## 2012-01-30

### Book of War Expansion: Partial Hit Dice

If you look closely at the Book of War rosters for fantasy monsters, you'll see that the hit dice listings strip out any partial hit-point modifiers (for example: goblins are listed with HD1, ogres HD4, trolls HD6). This makes sense, because in our scaled-up system, each HD represents an integral number of mass "hits" that the creatures take before elimination. (For what it's worth, this is also how I play OD&D, just disregarding most of the partial HD bonuses.) Let's see how we should handle other such types. To make a long story short -- the partial hit-die modifiers don't really make any difference at 1:10 scale.

Consider a very basic fight in OD&D; for example, 1st level vs. AC5 (chance to hit is 7/20 = 35%). Of course, the basis for damage is a 1d6 weapon versus a 1d6 HD target; which has a kill-chance, on a successful hit, of 21/36 = 58%. So the overall chance to hit and kill with a single attack is 0.35 × 0.58 = 20% (note that's slightly better than 1-in-6.)

Now, adding or subtracting one extra hit point to the target doesn't change this much. If the target is HD1+1, then the chance to hit & kill is 0.35 × 0.42 = 15%. If the target is HD1-1, then it will be 0.35 × 0.72 = 25%. Even against a measly ½d6 target, the chance is still only 0.35 × 0.83 = 29%. Note: All of these probabilities are within 16% of each other, which is to say, they don't make even a single 1-in-6 chance difference using the BOW-scale d6 mechanic.

Further note: These numbers change by maybe one single percentage point if you switch to the post-Greyhawk system of 1d8 HD and 1d8 damage for weapons like a normal sword (specifically: the hit & kill chances will be 20%, 15%, 24%, and 28% respectively). Here's an Open Document Format Spreadsheet that lays out all the details, if you like:

At this point, further consider the normal BOW mechanic that awards a mass "hit" (i.e., 10HD eliminated) on a d6 roll of 3/4/5/6 against no/leather/chain/plate armor. If we try simulating the same attacks against partial-hit-die modifiers, then it likewise turns out to make almost no difference at all:
• Against HD 1d6+1: Hits score on 4/5/5/6 vs. the four armor types. So this might make a one-point difference at the lighter armor types, except that no such monsters come at those armor types in D&D. Example: Hobgoblins have chain mail (AC5) and so would be hit on a 5 in BOW in any case.
• Against HD 1d6-1: Hits score on 3/4/5/6 against the four armors -- absolutely no change at our abstracted scale. Example: Goblins in BOW are indeed equivalent to a full HD1.
• Against HD ½d6: Hits score on 2/4/5/6 versus the various armor types -- again, no change except for a case of completely unarmored monsters (AC9 or 10), which doesn't occur in stock D&D. Example: Kobolds may as well also be shown with a full HD1 in leather armor (AC7 = AH4); and the same goes for OD&D skeletons.
These values were found with the obvious modifications to our BOWCoreRule.java combat-simulator program. And here's a text file collecting the various program outputs:

So: Although the other low-level humanoid types weren't included in Book of War for space and technical reasons such as these, there's no reason we can't start using them on the battlefield, in each case with the standard mechanics and showing HD1 each. A few modifiers for spice, perhaps: Hobgoblins won't suffer from the morale light-weakness penalty, and if you like, you can dress them in leather & shield and still get the full AH5 (see above). Kobolds with their half-D&D-hits will suffer double effect from a death spell, and let's also assume that they only do 1d3 D&D damage, reflected as a −1 to hit in BOW scale (effects included in the text file above). Modify or retract any of these if you prefer. Text between the rules below is Open Game Content per the OGL:

 Unit Cost MV AH HD Notes Kobolds, Infantry 3 6 4 1 Light-weakness, atk at −1 Kobolds, Slingers 4 6 4 1 Light-weakness, atk at −1, slings Hobgoblins, Infantry 4 9 5 1 (No modifier) Hobgoblins, Pikes 5 9 5 1 (No modifier)

Kobolds: These small creatures always attack at −1 on attack dice (representing low damage capacity). Death spells kill twice as many figures as normal.

Hobgoblins: These monsters generally function as orcs, but without light-weakness morale penalties. Note that even in light armor they would have effective AH 5.

[Photo by Dean Terry, under CC2.]