Comments Completed

 I had a chance this week to go read the comments backlog I've been remiss on since March. If you asked a question at some point and were waiting on a response, you might want to go back and check at this point.

Also: More Book of War wargame testing live on the Wandering DMs channel tonight, 9 PM EDT.

Weather and Book of War 2E Units

You may have seen on the Saturday night Book of War wargame livestream that Isabelle & I have started playing with monster-types and variant weather rules (which is important for balancing light-sensitive monsters, missile troops, etc.) I've been grappling with balanced, easy-to-use weather rules for eons, trying to get something that works efficiently across (1) the wargame table, (2) D&D wilderness exploration, and (3) the 6th-level control weather spell.

Here's the current, very simple idea: just roll 1d6 each day.

1. Clear
2. Scattered
3. Broken
4. Overcast
5. Light Rain
6. Heavy Rain

On results on 1-2 you have "full daylight or bright light" sufficient to trigger goblin and orc weakness in the daytime. Results 3-4 have no special effect. The 5, Light Rain result has no effect in large-scale operations (wargame or long-distance travel), but applies −2 to missiles in the man-to-man context. The 6, Heavy Rain result gives 1/2 movement for all (doubled for mounted troops), −4 to missiles (converts to −1 in wargame scale), and all mounts and pikes lose special bonuses.

These might seem rather gentle for top-level weather penalties. In particular I've snipped out the "Stormy" category that I had in Book of War 1E. But this closely mirrors the possibilities in the Chainmail system, Dragon #68 (official Greyhawk weather), Battlesystem, etc. The distribution of rainy days is a pretty good match for historical data in Europe and the U.S. in the summer. In wilderness adventure situations, you basically just need to roll an extra 1d6 each day and look for the "6". And the effects seem basically game-balanced, and something for which we don't need to gimp control weather too badly (i.e., okay for it access any level on demand).

As an aside, I did some assessments of the unit matchups in the different weather conditions: the upshot is the a player opting to take goblins/orcs is taking a big gamble. In the 1-2 sunny state, they're pretty close to useless trash. In the 3-5 cloudy state, they're at the top of the heap; especially the archers and wolves. In the 6 rainy state, then it's the close-combat infantry types that have a big advantage; and meanwhile it's any mounted type that gets put in the effective garbage bin (including wolves). We'll see in further tests if that makes for acceptably interesting gameplay.

Here's the current list of all units being tested. Comments welcome!

Book of War 2E Units List - 200726

Falling Re-Revisited

For some people, the dueling physics articles about falling damage in Dragon Magazine #88 (August 1984) were the worst thing ever, but to me they're the best. I did a deep dive into them on a number of points two years back.

Somehow I got sucked into them again, almost unbelievably, as I was preparing for a Marvel Super Heroes FASERIP game that we ran on the Wandering DMs Solo Play show the last few weeks. (The MSH Charging rule was massively changed between Basic & Advanced versions; which is best? Well, the best physical model I could think to base it on was falling, and as a result I sort of house ruled all of time-distance-height-falling scale rules as I'm wont to do.)

Previously I've was always sold on Steve Winters short argument "Kinetic energy is the key", in that kinetic energy is linear with height, and so falling damage would be as well: say 1d6 per 10 feet. Simple and nifty.

But for some reason it finally dawned on me that both articles in Dragon #88 entirely ignore an important issue: air resistance. Maybe they didn't have sufficient computing power to model it at the time?

Now, it's close to common knowledge that energy and velocity are related by the formula E = ½mv² e.g., this is brought up in almost any discussion of the danger of high-speed car collisions. The fact that Parker's main article actually quotes this formula and then explicitly discards it (in an attempted counter to Winter) is so incredibly wrong that in retrospect that I almost feel physical pain at the embarrassment from it.

The problem with using kinetic energy to determine damage is this: kinetic energy is a function of the square of velocity. Everyday physics (the classical mechanics) is very much intuitive. It does not make sense that the square of velocity linearly relates to falling damage; it does make sense that velocity itself directly relates to damage. When a person hits the ground at speed 2x, he should take 2d of damage -- not 4d. Therefore, we should feel free to discard the concept that kinetic energy is linearly related to falling damage.

