Monday, May 29, 2017

Slings and Arrows and Outrageous Formulae

The word "sling" appears nowhere in the entirety of Chainmail or any of the core books of Original D&D. (Well, one exception: a reference to a "sling-ended catapult" used in aerial combat in Vol-3). It does appear in Supplement I in the damage table (1d4 points vs. man-size, p. 15) and corrections list ("All hobbits add  +3  to hit probabilities when using the sling", p. 68). But without anywhere the rules giving them a range, rate of fire, or cost, it's a bit of a murky issue. In AD&D Gygax gave them a range in between that of a short- or longbow, and a rate of fire half that of bows. I wanted to do some research to make sure that was dialed in correctly for my games.

The amazing thing is that numerous sources state that slings had a rate of fire at least as fast as bows, and a range that likely exceeded them, with a heavier and faster projectile, that was possibly more accurate and more damaging. How can this be? Of course, you also have the case of the crossbow with clearly deficient rate of fire, and thus borderline useless in standard D&D play. And yet at a late point it was favored over the bow. Why?

Among other resources, I came across a very nice article by Chris Harrison (Assistant Professor at Carnegie Mellon Human-Computer Interaction Institute), originally published in The Bulletin of Primitive Technology (2006). Near the conclusion he writes:

When looking at the evolution of ranged weapons, there is a trend towards increasingly simple operation. The sling requires enormous skill, one that can generally only be obtained with training from childhood (Hawkins, 1847; Korfmann, 1973; Wise, 1976; Ferrill, 1985). Without this mastery, a person armed with the weapon would be practically useless. The sling is exceptionally difficult to aim because it is being rotated when fired. It is common for people to fire projectiles backwards when they are first learning, meaning a high degree of proficiency is needed before they can be safely placed in a battlefield situation. On the other hand, the bow could be taught at any point in life, and be deadly with minimal experience. The bow does not suffer from the sling’s accuracy problems because of its ability to be drawn and then aimed. However, archers did have to be strong, which increased the required training time (Wise, 1976). The development of the crossbow with a mechanical device to cock the weapon enabled anyone to use it and have the ability to kill even an armored soldier at distance. The crossbow was the first true ‘point-and-shoot’ weapon, as it could be cocked and then easily aimed using the large stock. Although much slower to reload than bows, it was seen as an acceptable tradeoff for the ease-of-use gained. The shift to firearms was similar. They were even slower than the already sluggish crossbow, at least at first. However, the operation was simple and there was no physical strength needed to load the weapon. Also, its ‘point-and-shoot’ nature made someone with almost no experience immediately useful on the battlefield, and very deadly. This evolution occurred primarily because of changes in military and governmental organization. In feudal times, lords could recruit their serf population as soldiers (Wise, 1976). Many of these men were already proficient with the bow or sling, which were used for hunting game. However, by the High Middle Ages, nations and cities had developed large standing armies, which were recruited, sustained, and equipped by the government (Martin, 1968). An increasing number of these recruits were from urban populations which had far less exposure to ranged weapons. These units had to be trained from scratch and there was a high turnover. This led to the increased use of weapons that were deadlier with less training. The sling was perhaps the least effective choice of ranged weapon in this role. 

See the full article here. We might phrase that observation in economic terms; the advance of missile weapons was to get cheaper and faster -- lower quality, but able to be fielded in larger numbers and in that way more powerful. (We might well look to many things in our own era that became dominant by virtue of being crappier but cheaper: MP3 audio encoding, travel agencies, car ride services, etc.) Gygax actually makes much the same observation in an article in Strategic Review #7, "The Missile Weapon in Classic Warfare". (!)

That said, this is not something that D&D models very well. By default Fighters simply have proficiency in all weapon types. If the sling were the best missile weapon in an expert's hands, then every Fighter would be carrying slings and nothing else. If we want our game to look like the medieval era that would be a bit jarring. In any heroic story, the protagonist uses the weapon common to his people; e.g., David with his sling, Robin Hood with his longbow, William Tell with his crossbow, etc.

So in lieu of modelling more ancient/personalized weapons as taking greater amounts of training time and commitment, AD&D reverses the statistics to make sure that slings are a deficient choice for adventurers. What could we do to give slings their real-life fire rate and range (and advantages in small size, low weight, conceal-ability, etc.) without their completely eliminating the use of bows by PC adventurers? Or would that actually be acceptable?

