Monday, August 21, 2017

Exploration Movement Rates

How long would it really take to explore a dungeon or cave? I'm just talking moving through the place and roughly mapping the perimeter. Not included: Searching through chests, desks, libraries; looking for secret doors; disabling puzzles or traps; spelunking through tunnels; etc. It does presume at least being on the lookout for possibly dangerous animals or enemies. It's hard to say how you'd even be able to measure this.

Here's the best stab I can take at it so far: the U.S. National Park Service has a very nicely laid-out website for Mammoth Cave National Park in Kentucky. In particular, it details over a dozen different tours on the site, including specifics for duration, distance, and difficulty. From these we can compute the average speed on these cave tours:


Method: The first four columns above are transcribed from the NPS website; "difficulty level" is an enumeration I added for the different difficulty descriptors; and speed is calculated as expected. Side observations: The "Trog" tour is, perhaps ironically, for kids only. The "Violet City Lantern" tour uses only open-flame lanterns (no modern lights) so as to recreate the experience of exploring the caves -- and living in an underground tuberculosis hospital that was located there -- in the early 19th century. (This latter sounds like among the most interesting to me!)

Conclusions: The speeds on these tours range from a minimum of 0.2 mph to a maximum of 1.5 mph, with an average of 0.7 mph. There is effectively no correlation between difficulty level and speed (R² = 0.04). For example, the "Easy" difficulty tours include both the slowest and the fastest speeds. There is a statistically negligible trend for the more difficult tours to be a bit faster.

Can we use this as a metric to properly gauge dungeon exploration speeds? Obviously, the experiment lacks many things: They are all safely pre-mapped routes, no one is in fear of being attacked, they're being led by knowledgeable guides, etc. On the other hand: The tours all have to account for civilians in all kinds of shape, they are organizing fairly large groups, the guides are stopping for discussions and questions, they're being environmentally careful (unlike tomb-robbing adventurers), they go up-and-down through rugged cave areas (whereas dungeons are mostly level constructions), etc. I'm sure the data is biased one way or the other, but I can't tell which.

Let's look at the exploratory move rates in OD&D. First, recall that standard human walking/marching speed is around 3 mph (from whence we get the "league" unit). OD&D sets basic encumbrance levels and move rates on Vol-1, p. 15 (and these are basically copied from Chainmail), with the exploratory turn movement in Vol-3, p. 8. This latter is described as "ten minutes to move about two moves -- 120 feet for a fully armored character". In summary we get this:


So that's pretty slow; only about 1/4 mile per hour for unburdened men; or, approximately equal to the slowest (and easiest) tour at Mammoth Cave Park. Of course, AD&D reduced the rate even further, dictating not "two moves" but only a single move of 10' per inch in a 10-minute exploration turn -- that is, half again slower than the numbers in the table above (1/8 mph at the maximum). The OD&D rate is slow, while the AD&D rate is very slow.

So today I'm thinking that those movement rates are probably too slow. Consider the following: These days I'm in the habit of using half-hour exploratory "turns". That seems like about the right pace for wandering monster checks, and it's also scaled to the approximate number of encounters per game session (e.g., many tournament writing guides suggest planning on about 7 encounters in a 4-hour game slot, plus time for setup; and in my experience this is roughly accurate). If we set exploratory movement conservatively below the average Mammoth Park tour speed, at say 1/2 mph, then this conveniently converts to nearly MV (in inches) × 100 feet per half-hour. This proposed rate is shown below:


Obviously, that's roughly double the exploratory move rate given in OD&D Vol-3 (and 4 times the rate seen in AD&D). On the other hand, it's half the underworld tunnel move rate specified in module D1-3, on the order of 1 mph  (one mile per MV per day, that is, 12 miles in a day for a person with 12" move). This seems possibly about right. It also seems roughly to scale with what my players cover in real gaming time when exploring and mapping, which I like as a usable rule-of-thumb. Of course, extensive area searches, fighting encounters, etc., add to this simple movement figure. Movement through previously mapped/cleared areas can be at a rate of 5 times this (as in AD&D PHB), so around 2.5 mph, a bit less than normal walking speed.

Can you think of any better way to model dungeon exploration move rates with real-world experimental data?


31 comments:

  1. Other than getting a hold of spelunkers or stumbling on another set of quality YouTube videos, this seems about as good a source as one can get.
    It does "feel" right though. At least the right order of magnitude, and maps well to easy to remember numbers.

