Friday, January 29, 2010

OED Update (v0.6)

Just updated the Original Edition Delta house rules today to Version 0.6 (see sidebar for link). First, some tweaks to language and grammar (which I think I'll always be engaged in). Primary rules edits were:
  1. Demi-humans: Gave dwarves & halflings base 9" move (after observing monster move rates in Chainmail, OD&D, AD&D, and Gygax quote on Dragonsfoot in 2005). Gave elves infravision (per Chainmail table p. 43), removed attack bonus for orcs/goblins.
  2. Missile Weapons: Removed range modifiers for short indoor usage, as per recent investigation. Set composite bows to 18" and noted usage from horseback (per Chainmail). Gave slings 12" range and use every other round.
  3. Combat Modifiers: Added a short section on modifiers. Horsemen attack at +1 vs foot, rear attacks +2, silent rear attacks +4, helpless targets auto-hit for max damage (taken from Chainmail, Sup-I, and AD&D DMG).

If you can read an ODF file, you'll see the sidebar notes, et. al., here.

Wednesday, January 27, 2010

Universal Scales

Just to expand on the "Matters of Scale" posting the other day, I couldn't help but further generalize the findings to see what other scales might look like. With some fairly crude estimations, I get something roughly like this:


Notes: In actual use, you would of course want to round the numbers off to whatever values you find convenient. The bowshot (longbow) ranges are for outdoors usage; divide by 3 if used indoors (10' ceiling). Again, the whole system has been arranged linking distance & time scales so that movement is fixed at any scale (12"/turn for normal men).

In addition, at some high-level scale, our overall assumptions for a medieval-style wargame would break down and become unusuable. For the higher values, it would be: (1) historically inaccurate to have so many homogenous troops in a single block (requiring a game of greater abstraction to reflect mixed troop types), (2) historically inaccurate to have so many ranks in a single formation, and (3) quite unplayable to have ranged weapons that shoot miniscule distances on the game board. Exactly what level that breakdown occurs at (500 or 1,000 or so?) would be a subject for further research.

ODS spreadsheet here.

Monday, January 25, 2010

Matters of Scale

The root of our game is historically-based. "Besides providing you with an exciting and enjoyable battle game, we hope that these rules will interest the wargamer sufficiently to start him on the pursuit of the history of the Middle Ages. Such study will at least enrich the life of the new historian, and perhaps it will even contribute to the study of history itself." (Chainmail, p. 8). It's eminently clear that the author of Chainmail's basic, historical mass-combat game paid attention to simulating realistic scales of men, distance, and time. Continuing in that tradition, let's think about what games are possible at different scales, if we apply the same precision to our research and foundations.

We can begin by taking certain real-world measurements as our limiting factors; the speed and size of men in an army, the time it takes to make one attack or bowshot, the size of the miniature figures we might use, etc. Then we can select a certain figure scale and deductively reason out what that implies for the scales of distance, time, movement, bowfire, etc. (Note that all of this can be based on real-world data, with the sole exception of areas of magical effects, which are not considered here).

Here are my starting assumptions: Men in a line take up approximately 3 linear feet; they advance in a "quick march" gait at about 4 mph. A longbow effectively fires some 200-plus yards maximum outdoors (200 feet indoors), and it takes about 10 seconds on average to fire an arrow or make one potentially damaging melee attack. Finally, the standard miniature figure that we use is 28mm tall with a 20mm (3/4 inch) square base.

Evidence for each of these base assumptions is linked above, and we'll leave aside any further discussion on those for now. Certainly, each of these items will have some wiggle room and potentially individual debate on the specifics, but I don't think anyone can much argue for an order-of-magnitude change (double or half) of the figures given.

1:1 Figure Scale

Let's consider the case where 1 figure = 1 man (i.e., man-to-man combat). Since the figure is representational, we should use an equivalent distance scale of 1 inch = 5 feet (6 ft man/ 28 mm fig * 25 mm/inch = 5 ft/inch). Since attacks should also be resolved on a one-for-one level (i.e., one damaging blow or arrow shot per attack) use a time scale of 1 turn = 10 seconds (see attack rate assumption above).

