Chainmail Missile Hit Chances

One of the critical observations that I've made in the 7 years since releasing the first edition of the Book of War mass combat game for D&D (see sidebar) is that missile fire is definitely not scale-invariant. That is, at a given range (say: max range for a longbow), an individual firing at an individual may find it effectively impossible to hit, whereas at the same range an army firing at another army may find it effectively impossible to miss. So using the same range modifiers for both cases doesn't make sense.

Now, post-D&D wargames from TSR lead us in the wrong direction on this score: both Swords & Spells and Battlesystem use modifiers for ranged missile fire which are direct carryovers from the RPG system (respectively from OD&D and AD&D). On the other hand, arguably the original Chainmail had a better understanding of this; there are no ranged modifiers for mass combat (even though there are for man-to-man combat). However, on investigating this, the Chainmail tables are a little hard to analyze; they are organized in an unusual fashion where you will be rolling just a single d6 for as many as 10 or 20 mass figures jointly. Here, then, is a breakdown in which I try to estimate that chances to hit for each single mass figure:

Note that there are three armor categories here: Unarmored, Half Armor, and Full Armor. (We can very broadly correlate these to the D&D Leather, Chain, and Plate types.) The hit rates vs. Unarmored figures are very consistent: between 44-49% in any row. The Half Armor types are radically variable: 0% in the first row and 32-36% in the last three rows. Full Armor is somewhat less variable: 6-16% depending on which row your situation falls into. Again, note that range modifiers do not apply; the same chances apply for any target within maximum range of a shooting force.

If we convert this to a simplified and uniform roll-one-die-per-figure mechanic, then we could approximate these values this way: say, 3-in-6 (50%) to hit Unarmored, 2-in-6 (33%) to hit Half Armor, and 1-in-6 (16%) to Full Armor. That's slightly generous on average to the Half Armor case, but seems like a nicely coherent mechanic. That also just happens to be the same hit chances as seen in the core rules to Book of War (sans ranged modifiers, of course). But if we do go in this direction, then it may be a requirement to include rules as in Swords & Spells which reduce hit rates against small unit (or individual) targets.