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HMFY - Master Plan - January 2007
Master Plan - January 2007
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Dwarf Tossing in D&D (Part 1)

Warning: the following column has been rated MP-13 for gratuitous algebra and excessive equations.

This month, I'm going to climb down from my ivory tower and get a little more "applied" than usual. You see, I need some rules for a game I'm playing right now. I'm playing in the epic-level D&D 3.5 campaign. I have a Large-sized, half-dragon Barbarian with a Strength score of 36. When I'm raging, that goes up to 42.

To illustrate what that means, my character can take a leisurely stroll on a Sunday morning with 2,448 pounds of gear on him without breaking a sweat. That's over a ton that he can carry whenever. When he's angry, he can lift 16,640 pounds up -- or over 8 tons -- over his freakin' head! I like the simplicity of playing my big, simple, alcoholic warrior-prince & former leader of vast armies. He can perform all sorts of feats of strength, which is exactly what he was designed for.

Except that he can't toss a dwarf.

I've played GURPS for around a decade now, so I'm used to the game system having some answer for whatever crazy stunt I want to pull. You can imagine my disappointment when I told the GM that I wanted to throw something and see how far it could go, only to find that rules for throwing were very lacking. Now, in a more free-wheeling system, I could see just fudging the situation, but D&D is so rooted in the numbers that doing so -- which is something I do routinely as a GM in other systems and my players are happy with -- felt like a cop-out.

So we continued along without any epic caber tossing contests, and I decided to find some rules that would cover this for the next session. I did a bit of googling and my DM went to some forums, but we didn't find any answers. So, I figured that if I couldn't find native D&D help, I would import what I needed from another system, and GURPS came to mind.

Project: Dwarf Tossing in D&D
Scope: Rules addition that does not break current rules, concepts or base ideas in D&D.
Part: One -- Converting Throwing Stats from GURPS Fourth Edition to D&D 3.5

I should probably start this of by saying that going this route is probably a bad idea. GURPS attempts to root their numbers in the real world, while D&D roots their numbers in a game world. (Incidentally, I don't favor one over the other -- they both have their place.) At this very base level, the translation will be difficult at best. But that's no reason to not experiment and see what we get, right?

This experiment has two parts: generating the numbers & formulae I need and creating the rules that use them. This month I'll cover the first part, as there's a lot of math and it's a sizeable article on its own.

There are two questions we need to solve:

  • How heavy an object can I throw?
  • How far can I throw an object?

Since we're looking to convert something from GURPS to D&D, we need to know two things: what we're converting and what our baseline is.

Solving the question of "how heavy an object can I throw?" and "how far can I throw said object?" are handled in GURPS by Strength. In order to computer throwing power in GURPS, you need to know your Strength and your Basic Lift (which is derived from Strength). So, we know what we're going to be solving for in our conversion.

(Point of note for those familiar with GURPS: I recognize that there's a difference between the different functions of Strength, such as Lifting ST, Striking ST and Hit Points. For the purposes of simplification, although what I'm deriving is only for Lifting ST, I'm just going to refer to it as Strength or ST. That doesn't mean to imply that this method should also determine the other facets of Strength in GURPS.)

Unfortunately, we can't just go straight from D&D Strength to GURPS Strength. They're two sets of arbitrary, unit-less numbers that, while looking similar on the surface, involve too many assumptions to be strictly comparable. Lots of people have tried, and talking about it can stir up heated arguments on the various gaming forums -- rivers turn into blood, seas boil, that sort of thing.

This means we must look at derived elements to see if we can find an appropriate baseline. Looking over the Throwing section (GURPS Campaigns p. 355 or GURPS Lite p. 23), we see that answer the question of "how heavy an object can I throw?" involves Basic Lift -- a value rated in pounds rather than an arbitrary, unit-less number.