Ouch. It may "not make sense" to Parker, but it's the fact anyway. On the other hand, by relying solely on potential kinetic energy at the start of a fall, Winter makes something of the reverse error -- ignoring the fact that a lot of the kinetic energy will be scrubbed off by (non-damaging) air resistance. In that regard, we really should look at the velocity at the end of the fall, and convert (by squaring!) to energy actually released at that point. Additionally: It wouldn't make sense for damage/energy to really be increasing regularly with every unit of distance, and then have some abrupt point where that suddenly stops because terminal velocity was reached (as Winter posits).

I'm really astounded that this exclusion of air resistance in both articles never occurred to me before, and I'm scratching my head at how I overlooked it for so long. Let's see what we get if include that, and whether or not we want to observe that in a game system.

Somewhat surprisingly, Casio.com has a nice online calculator for falling with wind resistance that lets you compute time and velocity for a single fall at a time; the comments show it's mostly used by people in their TTRPG games. The formulas used look like the following (I'm not sure where the derivations come from, but the results closely match the figures quoted from Sellick's Skydiving in Dragon #88.)

Here's a tabulated set of results from those calculations:

If we take the 10' height as the basis for damage assessment, then the "Energy Multiplier" column is effectively the number of dice we should roll for damage from the indicated fall. Some observations: Due to the increasing effect of air resistance, the increase in velocity, and hence damage-per-unit tapers off with greater heights. For example, at 10' we roll 1d6, 20' 2d6, 30' 3d6, etc., as we're used to. But at 80' it's only 7d6; at 200' it's only 16d6. At extreme heights (probably pretty unlikely in most games), the damage-per-unit-height becomes effectively zero.

Here, we gradually approach terminal velocity as a limiting value, which makes a lot more sense than Parker or Winter with an abrupt cutoff at around 200' height. It's kind of interesting to see that even a 10' tall drop gets you to 15% of terminal velocity (last column), while 200' is only about 60%; 500' is about 80%, and not until a 2,000' drop is reached do you get to 99% of terminal velocity. But that smoothness is certainly more what I'd personally expect from the real world.

The damage increment at terminal velocity is 47 times the 10' fall; say about 50d6, which is what I've previously written into my OED house rules. Now, should we actually implement this slow drop-off in damage in-game? Since it's nonlinear, this is a case where the only legitimate way to do that is with a table (or a digital app, ugh), for which I don't think I'd want to spend time or space. So likely I'll just keep with the linear approximation -- it's pretty spot-on for distances up to 100' or so. Whereas the 500' fall should really only give about 30d6 damage, for me that's where I'll top out at the terminal 50d6 (being aware at the difference from reality).

Another observation is that when accounting for air resistance, weight matters. That is: as per the classic experiment by Galileo, if neglecting air resistance, we're used to saying that everything drops at the same acceleration, regardless of weight. But the formulas above actually do include a factor for weight (mass, m), and you get different results at different values. This reflects the observation previously by J.B.S. Haldane that for long falls, "A rat is killed, a man is broken, a horse splashes". For what it's worth, in my table above, I presumed a man of 150 pounds (68 kg, or 11 stone).

An additional item for me is that I recently broke down and decided to give a save for half damage on any fall (which both models the real survival rates for normal people a bit better, plus the bimodal rate of  whether someone hits their head or not). The downside is that for me this might trigger as many as 3 saving throws: (1) to avoid the fall, (2) for half-damage, (3) for a death save if hit points are depleted. But I think I'm willing to live with that in light of the other simulationist advantages.

Finally, a discussion like this can always lead into the "What are hit points, really?" discussion, and whether game damage is proportional to energy impact in the first place. But even if hit points aren't raw structural strength, it's unclear whether damage should be increased or decreased in light of that, which is outside our current scope.