At this point we'll compute second-order quatities, such as movement and bowfire. An unencumbered man at the "quick march" speed will move 12" per turn (4 mph * 5280 ft/mi / 3600 sec per hr * 10 sec/turn / 5 ft per inch = 12 inches/turn). Assuming action indoors, then we'll have a maximum 40" longbow shot (200 feet/ 5 ft per inch = 40 inches).

Now, here's a side note considering the movement rate above. Conveniently, since at every scale level we'll multiply the distance and time each by the same number (or at least approximately so), movement rate will be the same in inches for all scale levels. And it's doubly convenient because, of course, the 12" movement rate is in fact that specified as the base movement rate for men in classic D&D. In other words, it's accurate to use the D&D-specified movement rates (in inches) at any scale whatsoever.

Advantages of the 1:1 Scale: (1) Easiest to use with representational miniature figures (figure scale matches distance scale, so figures take up the appropriate amount of space in each dimension). (2) Every turn represents the opportunity for one single, simulated attack.

1:2 Figure Scale

This scale may be unheard of, but bear with me for a second. If 1 figure = 2 men, then we can basically double the distance & time as specified above. Distance will be 1 inch = 10 feet and, for time, 1 turn = 20 seconds. Movement will be the same as for all scales (12" per turn), and indoors we'll have an approximately 20" longbow shot (200 feet/ 10 ft per inch = 20 inches). While notable disadvantages are the awkward figure scale and need to resolve two discrete attacks per turn (e.g., similar to AD&D's 2/turn rate of arrow fire), there would be some notable advantages:

Advantages of 1:2 Scale: (1) Easiest to use mentally without representational figures (distance scale inches match the standard dungeon mapping at 1-square-per-10-feet). (2) Missile fire ranges in inches match those found in the D&D rulebooks.

1:10 Figure Scale

Let 1 figure = 10 men. Looking at the shape of our square-based figures, it doesn't make sense to assume that we have ten men in a single line; more reasonable is to have 2 ranks of 5 men each. Therefore, the distance scale here is most accurately set at 1 inch = 20 feet. (5 men/fig * 3 ft/man / 0.75 inch base per fig = 20 feet/inch). Since this is a multiplication of x4 over the root 1:1 scale, we should multiply time by the same amount; so you could say 1 turn = 40 seconds, but just to maintain a round number I prefer 1 turn = 30 seconds and call it "close enough".

Movement is again at the same fixed rate of 12" per turn (4 mph * 5280 ft/mi / 3600 sec per hr * 40 sec/turn / 20 ft per inch = 12 inches/turn). Assuming action is now outdoors, we'll have a 30" longbow shot (200 yds * 3 ft/yd / 20 ft per inch = 30 inches).

A side note here: From the observation that each figure represents two ranks, we can conclude that a missile-armed figure will make twice as many attacks as a melee figure in the same span of time (just as in Chainmail). The reason isn't that the bows themselves fire more rapidly, but rather that as one rank of melee troops makes immediate contact with an enemy, twice as many ranks of missile troops may be casting arrows.

Advantages of the 1:10 Scale: (1) Individual "special characters" of around 10 HD can potentially be represented as single figures. (2) Constructions such as castles & ships can be made to scale and still have space to physically contain the miniature figures we use. (3) There is a remarkable, elegant mechanic for mass-combat resolution at the scale of 1 turn = 3 rounds of D&D (which this margin is too narrow to contain, and so must wait for a future presentation).