Now we have a start. If I want to convert numbers so that I can approximate my throwing power, I'll use the amount of weight on can affect as the baseline. After a bit of reading and thought, three potential baseline points come to mind:

  • The highest weight one can carry before movement is affected
  • The highest weight one can carry at all
  • The highest weight one can lift
The Highest Weight One Can Carry Before Movement Is Affected

Let's start by trying the first one. In D&D, you're not affected by encumbrance as long as the amount you're carrying is within your Light Load. In GURPS, you're not affected as long as you're within No Encumbrance. Taking that as our baseline, we get:

DLight Load-Max = GNo Encumbrance-Max

Now, I thought that there would be some merit to converting one's DSTR into DLight Load-Max without having to use the table (D&D PHB p. 162) to look it up. After a couple hours of poking around the math, I discovered three things:

  • Max Light Load is one-third, rounded down, of max Heavy Load.
  • Heavy Load can be roughly calculated by: DHeavy Load-Max = 25 * 2STR/5, for D&D Medium-size creatures with STR values of 10 or higher.
  • None of that is useful, since we don't actually need to calculate that amount -- we already have it and we should to use the values from the text.

Getting back to our point, the maximum weight allowed in GURPS No Encumbrance is equal to GURPS Basic Lift. This means we have the number we need to know how heavy an object we can throw, and can derive the GURPS Strength. So, if:

DLight Load-Max = GNo Encumbrance-Max
GBasic Lift = GNo Encumbrance-Max
GBasic Lift = GST2 / 5

Then:

DLight Load-Max = GST2 / 5

Solving for GURPS Strength, we get:

DLight Load-Max = GST2 / 5
5 * DLight Load-Max = GST2
GST = √(5 * DLight Load-Max)

This means that a D&D Medium-sized creature with a STR of 10, which has a maximum Light Load of 33 lbs., has a GURPS ST of:

GST = √(5 * DLight Load-Max)
GST = √(5 * 33)
GST = √(165)
GST = 12.85

For the purposes of displaying numbers in this article, I'll round to two decimal places. For game purposes, I won't determine how or when to round until the end -- doing so now would be premature, since we aren't done yet. Plugging those values into the throwing chart (GURPS Campaigns p. 355 or GURPS Lite p. 23), we get:

Weight (lbs)Distance (yds)
1.6544.96
3.3032.11
4.9525.69
6.6019.27
13.2012.85
16.5010.28
33.007.71
49.505.14
66.003.85
82.503.21
99.002.57
132.001.93
198.001.28
330.000.77
396.000.64

Of course, D&D uses feet instead of yards, but we were all taught that conversion in grade school, right? We’ll want to multiply every value under Distance by 3 when we're creating our chart rather than every time we want to use it.

We have found that once we have the Basic Lift translated, we can compute the equivalent GURPS Strength, which in turn gives us everything we need to compute max weight & distance. But let's take a look at the other two ways I listed that could be our baseline. Since they all deal with Basic Lift, we can simply solve for that and we'll get us to exactly where we need to be.

Before we do, though, let's generate the numbers we need for a comparison. A Medium-sized STR 10 character in D&D as a GBasic Lift of 33 lbs. and a GST of 12.85. My effectively Large-sized STR 42 character has a GBasic Lift of 5536 lbs. and a GST of 166.37.

Light Load Baseline
 GURPS Basic LiftGURPS ST
M STR 103312.85
L STR 425536166.37
The Highest Weight One Can Carry At All
DHeavy Load-Max = GExtra-Heavy Encumbrance-Max
GExtra-Heavy Encumbrance-Max = 10 * GBasic Lift
DHeavy Load-Max = 10 * GBasic Lift
GBasic Lift = DHeavy Load-Max / 10

Already, I can tell that this isn't going to work well, since DHeavy Load-Max is three times (roughly) the weight of DLight Load-Max, but GExtra-Heavy Encumbrance-Max is ten times the weight of GNo Encumbrance-Max. So while we're multiplying one side of the equation by three, we're decreasing the other by a factor of ten -- a significant difference. The point of this was to generate numbers to compare by, though. We'll have to change our formula for computing the GURPS ST as well.