Monday, May 22, 2017

Guest Post: Medieval Magic

I think this is the first-ever guest post on this blog. In an online discussion a few weeks back, Landon Schurtz made what I thought was a fascinating comment about the spell list he uses in his low-magic D&D campaign. A problem might arise in determining spells appropriate for that milieu. Solution: Why not use his copious literary skills to find and read up on actual medieval grimoires and see what writers of the time thought was really possible? Notice again how this links to our project of using real-life research to actually simplify the game (three weeks ago); and also to craft a set of wilderness rules to fix the blindspots from original D&D (last two weeks).

Landon Schurtz is a professor of philosophy and a roleplayer for the last thirty-plus years, not in that order. He is currently working on a never-to-be-completed project to build the "perfect" fantasy roleplaying system by cannibalizing pieces and parts from various "old-school" games.

It started with Leomund’s tiny hut.
In AD&D, Leomund’s tiny hut is a very useful spell for adventuring magic-users to learn, as it allows creation of effective shelter when traveling. I’ve played many magic-users in my day, and they all acquired the spell as soon as possible – it just made good sense for a traveling spellcaster to have it. And therein lay the problem.
Even without dealing with the longer-lasting (and thus more effective) versions available in later editions of the game, I quickly became annoyed that Leomund’s tiny hut was too effective – its existence allowed parties to sidestep certain challenges that seemed to me to be integral to the kind of game I was trying to run, which, in this case, was the kind of game where player characters, no matter how high and mighty, could never fully insulate themselves from the basic threats of a pseudo-medieval setting. I wanted travel to be arduous and chancy, food and water to be precious, and so on. In short, I wanted my games to feel more “medieval,” something closer to low fantasy than high.
So it was that several campaigns ago I began going through the spell lists and eliminating certain spells. Those that made travel a non-issue or something very close, like Leomund’s tiny hut and teleport, were the first to go; next followed spells that eliminated the need to think about rations and foraging, such as create food and water; and so on. Eventually, I even eliminated all cure...wounds spells from my game, though I “replaced” them with a different hit point mechanic that rewarded tactical retreat by allowing characters who were not below half hit points to recover fully in just a few minutes.
Though this method was getting good results in general, I still felt I could do a better job of getting a “real medieval feel” for my world, so I took a different approach: I went back to the sources. I conducted a fair bit of research on beliefs about magic in the Middle Ages, starting with scholarly works like Richard Kieckhefer’s indispensible Magic in the Middle Ages and eventually moving on to what proved to be my definitive resources, actual medieval grimoires.
Books like Liber Juratus and Sword of Moses, which date to the 13th and 10th centuries, respectively, can be found in digital format at, a useful resource for anyone looking to inject a little authenticity into their games. I began perusing these and other grimoires in an effort to see what a “real” medieval wizard would have been (thought) capable of, and I was pleasantly surprised to find that many spells in AD&D had “genuine” parallels – the Sword of Moses purports to hold the secrets of how to cast spells that would equate to protection from fire, silence, and blindness, and Liber Juratus describes incantations that could credibly be translated in game terms as telekinesis, phantom steed, and even Drawmij’s instant summons!
Using these, I was able to construct spells lists that I feel have a real “medieval” flavor. Magic-users still have considerable power, though they have much-reduced capacity to deal direct damage. Gone are high-fantasy staples like magic missile and fireball, but in their place, wizards gain many abilities previously restricted to illusionists, clerics, and even druids. I have divided the spells into four categories: thaumaturgy, which I take to be the “default” sort of magic employed by magic-users; elven magic, which, as the name implies, is the kind of magic employed by elven spell-casters and rarely taught to outsiders (I haven’t decided whether elves can also use thaumaturgy or are restricted to elven magic alone); black magic, which encompasses most “evil” magic; and white magic, wherein one finds the spells of binding and banishing extraplanar creatures. Except for the division between elven magic and everything else, this choice was made more for organizational purposes – I originally included white and black magic on the main thaumaturgy list, though perhaps a DM might allow for certain villains to have access to black magic only, thanks to, say, a demonic pact.
A few notes:
  • I do not use clerics or druids in my games, nor illusionists, now that I have this new spell list. The thaumaturgy list has many spells that were once the province of one of those three classes.
  • The vast majority of spells are taken from the PHB and UA, while a few (mostly in the elven magic section) come from Oriental Adventures, which has a wide selection of “elemental” spells. The various “undead production” spells come from the description of the Death Master class, in Dragon magazine; for DMs who would prefer to just use animate dead, the switch could easily be made.
  • All spells function as described in the books except cure disease – in this system, a different cure [disease] spell is needed for each ailment.