1:20 Figure Scale

Assume that 1 figure = 20 men. Like the preceding, to make sense of our square figures we must assume multiple ranks of men, in this case say 3 ranks of about 7 men each. Therefore, the preferred distance scale here can calculated to be close to 1 inch = 30 feet (7 men/fig * 3 ft/man / 0.75 inch per fig = 28 feet/inch). Since this is a multiplication of x6 over the root scale, time should be similarly multiplied, i.e., 1 turn = 60 seconds. (In other words, 1 inch = 10 yards and 1 turn = 1 minute.) Movement is the same as at any other scale, while bowfire will have a 20" longbow shot (200 yds * 3 ft/yd / 30 ft per inch = 20 inches).

You'll notice that all of these measurements precisely correlate with those found in the basic Chainmail game(!). One thing that doesn't quite match up is the rate of missile fire; since we here assume that figures are 3 ranks deep, archery figures should have an attack rate 3 times that of melee troops. While Chainmail only has a rate-of-fire of 2/turn, the later Swords & Spells game did increase this number to 3/turn as we would desire here.

Advantages of the 1:20 Scale: (1) Figure, distance, and time scales are exactly as specified in the original Chainmail game. (2) Movement and missile fire ranges in inches are also exactly as specified in Chainmail and classic D&D.

Conclusions

Any of these hypothetical game scales have significant good reasons for using them. It's interesting that with some reasonable base assumptions and arithmetic, what results for the top-level scale is absolutely identical to the Chainmail system for figures, distance, time, movement, and ranges. The original system was clearly not a fantastic accident, but very carefully designed; and our other scales can be thought of as smooth interpolations of this same system. It's also interesting that if we use miniatures for man-to-man combat, 1" = 5 ft is preferred, but with imagined combat and no miniatures, then 1" = 10 ft seems more efficient to use mentally. Granted that the designers of original D&D fundamentally stopped using miniatures, then it's no surprise that the latter scale came to be embedded in the core texts. The one thing that I continue to be highly critical of is the holdover of the 1 turn = 1 minute scale from Chainmail into D&D man-to-man combat; if figure and distance scales change, then the time scale really should do so as well.

Thursday, January 21, 2010

Bow Ballistics And Scale

I like to think that the roots of our game (Chainmail, et. al.) are well-thought out with a good grounding in historical reality, insofar as scales, movement, and ranges go. They're not entirely fantastical (and inasmuch as that is so, we can continue the tradition of leveraging connections to real-life research to enrich our games). Let's think about longbows for a bit, and at the end we'll consider whether our game uses a good scale for representing them or not.

A few specific resources I'll use here. One: I tend to use Wikipedia as an acceptable source of raw data, especially in the rough context of a game (colleagues pointing to specific, better research is fair game, but people simply crying, "no, because it's Wikipedia!" is a pretty weak excuse). Two: Google does instant unit conversions (did you know that)? Three: Green Man Longbows page on arrow-speed tests taken by chronograph. Four: Stephen R. Schmitt's Ballistic Trajectory Calculator using JavaScript (illustration above taken from Stephen's site).

Okay. It seems like we can identify two different classes of longbow. The first I'll call the normal longbow, which basically matches the historical hunting longbow used globally, and also the modern longbow, of about 50 pounds draw weight. The second I'll call the warbow longbow, equivalent to the African elephant bow or the famed English longbow (which took a lifetime of practice and literally bent the bones of the users), of about 150 pounds draw weight.

According to Green Man Longbows, an estimate can be made by "adding 100 to the bow's draw weight and using this number as the expected arrow speed for that bow" (and note that all of their practical tests are done on the "normal" type, averaging around 40 pounds draw weight).

Let's calculate the maximum range of the normal longbow, assuming simple ballistic flight (tail feathers will modify this, but it's unknown by how much). We expect the launch velocity to be 50+100 = 150 ft/sec (46 m/sec), max range at 45 degrees (known from ballistics, or else experiment and recognize that any other angle lowers the range), and a launch height of a man's shoulder at 5 ft (1.5 m). Pumping this through our ballistics calculator, we see a maximum range of R=217 m, i.e., 237 yards.

