Saturday, March 17, 2007

Realistic Time in D&D

An analysis of the proper time scale in D&D follows. Let's start by considering movement. First, note that a speed of 1 mph is about 100 feet per minute (actually 88 ft/min, but close enough).

Consider an article on human gait, including standard military march times (http://en.wikipedia.org/wiki/Gait_(human)). Both original Chainmail and 3E D&D scale are pretty close to assuming that base move matches a standard "Quick March" speed, that is, about 300 ft/min (3 MPH). If we use OD&D movement (12" for an unarmored man), and a corrected scale of 1"=5 feet (i.e., 60 ft per move), then the proper scale round would be about 1/5 of a minute, that is 10 or 12 seconds. We can double this number for a good "Double March" speed (a sustainable jog/run at 600 ft/min, or 6 mph), or double again for the maximum run which can be sustained for a few minutes at most (say 12 mph).

(As an aside, consider a flat-out sprint which only lasts 10 or 20 seconds or so. Modern research shows that slower runners can attain about 15 mph, intermediate runners 20 mph, and the world-records for 100m and 200m sprints are held at a speed of 23 mph.)

Now let's consider a separate consideration: how quickly attacks take place in combat. This is a lot harder to pin down, unless we had real-life medieval combats taking place to analyze and time. The best thing I could come up with is professional boxing, using data from the "CompuBox Stats Archive" (http://www.compuboxonline.com/). I've taken a fairly quick, random sample of 3 different bouts (6 fighters) in each of the light-, middle-, and heavyweight classes. Each bout lasted a full 12 rounds (36 minutes plus breaks), and I've only considered "power punch" statistics, which in theory could actually do some kind of damage. (That is, I left out "jab" counts, which are presumably only maneuvering setups for actual damaging attacks.)

So, a few things become clear about the "sweet science" from this table (note the "P/M" column, which indicates average punches-per-minute). The number of punches thrown goes down as the weight class goes up -- presumably this would continue downwards when using heavy martial weapons? The overall average here is 9 punches/minute (but possibly only 6 if we take another step down in weight categories). That again argues for a D&D round length of about 10 seconds or so (6 per minute) -- that provides a base number of attacks; expert fighters, such as these top-level boxing professionals, conceivably have the capacity to increase punches up to 2 per round at this scale (or maybe 3 as an absolute upper limit for unarmed lightweights).

Note also that power punch success rate is only about 35% for all of these top-level fighters (i.e., 14-20 on a d20). I think this argues for an unarmed combat system which highlights a lot of defense and blocking capacities (say, at least -4 to hit with unarmed attacks). Recall that I left out jab statistics from these numbers; that successful landing percentages for those are even lower than the power punches shown here. Also consider that these fighters are receiving one or two hundred of these so-called "power punches" (with gloves) and continuing to fight, so individually only a tiny fraction of them can do actual hit-point damage in D&D terms.

Let's look at it from another perspective, like bow fire rates (http://en.wikipedia.org/wiki/Bow_(weapon)). It's said that a longbow could fire "as many as 20 shots a minute". But, consider a few other details: (1) that presumes a top-level expert bownman, (2) it considers a relative lack of aiming, as would be acceptable in a mass battle barrage, and (3) it also implies that "an archer could loose (shoot) 3 arrows before the first arrow hit its target"! Now, we certainly don't want to have to adjudicate a single arrow being in-flight over the course of 3 rounds or so. So what we should do is take these numbers and divide: 20/3 = 6.66 is the discrete number of arrows that can be carefully aimed, fired and landed sequentially, in one minute -- and hence the best number of rounds per minute. Again, we can use a 10-second round (6 per minute), assume carefully-aimed missile attacks, and allow top-level fighters to possibly make 2 (or maybe, at the very best, 3) attacks per round, and the result is quite close to real-life.

There are other reasons to support a 10-second round for man-to-man combat. (Another one that I like is to assume you can hold your breath for your Constitution, in rounds, and the result is again very realistic.) So, that's the final uptake on all this for my preferred games of D&D.

Conclusion: One combat round should last 10 seconds.

1. In the spirit of constructive pedantry: -

A Quick March is actually four miles per hour, not three.
Quick Time (the marching rate of a Quick March) is defined as 128 paces per minute at 33 inches per pace. Which works out at 352 ft/min, or exactly 4mph.

You don't get Double Time (which is considered to be a run, not a march) by doubling Quick Time.

It was originally defined by doubling Slow Time, which put it at 150 paces per minute (412.5 ft/min, or 4.69mph).

However, it is now defined as 165 paces per minute of 33 inch paces, which gives 453ft 9" per minute, or 5.16mph.

In the US it's a bit faster: 180 paces per min at 36 inch per pace, which is 540ft/min or 6.14mph -- which is the one that most closely matches your figures.

Hope this helps!

2. Good article. Please post more.

3. I can't contain myself: This is the single best analysis of a semi-controversial mechanic in D&D-like games that I've ever read. Severe kudos!

4. Peter, thank you! (Sometimes I do find myself coming back to this writeup myself, actually.)

5. ^ Also, I finally just inserted the CompuBox stats table that's been pending for about 5 years, ha! (Plus updated the broken link.)

6. If you want a good guide for actual Medieval weapon speeds, the Society for the Creative Anachronism is a good resource. I have a lot of SCA friends, and there are some people who have a lot of research on those subjects. Some of them are even gamers, and might have adjustments you can use.