Saturday, May 20, 2017

How to Include Justifications in a Rules Document?

As a final thought to the wilderness rules ideas the last two weeks: You'll notice that each of the separate sections had an appendix of notes and references for different rules at the bottom of each page.

This is something I struggle with a lot in the context of paper rules documents. You want the rules to be terse, be immediately interpretable in play, and be easy to memorize. But on the other hand I think it's useful to include specific justifications, motivations, and references; I have the feeling that without those, I (and maybe many others) wind up repeating the same research projects over and over again, often recreating the same conclusions as other game designers. Now, those justifications may actually be longer than the rules themselves. My OED House Rules document has copious sidebar annotations (invisible in the distributed PDF form), likely longer than the rules themselves.

So I ask: What's the best way to include reference/citation/justifications in a rules document? Sidebar notes on each page? Footnotes? A block of references in each section? A consolidated appendix of commentary at the back of the book? A separate supplemental document entirely? Hyperlinks to multiple outside articles?

Thursday, May 18, 2017

OED Wilderness Rules Draft: Weather Events

The fourth and final part of a draft of modified wilderness adventuring rules for OED-style games. Something like this was playtested at Helgacon this year. The principal feature it that it exchanges the daily Lost die for a simple Weather mechanic. Whereas in the past I've struggled in Sisyphean style with super-complicated weather rules (e.g.: Dragon #68 "Weather in the World of Greyhawk", AD&D Wilderness Survival Guide), this simple d6 roll is making me perfectly happy in play now. Thoughts?

Weather Events

In wilderness adventures we replace the daily Lost die roll (see Vol-3, p. 18) for a Weather roll. Thus two dice a rolled each day: a red die (for Encounters) and a blue die (for Weather). On a roll of 5-6 some weather Event occurs; consult the table to the right. The default situation assumes a temperate environment in the summer, with a base daily temperature of Warm (clo 0).

Heat Wave: Daily temperature is Hot (clo –1). No travel or work can occur without magical protection.

Light Rain: Travel may be attempted normally, but there is a 2-in-6 chance of becoming lost (mostly travel in circles, end move 1 hex in random direction).

Heavy Rain: Travel is impossible (except possibly for large creatures like giants, ents, balrogs, etc.)

Thunderstorm: Travel is impossible, and parties not in shelter have a 1% chance of a random character being struck for 6d6 lightning damage (save for half).

Travel prohibitions generally mean that no encounters can occur (except as indicated). We assume that no long-range movement occurs in the winter season (due to snow, cold weather, muddy roads, blocked mountain passes, etc.), including sea travel. The DM is encouraged to create Event tables for other climactic zone as desired.

Notes and References

  • The specific frequencies of events above were modeled on northern Europe; specifically the Paris Le Bourget airport in June to August. We downloaded daily historical weather data for these months 2001-2009 and computed statistics as above. Paris was chosen as central to battles in the Hundred Years War. Technically, a d8 Event die would be more realistic (1-in-8 heat wave, 2-in-8 thunderstorm), but the d6 was used above for simplicity in play.
  • Frequency of rainy days may be 25-50% in Atlantic region, northern Europe. Heavy rain (> 10mm per day) occurs in eastern United States about 15% of days (1 in 6), Europe somewhat less. Rainy days evidence clustering (suggests roll for multi-day duration, or increased chance next day?).
  • This short table of middle ages battles shows battles occurring from March to October, with the largest cluster from June to August, which we used as the assumed “adventuring season”:
  • People walk in circles when lost (contrast this with the rule in Outdoor Survival/OD&D in which being lost causes travel in a maximal straight-line path, being unable to turn or stop):,
  • No winter sea travel as given in Unger, Richard W., The Ship in the Medieval Economy 600-1600. (p. 128, 131; but compare to later era on p. 175). If winter sea travel permitted, then weather should also be modified in that season.
  • For a translation of a year-long medieval weather record, possibly by Roger Bacon, see the link below (cites C. Long, “The Oldest European Weather Diary?”, Weather, Vol.29:6 (1974) pages 233-237):
  • For more exotic weather options reported in medieval times (such as cooked wheat, barley, beans, fruit, fish, snakes, stones, ash, rocks, people, slabs of ice, and blood), see Paul Edward Dutton, “Observations on Early Medieval Weather in General, Bloody Rain in Particular”, The Long Morning of Medieval Europe: New Directions in Early Medieval Studies (Chapter 9) (currently available on Google Books search).