Obviously this is an abstract estimate, so how does to it compare to other sources? Wikipedia says "Modern longbows have a useful range up to 180 m (200 yd)". Our games of Chainmail and D&D give the longbow a maximum range of 210 yards. So, our result seems compatible with a wealth of different sources -- somewhere in the low 200-yard range.

Let's do the same for what I'm calling the warbow style longbow. Here we expect a launch velocity of 150+100 = 250 ft/sec (76 m/sec), again at a 45 degree angle and a 1.5 m launch height. For this the ballistics calculator reports a maximum range of R=590 m, i.e., 645 yards.

How does this compare to other reports? Not quite so well; Wikipedia documents tested ranges of around 360 yards, and that "A flight arrow of a professional archer of Edward III's time would reach 400yds". So we're off by about 50%, but not by a whole order of magnitude. Furthermore, we can conclude that D&D longbows are better interpreted in terms of the "normal" hunting-style longbow of around 50 pounds, usable by any fighter-type, without requiring exceptional strength or a lifetime of training.

So let's consider our findings so far. Are D&D (Chainmail) longbow ranges accurate? Yes, they are in fact very accurate as given by a variety of sources and calculations -- assuming we mean the "normal" type longbow of around 50 pounds draw weight. A bit more than 200 yards is an excellent simulation of its capacity.

Now let's do something a bit different. The preceding assumes use of a bow outdoors, i.e., with no ceiling overhead to interrupt the flight path of the arrow. If we instead assume a limited ceiling height, how far is our maximum shot then? Here's how we'll do that: go to our ballistics calculator and by trial-and-error input different shot angles until the maximum height h is less than our ceiling height (say, a 10' tall corridor, i.e., 3 meters). The resulting range R will be our maximum indoor shot.

Do this for the normal longbow. Start velocity is 46 m/sec, best angle is then 6.7 degrees with a 1.5m start height. Resulting max range is R = 61m = 200 feet. Also do this for the warbow style weapon. Start velocity is 76 m/sec, best angle is then 4.0 degrees with 1.5m start height. Resulting max range is R = 100m = 328 feet.

Now here's the interesting thing, looking at the first type, which is apparently the D&D longbow. I tend to ridicule Gygax a bit for shifting the dungeon game scale in D&D from "yards to feet" as a rather short-sighted cop-out. But it turns out that the normal hunting longbow (50 lb draw weight) does have a max outdoor range of about 200 yards, and it does have a max indoor range (limited by 10' ceiling) of precisely 200 feet. So we see that, to my immense personal surprise, the yards-to-feet conversion for dungeons is rather freakishly accurate, at least for the limited domain of ballistic missile ranges.

I'll even go so far as to say that I didn't really want this to be the case; I prefer a game scale of 1"=5 feet (matching miniature scale), but this finding is certainly easier to apply for a scale of 1"=10 yards outdoors, and 1"=10 feet indoors (thereby matching D&D ranges given in inches). Another interesting implication is that while outdoor bowfire is very much "indirectly arced" at the maximum range, indoor bowfire is always basically a directly aimed shot (only 4 or 6 degrees angle at most). We could then conclude that dungeon bowfire is always effectively at "short" range, and should simply not be subject to any range penalties at all (which is actually the converse of the rules given in Chainmail, where mass fire outdoors has no range penalty, but man-to-man fire does).

Addendum: Let's add an assumption that you need access to the target's head for a normal D&D to-hit roll (i.e., not just their foot, but potentially at least 2m off the ground at the end of the shot). Then by my calculation the maximum indoor range would be R = 45m = 148 feet, still on the same general order of magnitude.