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  2. I'm not sure if it was a post of yours in the past that prompted me to think about this or some posts on Dragonsfoot or a similar site.

    I rule that the standard book rate assumes the PCs are pacing out distances and carefully mapping. Essentially, I'll draw the map for the players.

    Up to twice normal speed, they get descriptions and approximate distances (using the radius of their light source as a metric can yield fairly accurate measurement).

    Anything faster just gets some vague descriptions as to shape and size, little info on how far they've travelled, etc.

    Running would just get players info when they reached a decision point, no descriptions or indication of distance travelled: "you run forward, come to a branch to the right."

    I haven't run a dungeon game in a while, and I can't find the full text I wrote up right now, but I had some stuff about searching bound up there, too.

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    1. That's an interesting take on it, and well-justified. For me, I'm not sure I'd want to take the player challenge of drawing the map away at the base level.

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  3. Firefighters again?

    "The officer knows that one firefighter can cover about 1,000 square feet in five to seven minutes [...] each 1,200-square-foot apartment could be searched in approximately seven minutes".

    http://www.fireengineering.com/articles/print/volume-154/issue-2/features/searching-smarter-part-1-the-basics.html

    This is with full mask and SCBA air tank in a search and rescue scenario in a building that is on fire!!!

    I worked this out to be 1/5 mph or 0.2 mph which appears above in OED as Armoured Foot and in OD&D as Medium foot and also as the slowest cave tour.

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    1. I'm really glad you posted this addition; the extra calibration point for encumbered searchers adds a lot of confidence.

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    2. Oh, that's truly excellent. Thank you!

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  4. I have noticed often that applied maths/stats people try to build intricate models on flimsy principles/assumptions. My observation here is that there is no point being more precise than your ability to perceive the fundamentals will allow.

    The fact that explorers are moving through (i) an unknown environment (ii) where there are monsters in the dark from tiny spiders or god knows what upwards which are trying to kill them overwhelm any considerations you have made which ignore those facts.

    Armour and encumbrance would IMO have no bearing on the movement rate through unexplored lethally hostile territory.

    Cave tour guide stats have as much relevance as olympic sprint stats which I seem to recall you referencing before. Stats give a phony impression of accuracy unless you can make sound judgements first and in that case they are rarely necessary.

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    1. I've interpreted Delta as asking "what would exploration LOOK LIKE"? Since we only play at it we must gain some perspective from somewhere if we want to visualize it.

      For me this isn't about accuracy, it is about building a picture.

      If tours and firefighters are strolling or crawling at 0.2 mph then it seems (from this perspective) that an armoured foot soldier exploring at 0.07 mph (in AD&D) is moving so slowly so as to not jingle his armour! I had trouble imagining this prior to this post but now I've gained some perspective that I didn't have before.

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    2. https://en.wikipedia.org/wiki/Fermi_problem

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    3. If calculus can assume that a horse is a cylinder, we can make some assumptions about caves. :) Like a lot of game mechanics, it is about finding the sweet spot between Real, Believable, and Workable.

      I like Rando's point about having a mental hook to picture the action from. I can see the fighter in plate just moving point A to B at normal move rate while the thief is popping his head into every nook and far edge of a cavern or dungeon room.

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    4. This is what research looks like. The initial model is flimsy. The call goes out for more evidence. It gets better.

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    5. Dumb/rude comment deleted here.

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  5. "Can you think of any better way to model dungeon exploration move rates with real-world experimental data?"

    I have no idea how you'd actually get significant amounts of data to use, but the first couple of things that come to mind are real-world labyrinths (e.g. corn mazes), on the one hand, and haunted houses, on the other. The first might model exploration of unfamiliar territory in a very dungeon-like environment of rooms and halls of gradually-revealed layout, while the latter might model how people behave when they're on guard against attack and taking time to interact with the environment.

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  6. As part of my job as an architect I have walked thru and measured numerous buildings. While I've never been attacked by monsters in the dark I've got a pretty good idea of how fast you can reasonably map a place. For drawing and measuring a basic house it will take about 1-2 hours for 2 people (one to measure and one to write). So 5-7 rooms with about 15 min in each room - you're not too concerned about the location of a toilet in D&D but you are looking for hidden objects and other things. I once measured an indoor glow in the dark miniture golf place with only a headlamp for light - closest to a dungeon exploration I think I'll ever get!

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    1. I'm thinking property assessors might be a similarly valuable data point - moving through a building, taking detailed measurements, inspecting fixtures, etc.

