Thursday, June 24, 2010

Movement Rates

I've mentioned on the S&W forums that movement rates have always baffled me and I've sat down today to try to work them out from the ground up. I think one reason they confuse me so much is that there are so many variables involved: encumbrance, indoor vs. outdoor, combat vs. exploring, even differences in speed due to species.

Let's try to constrain the variables as much as possible we'll talk about an unencumbered human walking outside of combat. (the whole indoors/outdoors seems an artifact of wargaming to me and I'm going to ignore it, last I checked I walk the same pace indoors and out).

Average human walking speed is a little less than 3 mph. Jogging is somewhere around 6 mph-- once you get around 8 mph people consider it running. And what about the top end? world record sprinting would be in the 23 mph range, with short bursts higher than that.

That works out pretty nicely; if we aren't too worried about realism we can say there are four movement rates that double in speed at each step:
  • walk 3 mph
  • jog 6 mph
  • run 12 mph
  • sprint 24 mph
Yes, your turnip-fed cleric is not going to be hitting 24 mph, but the doubling will make this very easy to remember so we can either wave our hands here a bit, or drop the walking speed to 2 mph and double from there. Which wouldn't be too far off; I think the actual average walking speed for Americans of all ages (don't forget your doddering wizards) is closer to 2.7 mph and the fastest rates are all recorded under pretty optimal conditions (smooth tracks, clear weather, no one chasing you with a long sword).

Okay, so lets see how the latter approach might work:
  • walk 2 mph
  • jog 4 mph
  • run 8 mph
  • sprint 16 mph
But why do we want rates at all? Seems like two reasons 1) to know whether you can outrun the bugaboo chasing you, meaning how long can you sustain the sprint, and 2) how far can you move in a typical combat round.

Let's look at 1. How long can these rates be sustained?

Sprinters can sustain speeds near 20 mph for 40 -50 seconds. So, if you consider a combat round 30 seconds, a character should be able to sprint for one round. That's easy to remember and elegant. Unfortunately, I tend to think of my combat rounds as 10 seconds-- 30 seems incredibly long for a brutal, non-ceremonial fight. Hmm, do I say players can sprint 5 rounds? I'll have to think about that.

How about the other speeds? We're calculating very roughly here, but I think the next tier of speed would be the 5000 and 10, 000 meter races. There you have people sustaining a pace of 16 mph and 14 mph for 12 and 26 minutes respectively. I'm going to go with that 12 minute mark and say it is closer to a turn. So, our characters can run for 10 minutes.

After that it gets less critical, people have sustained speeds of 6 mph on a treadmill for 24 hours. And it's probably less likely that such careful measurement will be required outside of combat. Average US marathoners maintain ~6 mph for 4.5 hours. We could say a jogging pace could be sustained for somewhere between 2-5 hours. I don't have a clear preference pulling me on this.

The walk pace can be kept up as long as you go without sleep. I'm no athlete and I've done 27 miles in a day that included going up and down Mount Whitney. So, yeah, characters should probably be able to do 30 miles a day without pushing too much , which equals 3 mph for 10 hours.

That's at least some rules of thumb. How about answer 2. from above. How far can you move in a combat round? Going with our second speeds above and assuming a tabletop inch equals 10 game feet, and also assuming my 10 second round (man this is feeling like the SAT or something) characters can:
  • walk 3 in
  • jog 6 in
  • run 12 in
  • sprint 24 in
Okay, I think that's enough for a part one. Let me know if I'm making any stupid mistakes or assumptions.


  1. Looks good except for the run duration. Having participated in a couple of marathons, I can say that a heck of lot of people can sustain a pace of 8mph for well over an hour. Now, if it were 12mph for a run, I'd buy the 10 minute assumption (still low for trained athletes). But a healthy adventurer could definitely go at an 8mph for longer than 10 minutes.

    That being said, I'm assuming *zero* encumberance. Add in even a small amount equipment and the 10 minutes estimate is looking more realistic.

  2. Thanks Risus. I started out with all my examples pointing to running being around 12 mph, then had the idea of reducing the whole scale while writing the post.

    Arrgh, this is so complicated. And I'm not even striving for realism, I just want to base my abstractions on something substantial.

    But, now that I think of it the base rate in S&W allows for up to 75 pounds! So maybe we can assume some gear for all these stats. So, characters have boots and belts and a weapon, probably rations, and can still manage 8 mph for 10 minutes.

    I'll have to do some more figurin'

  3. I like basing movement on real-world rates, but there are two complications I have yet to resolve. First, I'd like to convert the real mph rates as they are into usable figure-in-dungeon rates. This would require some creative choice of units (time and distance) that my poor math skills are not up to. Secondly, I fear that such rates would make dungeon exploring a speed competition. Maybe rates would be halved to reflect careful moving and allow saves vs traps or notice rolls, while full movement would preclude or limit these.

  4. I think we're on the same page here. I just had a thought . . . don't we just need to rates: walk and RUN!

    What are the other rates for? I was also thinking that encumbrance is all wrong-- it doesn't make you move much slower, it reduces how long you can move!

    A walking human unencumbered and a human carrying 250 pounds aren't moving at very different rates, but the second will not be going very far.

  5. I can say for certain that even lesser loads will slow movement, but I agree that walk and RUN!, as you put it, are the important numbers here.

    Can I ask, though, for Feet rather than scale-inches, as I am still sorting MV rates in my game, and conversion will be easier. :)


  6. Sure, my pleasure. This is a job for a chart . . . but in the morning :)