Monday, May 15, 2017

OED Wilderness Rules Draft: Clothing and Temperature

The fourth and final part of a draft to wilderness rules for OED (add-on house rules for OD&D). In this part we connect levels of clothing, and hence comfortable ranges for temperature, to real-world "clo" thermal insulation measurements. While a very rough approximation of real-world research, having completed it, I find that this pretty accurately maps to my mental process for getting dressed on my way to the college where I work (which entails walking & waiting for city bus, usually outdoors for at least 30 minutes each way). Is it adequately useful for a game?

Clothing and Temperature

Clothing levels are matched to different levels of extreme temperature, as given in the table below:

Effects of Heavy Clothing: Encumbrance is given in stone units. The number shown under “Dex” is a penalty to all Dexterity-based rolls (including missile attacks and AC); the raw Dexterity score is effectively reduced by 3 times the number shown in the table. Clothing gives comfort in the temperature bands shown. Chain cannot be worn with clo 4, plate neither clo 3-4. The given clothing types are the best possible without magical construction
Modifiers to Temperature: Ranges for comfortable temperatures assume a moderate work load (e.g., marching). Sedentary persons will require +1 clo, while heavy labor needs –1 clo (e.g., running or fighting). If persons are not adequately clothed, then they must seek shelter to resolve the condition. Assume that garments are removed for comfort when needed. Standard mounts can work acceptably in temperature ranges clo 0-2. 

Lack of Proper Clothing: Living creatures suffer 1d6 damage at the end of each hour that they are outside their comfort range by one step. Additional steps accrue damage more quickly: Every 10 minutes for 2 steps, minute for 3 steps, and round for 4 steps. This damage cannot be healed until shelter is reached, at which point they regain 1 hp/level for each like time period. If under half hit points for this reason, then assume the creature’s movement is halved.

High Temperatures: Hot weather categories are not shown on the table, but they may be continued in like fashion: Hot (90-120° F), Very Hot (120-150°), and Extremely Hot (150-180°). These are not suitable for working or travel, and even at clo 0 creatures take damage as per the rule above unless sedentary or in shelter.

Notes and References

Thursday, May 11, 2017

OED Wilderness Rules Draft: Carrying Capacity

More suggested refinements to OD&D wilderness adventuring mechanics. Notice how in this installment we use modern research to establish a mathematical formula between real-world creature weight and carrying capacity (in line with our observations last week). So: It's simultaneously more realistic, and also (perhaps more importantly) simpler to judge and to generalize. Comments?

Carrying Capacity

Animal carrying capacity is shown in the table to the right, as well as average weights for such mounts. All weights are given in stone. Light load (full move) is considered to be up to 20% of the animal’s weight; heavy load (half move) is set at 40% of animal weight.

Vehicle and ship capacity is given in the next table; units here are in tons (160 stone). Note that as a convenient rule-of-thumb, the capacity of the vehicle is its cost (from Vol-1), divided by 100, in tons. Galley types are the exception, with a capacity half normal by this rule (or in other words, about 1 ton per crewman; see Unger p. 176). Do not count normal crew against the cargo capacity given here (although any added soldiers, pilgrims, horses, etc., will be counted). Treat longships as small galleys, and warships as small merchant ships for this purpose.

Of course, in reality both animals and ships vary continuously in their size, weight, strength, carrying capacity, etc. As DM you may wish to permit a range of sizes for each (and load capacity can be fairly easily found by the rules-of-thumb above). This is easier to do with ships (likely only one owned by a given party), and harder to do with beasts (where many may be owned per party). Maximum constructable size for a merchant ship (cog) may be up to around 400 tons capacity in this time period.

For simplicity, assume that an unarmored man weighs about 10 stone, and medium or heavy horse with one week of hay and water weighs 1 ton.