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    2. That's an excellent observation, thank you! I love the headlamp mini golf scene. :-)

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  7. Prompted by this post, I went over some records for an urbex I did last year. Covered probably about half mile of walking through an abandoned factory in dim to dark conditions, uncertain footing, about as close to a dungeon as you're going to find in a major urban area. Fair amount of poking around, no mapping, but would have had time to make at least a ring and spoke.

    Average speed was in the neighbourhood of 0.5 mph on the way in (exploring, moving quietly, investigating things), on the way out would have been normal walking speed, or near enough - just a beeline for the exit.

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    1. That's excellent, thank you! I was initially considering setting the base rate at 0.5 mph, but decided to err on the more conservative side.

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  8. I would also say that I don't see any reason why wearing armour would slow down your exploration movement at all. It's already so slow.

    If you were knocking 25% off the time of an obstacle course, sure, but if you're already moving at 1/6 speed, I don't see that wearing 60lbs of armour is going to make any difference.

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  9. I think it would be very slow -- walking a premapped cave saves you all the dead ends and places which can be traversed but only at great time and difficulty. Also, often there are stairs or other conveniences put in.

    Follow the link to learn about the surveying of wind cave.

    https://www.nps.gov/wica/learn/nature/cave-surveying.htm

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  10. Maybe take your cell phone with Runkeeper and take a walk through woodsy wilderness on a moonless night with only a flashlight. Wander around for a couple hours trying not to twist your ankle or poke your eye out with a low hanging branch. Take rests as needed. Then, divide total distance (from runkeeper) by total wander time.

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    1. I did this a year or two ago:

      http://spellsandsteel.blogspot.ca/2015/12/forest-excursion-night-time.html

      The TL;DR is: Under almost ideal conditions, I averaged about 2mph.

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    2. Interesting that if we use Delta's proposed rates and switch from feet to yards for outdoor movement, we arrive at a movement rate of 1.35 mph for lightly-laden travelers - not far from your experimental figure.

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    3. Charles, that's a tremendous writeup, thank you!

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  11. Luzy = Awesome

    Here's some haunted house data from the internets:
    http://www.exit13hauntedhouse.com/faq/

    30 minutes (+/- 15) to explore 13K sq ft. That area (but not the time) includes the line. So let's call it 30 minutes for 10K sq ft.

    That is 3 minutes per 1K sq ft. Compare to an encumbered firefighter taking about 5 minutes for a similar size area...

    Here's a corn maze:
    http://www.marinicornmaze.com/
    1.5 hrs to explore 8 acres, or 20 minutes to explore 1 acre. There's 43.5K sq feet in an acre.

    Those come out to:
    Big Maze: 1/4 minute per 1K feet
    Small Maze: 1/2 minute per 1K feet

    The corn maze times are orders of magnitude faster... Likely because "adventurers" are only exploring a small percentage of the available maze area. Most of the maze is full of corn, not paths. So I don't think its the best analogue.

    I also considered that we can consider a 10' wide dungeon corridor as an "area" to search or explore. Every 100 linear feet is 1K sq ft of floor space. At the above rates that gets us the following feet in an hour...

    Haunted House: 20K linear feet per hour (3.7 MPH)
    Firefighter: 12K linear feet per hour (2.2 MPH)

    Finally, I think the haunted house numbers are perhaps best to simulate movement through an already cleared area. There is little to no pathfinding/mapping required. The mapping part is the really time consuming part.

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    1. That's good stuff, thanks for that!

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  12. As an additional thought, I think ENC may not really factor into exploratory speeds. The most time consuming tasks (mapping, probing for traps, looking out for encounters, etc) are the limfac... Not your raw movement speed.

    Raw speed is more relevant for pursuit, tactical movement, or movement through already cleared areas.

    I've got a lot of experience backpacking as well as moving wearing heavy kit for work. Generally only if going from Point A to Point B is the weight of the gear the lim fac. Obviously wearing heavy gear sucks and slows you down somewhat...

    I think the simple way to express this might be to say something like:

    "Exploratory speed is always at 200 feet per 10 minute turn, except when heavily loaded (3") move, when it is half this speed.

    Movement through previously cleared levels is equal to 100 feet per 1" of movement speed per 10 minute turn."

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    1. That's an interesting thought, although I might be leery of making that adjustment from the normal game. I do tend to prefer more of a continuous gradient rather than more highly discrete dropoffs.

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