Wednesday, January 20, 2010

Dave Noonan on Classes

Dave Noonan, former writer for 3E/4E at WOTC, has a blog and has recently been posting on class issues. As an OD&D player it's a rather unsettling read, kind of like dealing with a foreign-language speaker with a lots of cultural differences between us. Just one example is that he doesn't even use the word "class", but rather the WOW/4E-jargon of "roles" (those being an overlayed concept on top of classes).

http://nnnooner.blogspot.com/search/label/roles

Here's a few quotes which I'll present without commentary. From the section "Let's Talk Psychographics":

Wizards R&D certainly believes that there are differences in player psychology that manifest themselves in role choice. In other words, some players are naturally drawn to play a leader, others a defender, and so on. I'm pretty sure that the Blizzard devs believe the same thing. And certainly some players are convinced that "you know, healing is really what I'm good at."


From the section "Set the Wayback Machine for 1982":
The other characters start standing in front of the magic user...and thus the traditional front-rank/back-rank tactic is born. More interestingly, the other characters start doing everything they can (attacks, verbal insults, silly/weird antics) to keep the monsters from focusing their attention on the magic user...and thus aggro management is born. If magic users were as durable as, say, the D&D thieves, I don't think either behavior would have become so pronounced.

From the section "Whither Healers?":
The simulationist in Gary followed a very reasonable line of thinking: If you get stabbed nearly to death, it should take you days or weeks to recover... But as anyone who has run a long-term campaign knows, long recuperation times can be hell on the ongoing narrative... It's worse if some players need to recuperate, but others don't; that's a recipe for splitting the party. And those long recuperation times wreak havoc with any sort of time deadline before the Great Evil Event happens. As a DM, you want that tool in your toolbox.

Tuesday, January 5, 2010

The Primacy of Tolkien

I disagree with some of my most respected colleagues on the relative importance of Tolkien to the game of D&D. Frankly, I didn't feel this way until I got copies of Chainmail and OD&D in the last year, and now it seems unavoidable. I grew up reading Gygax's deflections on the issue, but the truth is that he's very much an "untrustworthy narrator" on the issue, since the first and most dangerous legal challenge to D&D came early on from the Tolkien estate.

Consider the following article on Gygax's early play with fantasy miniature rules. Note how the entire context is inspired by, and driven in terms of, representing figures mentioned in Lord of the Rings:
http://grognardia.blogspot.com/2009/12/1972-gygax-article.html

(There are places where Gygax considers some alternative statistics to be better than Tolkien's, but nontheless, the idea for what character to begin playing with in the first place comes directly from LOTR.)

More keenly, consider the following list of figures presented in the Chainmail Fantasy Supplement. Note first that it begins with hobbits (!). Secondly, it seems like a pretty clear line can be drawn from the LOTR books directly to this ordered list:
Halflings, sprites (& pixies), dwarves (& gnomes), goblins (& kobolds), elves (& faeries), orcs, heroes (& anti-heroes), super-heroes, wizards, lycanthropes (shape-changers), trolls (& ogres), giants, treants, dragons, rocs (& wyverns & griffons), elementals (& djinn & efreet), basilisk (cockatrice), chimerea, giants spiders and insects, giant wolves, wights (& ghouls).

(Question: Of these 21 distinct creature type categories, how many are not found in the works of Tolkien? Any?)

Of course, these basic types are generally the same types found in the two-page listing of monsters in OD&D. I would agree that starting with Sup-I Greyhawk, the monster and spell lists are being created uniquely for the D&D game, but not before then. It's a bit silly for Gygax to argue that "some bits and pieces from Tolkien were thrown in to entice certain readers", when the fact is that all of the monsters and character-types of Chainmail and core OD&D come directly from Tolkien, nearly in the same order of appearance as in the LOTR books. Tolkien is the first fantasy author mentioned in Chainmail fantasy, and Gygax's earliest writings show that the whole game was played in that context.

Hey, that's not a bad thing! Tolkien is great, strong foundation to build from. I can see the Tolkien-to-D&D relationship as being analogous to that of Games Workshop-to-Blizzard corporation. Our art is strongest when there's lots of borrowing going on. Fie on silly copyright regimes that restrict and traumatize even our greatest creators to such a degree.