Note and References

Monday, May 8, 2017

OED Wilderness Rules Draft: Food and Water

In the last year, I've spent some tweaking wilderness adventuring rules to make myself happy. Although OD&D's rules were based partly on Outdoor Survival it has numerous blind spots; like having no mechanics for running out of food or water, reduced movement rates, weather, etc. (things that were at the very core of Outdoor Survival play). Partly what I'm doing here is bringing in some more parts of O.S., looking in places to real-world research on certain effects (re: last week's post), and shaving off the hard edges to make it more streamlined and easier to run in play. For your consideration and comment:

Food and Water

In standard terrain, only food for men needs to be tracked. Cost is 5 and weight is 1 stone per man/week. Otherwise assume that water is generally available in small ponds and streams (each man with a waterskin; half-gallon, 1/3 stone), and horses may graze daily.

Severe terrain requires that food and water be tracked for both men and horses. Such areas include: desert, open ocean, deep caves, mountain peaks, arctic locations, and winter season. Total cost and encumbrance per week of supplies is shown in the table to the right. Note that weight will be prohibitive in some cases.

If a PC party in the wilderness runs out of food, then they can supply themselves by taking down sufficiently large random encounters (e.g., giant animals, dragons; say 1 HD will feed 6 men for a week, but won’t last beyond that time).

Lack of Food or Water: Living creatures suffer 1d6 damage at the end of each week without food or each day without water. This damage cannot be healed until proper food and/or water is procured, at which point they regain 1 hp/level for each like time period. If under half hit points for this reason, then assume the creature’s movement is halved.

Standard Rations Only: Only standard rations are generally available. Iron rations may be available in exceptional circumstances (dwarven or magical construction, etc.; one-third weight).

Notes and References

Monday, May 1, 2017

Traditions of Real-World Statistics in Naval Games

So, I'm a naval-game junky. The first wargame I ever picked up as a kid was Avalon Hill's Bismark. Among the first video games I got hooked on was Sid Meiers' Pirates!. I'm always looking for the perfect D&D naval experience but haven't found it yet. The naval combat rules in OD&D Vol-3 (p. 28-35) are as close as I've found to date, but they have issues -- like (a) the move rates being scaled to around 2 or 3 feet per turn (so that ships zip across the board space in just a single turn), (b) the reference that melee be done by "Man-to-Man rules as found in CHAINMAIL" (so every individual man needs to be moved and rolled for attacks separately), etc.

As part of my continuing search, I recently, at long last, acquired a copy of the rules to Gygax & Arneson's first-ever game collaboration, Don't Give Up the Ship (DGUTS below). This is the 2nd Edition (1975), with added optional rules from Mike Carr (designer of Fight in the Skies, referenced in OD&D as inspiration for its detailed aerial combat rules). It's a great read, obviously made with a ton of love and affection to the milieu of fighting ships of the American Revolutionary period; and in very much the same style as a book like Chainmail. In some sense it has about what you'd expect: a Basic Game, optional Advanced Rules, super-detailed Single-Ship Action Rules, more abstracted Fleet Action Rules, rosters of possible ship-to-ship engagements (all historically based), a Bibliography of over a dozen historical texts, etc. The play involves tracking gun weights, wind direction & force (reminiscent of many tables in D&D), sailing points and gunnery with a protractor, and so forth. Boarding is entirely abstracted, with the mechanic based purely on opposed morale checks (and without any men being lost from such actions in the standard rule). Some of the DNA can even be detected in Swords & Spells; like, the overall format of the record sheet, and the percentage-based damage adjustments that likely require a calculator (e.g., the last ship-to-ship optional rule notes that "Various tests made have proved beyond reasonable doubt that U.S. shot was lighter than it should be", and so should do a proportional 7% less damage; whereas French shot was 10% heavier and therefore will do 10% more damage).

It's not immediately clear how this can benefit your D&D game, however. One thing I noticed is that the scale is wisely chosen: 1" = 100 yards, 1 turn = 5 minutes. It recommends ship models close 1: 1200 scale (note this varies from the surface equivalent to scale of 1: 3600, but by less than an order of magnitude). This is quite different from the D&D scale officially 1" = 10 yards, or arguably what should have been 1" = 5 feet to match the size of miniatures in Man-to-Man action. Yet despite this, OD&D recommends the same 1: 1200 scale for ships as DGUTS (Vol-3, p. 30), which is either 3 or 20 times too small depending on how you count that. (As an aside, we can reflect here how much earlier wargaming relied on the player to acquire or build their own materials from other products, as the rules were designed expecting toys like that to be commercially available; this is long before consolidated brands in which wargame rules are part of a company selling their own boxed products.)

