.

      The answer is clear - hit points are intended to create verisimilitude in their outcome, not realism in their "frozen" form within a given stat block or series of stat blocks. It is the living game where hit points actually acquire meaning, not the game Alexis is playing alone in his living room during game prep.

      Which is not to say that there is anything wrong with Alexis' method. Only his insistence that his method is objectively the One True Way is in error.

    3. I find that to be the case with many arguments that spiral out of control, both in the online D&D community and in the world. Definition of terms is essential, while arguing about tertiary and quaternary features of an argument devolving from incompatible terms is a waste of time. Alexis, like many other internet commentators, is not really interested in squaring the central difference of terms that gives rise to arguments. So while we may make arguments against self-consistency to defeat the extensions of the main premise, we can never reach the premise itself, which is taken as given.

      I wish he (and many many others) were more adept at handling argumentation and in defending (and ultimately abandoning, if they prove indefensible) their first principles. This is the cause of so much strife in the world.

    4. Agreed.

      I will endorse your candidacy in 2016. :D


  3. I'm clearly brilliantly adept at handling argumentation. I have all you little babies squalling over what I'm saying, like sychophants I've wound up and pointed at the subject I want. Only - and here is the part where you clearly are "really, really fucking stupid" - not my words, by the way - you've completely misrepresented my points or my purpose in writing anything. I presume because you're unable to read or because you're deliberately obtuse. Either way, it makes no difference. You're pouting in your beer about me and my world, and that's GOOD. I like that you revolve around me.

    Took two days for there to be enough pageviews generated by this post for it to show up on my browser. It's disappointing that you have to be such a small, miserable little clique. Could you please get more readers so that when you sit in the mud and scream, more people can hear you? That would at least sell a few of my books. As it happens, I doubt I've sold more than one to this fan club.

    1. Nice rebuttal, Alexis. Do you have anything material to say, or is all you have ad hominem?

    2. Just to be clear, further nastiness of this sort belongs on YDIS, which I assume is where you cribbed notes from before commenting. I'll leave this here as an example of the quality of your argument, but further YDIS-like posts will be deleted.

      I have no problem with anyone here buying your book, btw. As I posted earlier:

      Alexis Smolensk’s book, How to Run: an Advanced Guide to Managing Role-playing Games, is now out in both physical and electronic format. (Strangely, both formats seem to have the same price.)

      If you happen to purchase it, I would be interested in your serious critique. I have said it before, many times, but I will say it again: Although I do not always agree with Alexis, and I will take him to task when I think that he is both wrong and it is important or interesting enough to do so, he often does have good insights into the game.

      I know that Alexis often brings it upon himself, but I will have to echo him here: I am only interested in serious critiques or links to the same. This is not an invitation to YDIS or other forms of mockery. At the same time, “serious critiques” means both good and bad here, and that is not an offer you will get on Tao.

      I broke my own rule and wished him well in his blog comments, but as that is apparently not getting through his filter, I’ll repeat it here: Good luck with your book, Alexis!

    3. Shit, with advertising like he's giving, I'm going to rush right out and spend $50+ on his books. Well, actually no. I have no confidence that what he writes will be any better or more well-reasoned than his writing in this discussion. I will wish him luck on his books, though. With an attitude like he's spewing over a minor discussion like this, combined with his leaps of logic he's making, he's going to need it.

      I'm wondering why Alexis is so invested in a single interpretation that requires a massive rewrite of the game. It seems to me that it's better to take the material on its face and then figure out a reasonable justification - for ease of play if nothing else. On the other hand, "fantasy heartbreakers" have a long and illustrious tradition, so perhaps he will manage to come up with a new game that he can present to the gaming market. Because his new rationalization doesn't look very much like traditional D&D. In general, his attempts to revise the hit point system looks rather like RuneQuest, actually, but why should he look to prior art when he can reinvent the wheel?

  4. Alexis writes: [A]nd here is the part where you clearly are "really, really fucking stupid" - not my words, by the way - you've completely misrepresented my points or my purpose in writing anything.

    Not your words, Alexis? Was it someone else posting on your blog as you who wrote: Really, this is the sort of thing I assumed people could understand when I wrote my original post, but people - it turns out - are really, really fucking stupid. So it has to be said very slowly and in great detail so they will understand.

    Or do you just not remember what you wrote?

    1. It would be annoying if it were not so transparent. I don't know whether to feel amusement or pity.