Monday, March 29, 2004

D&D 3rd ed. movement rates, post #1:
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First of all, I want to say that I think the folks behind the 3rd (and 3.5) edition did a very good job at including enough detail about moving around for it to be tactically important, without bogging down. The simplicity of the system is brilliant.

My interest in this started when (over on the d-n-d blog) we had some people running behind some people on horses. Actually, my interest started before that, because my character's a dwarf, for whom movement rates are an important consideration. Dwarves have the racial disadvantage of having the base movement of a small character (20'), without the advantages (or other disadvantages) of being small (+1 to hit and AC, +4 to hide, less weight capacity and smaller weapons). [Parenthetically, a dwarf's speed doesn't go down if he carries more or wears heavy armor, so with some weight on him, he essentially reverts to what other normal-sized characters are like with the same encumbrance.]

So, let's talk about human speeds first, and compare horses later. Rules summary: the normal character base move is 30', meaning a move action in combat moves you up to 30'. Small characters (and dwarves) have a base move of 20'. A character can take up to two move actions in a six-second round, or if the character is all-out running, they can go 4 times as fast (for a human, that's 120' in a round.) The time scaling of movement is ridiculously simple: if your base move is 30' in a round, in a minute you're going 300', and for longer periods you're traveling at 3 mph. (That's multiply by 10 for distance in a minute, and divide by ten and change units to mph for longer distances.) For the larger scales, you can hustle, which means you go twice as fast, for an hour before you start suffering ill effects, and you can run (four times as fast) for a minute (or a little more if you have a high Constitution, but more than 3 minutes is nigh impossible.) Note that normal combat is hustling, since you can make two moves in a round. One last wrinkle: if you have the Run feat, your run is 5x your base move, instead of just 4x.

Note that this conversion cheats just a little: it would be exact if there were 6000 feet in a mile. Since there are only 5,280 feet/mile, this means that the long-term rate of speed (even walking) is a little bit slower over an hour than over a few minutes. A convenient simplification, and I can't really argue it's not realistic: I certainly don't walk as fast when I'm going for hours. It does mean that if you're traveling for half an hour, a good munchkin should try to convince the DM to use the ft/min and multiply by 30, rather than the mph divided by 2. :)

So, how fast are D&D speeds relative to the real world? Well, 3 mph is a brisk walk, and the average person can walk that fast all day with no trouble (assuming good conditions). 6 mph (hustling) is a ten-minute mile; from personal experience I can say that an average/healthy person can do this for an hour, and an athletic person can keep up that pace for longer.

Modern marathon winners run 26.21 miles in a little over 2 hours, or about 12.4 mph; in 1900, the record was around 3 hours, or 8.7 mph. Lest you think your D&D character isn't up to snuff, note that all these running rates are with virtually no weight, while a D&D character can run this fast in (light) armor and carrying considerable weapons and equipment. In addition, barbarians have a 10' increase in base speed, so they can hustle at 8 mph; the Longstrider spell has the same effect, and other magic effects (haste, Boots of Striding and Springing) can double the base speed, so characters can run (in armor) nearly as fast as a marathon champion, with a little help. In addition, a D&D character can go for hours at this speed, although this requires taking nonlethal damage. (I think it's fair to argue that marathon runners take nonlethal damage too). For example, any human 1st level fighter can run for 4 hours at 6 mph; this amounts to finishing a marathon in a little over 4 hours, which most of us can only dream of.

What about the shorter distances and time frames? At this point, I think it's safe to say that all the record holders and star running athletes are the equivalent of "having the Run feat." With that in mind, until recently (1954, when Roger Bannister proved it could be done), running a mile in under 4 minutes was thought impossible. A 4 minute mile is 15 mph, or 440 yards/minute. A running D&D human travels at 400 yards/minute, and can only do it for a few minutes; not quite a 4 minute mile. With the run feat, however, a D&D human travels at 500 yards/minute; it would take a lot of Constitution and even more luck, but if they could keep up the pace, such a character could run a mile in just over 3 and a half minutes, which would crush the current world record of 3 min 44.39sec. The chances of that are miniscule; however, a character with a high Constitution could easily run for 2 minutes (1000 yards), walk for a minute (100 yards), then run again and reach a mile in just under 4 minutes 20 seconds. Not too shabby. A barbarian can run even faster, and a barbarian with the run feat is scary to think about: such a character could conceivably run for 2 minutes, walk for one, and then run again and complete a mile in 3 min 26.4 sec, and with a decent Constitution, this could be done with regularity.

The aforementioned "barbarian with the run feat" is outrageously fast: in the other cases D&D characters are seen to be "larger than life" but still in the ballpark of today's athletes, a character who can run 200' per round is a cut above that. This character runs at just over 11 yd/s=22.7 mph, and can keep it up for at least a minute. In comparison, Michael Vick has run 40 yards in 4.25 seconds: that's 9.41 yd/s = 19.25 mph. Ben Johnson holds the world record for 50m at 5.55 seconds, which is 9.91 yd/s = 20.27 mph. As far as running for a whole minute goes, the world record for 500m (indoor) is very close to 1 minute; 500 m in 1 minute would be 9.12 yd/s = 18.65 mph. Conveniently, this would be 164' in a round: compare this with 150' (a human with the Run feat) or 160' (a barbarian without the Run feat). Pretty close, I think.

Considering the simplicity of the move system in D&D, they have done a marvelous job at making characters comparable to Olympians -- the peak of human ability, without overdoing it too much. As far as the 20' movement rate for Small characters and dwarves, I don't think there's anything in reality to compare it to -- it seems sensible that short-legged characters would move slower, and beyond that, comparing speeds with track and field records of people suffering from dwarfism seems just wrong.

Next post, I'll put up a little bit of background on horse speeds, and compare the D&D horse to the real world a little bit.

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