In summary: Steve Winter's "Kinetic energy is the key" is certainly a lot more correct than the Parker article -- but it would have been nice to acknowledge the effect of air resistance and know exactly how much of an approximation is being made for a game rule. By looking at velocity at the end of the fall, and computing the energy thereby transferred, in some sense we get a model that's in between the Parker and Winter models. That said, it's close to 95% Winter and 5% Parker in their proposals.

Marvel FASERIP House Rules

The last few weeks on Wandering DMs, we've been playing sessions of the classic Marvel Super Heroes FASERIP system, with me introducing Paul to the system for the first time. In case anyone's interested in the house rules I use for that system, you can see those linked here. Primarily I stick with the original set rules because (I guess as usual?) they seem generally more coherent and a better synthesis than the Advanced and Revised elaborations that came later; in some small number of cases I pull out rules from the Advanced set and do use those, as noted. Comments welcome!

Marvel Super Heroes House Rules v. 1.0.6

The Big Bad

Geez, 2020, am I right?

Between pandemic, online teaching, medical emergencies, quarantines and curfews... etc. ... we all deserve some hefty XP for staying in the game. "May you live in interesting times", as the saying goes, and we do. I owe lots of people a bunch of posts, replies, and emails.

Here's another thing I've been working on feverishly with Paul at Wandering DMs: The Big Bad. It's a new online show that we'll be releasing in the fall, and we're so excited about it that it's almost painful. We chatted about it publicly for the first time on Lord Gosumba's 100th Episode of Greyhawk Gabbin' on Twitch last night, you should check it out of you're intrigued (about an hour into this marathon episode; the whole thing's great -- note luminary Len Lakofka/Leomund on with us).

Right now we have a dedicated page where we'll roll out more information and clips as we record sessions through the summer.We hope you'll follow us on YouTube and The Big Bad website for more information, coming soon!

Also, wear a mask because we want you at full health.

Athena Toolset 1.0.2

Update on the program package from two weeks ago for OED rules assessment of character levels, demographics, treasure and XP, monster strength, NPC generators, etc., etc.: In place of the list of separate tool downloads, I've replaced it with a master program and a single ZIP file to make downloading and getting started easier.

If you get the ZIP at the linked page below, extract it, and on the command line type java -jar Athena.jar. Append the name of the tool you want to run (Arena, Marshal, MonsterMetrics, or NPCGenerator), as well as any desired arguments (run with -? to see the available options). That probably looks a lot nicer as a single package download. Also I added a link to the JavaDoc pages for the whole package. Good luck!

OED Games Software Tools Page

Vancian Magic is Mathematics

I saw someone on Twitter this week claiming that seeing Vancian magic as mathematics was a mistaken reader interpretation (and claimed that something very different was the case). I knew it was, rather, explicitly described as math, but it took me a few minutes to find the quote. In case I need that again in the future, here it is (page 12 of my copy of Dying Earth):

In this fashion did Turjan enter his apprenticeship to Pandelume. Day and far into the opalescent Embelyon night he worked under Pandelume's unseen tutelage. He learned the secret of renewed youth, many spells of the ancients, and a strange abstract lore that Pandelume termed "Mathematics."

"Within this instrument," said Pandelume, "resides the Universe. Passive in itself and not of sorcery, it elucidates every problem, each phase of existence, all the secrets of time and space. Your spells and runes are built upon its power and codified according to a great underlying mosaic of magic. The design of this mosaic we cannot surmise; our knowledge is didactic, empirical, arbitrary. Phandaal glimpsed the pattern and so was able to formulate many of the spells which bear his name. I have endeavored through the ages to break the clouded glass, but so far my research has failed. He who discovers the pattern will know all of sorcery and be a man powerful beyond comprehension."

So Turjan applied himself to the study and learned many of the simpler routines.

"I find herein a wonderful beauty," he told Pandelume. "This is no science, this is art, where equations fall away to elements like resolving chords, and where always prevails a symmetry either explicit or multiplex, but always of a crystalline serenity."