The really startling thing (to modern eyes) is none of that, however. First let me observe that DGUTS seems to owe a rather large inspiration and debt to a halfway famous older game, Fletcher Pratt's Naval War Game (published in 1943, but developed and played for more than a decade before that). Pratt's game simulates fighting ships contemporaneous to its play in the era between the World Wars. The intriguing thing that Pratt did with it is to rely on the real-world publication of Jane's Fighting Ships for its ship statistics. I wouldn't know much about Pratt's game it weren't for Jon Peterson's sublime Playing at the World. Peterson writes (p. 280):

Pratt borrowed Jane's method of classifying ships, especially his notation for measuring arms and armor. The thickness of armor and the size of guns are quantified and compounded in an elaborate mathematical formula, to which additional figures are added for amenities like torpedoes or the ability to carry aircraft. This sum is multiplied by the speed of the vessel in knots, and finally the tonnage is added to determine a "value" for the ship. Ship values tend to be large; one example boat given in the rules has a value of 23,034. Guns, when they score a hit with a shell, inflict a certain number of points of damage depending on their size; the weakest 37mm guns might inflict 23 points of damage, the standard 4.7" cannon hits for 244 damage, while the implausibly large 16" cannon deals a whopping 10,550 points of damage. As a ship suffers points of damage, it begins to lose capabilities, including movement speed and the use of its guns. For the convenience of players, a "ship card" typically lists all of these attributes and details exactly which capacities are sacrificed at the various levels of disrepair. When it has taken damage greater than or equal to its value, a ship is sunk. 

Gygax & Arneson's (and Carr's) Don't Give Up the Ship uses the same basic idiom, somewhat simplified, for its ship statistics. Two types of damage are tracked: high (sails & masts) and low (deck and hull). The high damage score is simply half the real-world ship's actual tonnage, with these points split proportionally among each individual sail and mast on the actual vessel -- lose a sufficient number of points, and sails/masts are lost, reducing speed appropriately. The low damage is equal to the real-world ship's tonnage -- when damage scored is over 70%, the vessel may possibly sink slowly, while at 100% the vessel sinks automatically; in addition, crewmen are lost proportionally following any low damage scored. Specifically: "crew factors" (CF) are tracked where a ship has one CF for every 21 men on the real-world ship (a seemingly odd conversion rate, but this comes from an estimated 7 men to operate a gun, times 3 guns per fire unit; see p. 17 and below).

Likewise, guns are based on whatever guns the real-world ship was known to have. For example: Ship A in the simple "Training Game" scenario has 12 24-pound guns, 15 12-pound guns, and 3 9-pound guns (denoted 12-24#, 15-12#, 3-9#). Every 3 guns of a given type allows one "fire factor", that is, one d6 roll on the very simple combat table per turn (which can result in either a high or low hit or a miss, depending on range). Damage is simply equal to the poundage of the gun type firing -- for example, one hit from a trio of of 12-pound guns does 12 points of damage. In its way, a breathtakingly elegant mechanic!

The thing that I like about these systems is that by making an explicit connection/formula between real-world entities and game entities, the designers have immediately populated their game world with everything (of the appropriate category) in one fell swoop. Pratt doesn't need to include rosters of ships; he can just direct the reader to Jane's Fighting Ships, or other reference works. The ship rosters in Gygax & Arneson's DGUTS aren't really game statistics, they're just real-life profiles of historical ships (in terms of real tonnage, guns, crew, etc.). The designer doesn't have to spend time laboring over individual game-piece statistics. One's game is enriched by, and stands on the shoulders of, the amount of attention and detail given by military scientists tracking and documenting the things in the real world. If any balancing or revisions are needed, they are only in the game rules themselves (perhaps tweaking the mathematical formulae that simulate ships in the game).

Note how briskly this tacks against the fantasy gaming headwind that attention to simulating concrete, real-world elements cannot have any benefit (link). And how synchronized it is with our long-running observation that real-world solutions almost always give the most elegant in-game mechanics (link). In fact, by making the link explicit and mathematically precise, we instantly profit by the whole universe of whatever real-world thing we have simulated.

Of course, this assumes that there is a pre-existing compendium of measurable information compiled about our topic of inquiry, which we have in abundance for fighting ships -- and much less so for individual people, arms, creatures, or of course fantasy creatures. But I am tempted to think about what other quantitative fields of study exist that we can port semi-immediately, and connect explicitly, into our D&D games to their benefit. Let's be on the lookout for that in the next few weeks.

Can you think of any such field of study that we can mathematically connect to our D&D games in order to enrich them?