GBasic Lift = GST2 / 5
GBasic Lift = DHeavy Load-Max / 10
DHeavy Load-Max / 10 = GST2 / 5
DHeavy Load-Max / 2 = GST2
GST = √(DHeavy Load-Max / 2)

That gives us the following for our examples:

Max Load Baseline
 GURPS Basic LiftGURPS ST
M STR 10107.07
L STR 42166491.21
The Highest Weight One Can Lift
DLift-Max = GLift-Max
DLift-Max = DHeavy Load-Max * 2
GLift-Max = 8 * GBasic Lift
DHeavy Load-Max * 2 = 8 * GBasic Lift
GBasic Lift = DHeavy Load-Max / 4

Unsurprisingly, we get a result that's incompatible with the first two, though it is closer to the first result, since Light Load is Heavy Load divided by 3. To re-derive our GURPS ST formula:

GBasic Lift = GST2 / 5
GBasic Lift = DHeavy Load-Max / 4
DHeavy Load-Max / 4 = GST2 / 5
5 * DHeavy Load-Max / 4 = GST2
GST = √(5 * DHeavy Load-Max / 4)

Using this method, our example creatures have:

Max Lift Baseline
 GURPS Basic LiftGURPS ST
M STR 102511.18
L STR 424160144.22

Now, this entire numbers game is all arbitrary, and I could keep generating baselines for the foreseeable future. The trick is picking one and sticking with it, so I'm going with the third formula partly. Being able to lift something over your head seems to be closer to the idea of throwing something that the concept of how much you can carry is, and it's the middle of the three estimates I worked out.

Simplification

Since this is simple a numbers game, I am free to change this up as much as I'd like. While any arbitrary changes would cause this to drift away from a purely conversion, sometimes to make a conversion usable requires a bit of tweaking. After all, who wants to figure out a square root in the middle of play if their Strength score is suddenly buffed up or reduced? Now that I have a formula that gives me some numbers I can plug into a chart and get information for, it's time to see about simplifying it.

The formula uses GURPS Basic Lift to derive the amount of weight that can be thrown and GURPS ST to derive distance. At this point, we should start calling them something else, like "Base Throwing Weight" and "Base Throwing Distance" respectively.

Base Throwing Weight is already simple, just dividing a number we already have -- maximum Heavy Load. Base Throwing Distance is what we need to look into simplifying. For that, let's turn two the two elements that define the Heavy Load we use in the first place: Strength & Size.

I'm going to look into Size first, because Size simply is a multiplying factor. Let's take the standard Medium-size STR 10 creature. The size multiplier for encumbrance is x1, so the maximum Heavy Load remains at 100 lbs. Dividing that by four gives us the Base Throwing Weight, or 25 lbs. Plugging that into the Base Throwing Distance equation, we get approximately 11.18.

Let's do this for multiple sizes:

STRSizeMultHeavy LoadB.T.W.B.T.D.RatioEst. Mult
10Mediumx11002511.181x1
10Largex22005015.81~1.41x1.5
10Hugex440010022.362x2
10Gargantuanx880020031.62~2.82x3
10Colossalx16160040044.724x4
10Smallx3/47518.759.68~0.87x1
10Tinyx1/25012.57.91~0.71x3/4
10Diminutivex1/4256.255.590.5x1/2
10Finex1/812.53.1253.95~0.35x1/4

In short, increasing the Base Throwing Weight by a factor of two increases the Base Throwing Distance by a multiple of the square root of two. I've thrown an "Estimated Multiplier" column up that approximates the value without actually needing to square anything. It favors Large, Gargantuan, Small and Tiny creatures and unfavorably disadvantages Fine creatures, but that is the price of a simplification, and I accept that as adequate.

Now that we're free of the effect of Size on our formula, we can turn to seeing what the effect of purely increasing the Strength score is. We know a few things here:

  • The formula for computing the encumbrance values is different for Strength scores of 1 to 10 than it is for 10 and higher. (10 works for both formulas.)
  • For the encumbrance values for STR 15+, you can simply take the value for (Strength - 5) and double it. This is because the encumbrance formula is exponential.
  • Most important: D&D doesn't make you do any math to figure out your encumbrance, it just tells you to look at a chart -- at least, until you start dealing with large Strength scores or different Sizes. So then why couldn't I just do the same thing?

Thanks to the power of Excel, I can use my formula to generate a chart and then just tell people how to use it and how to find values for their high Strength score or different Size. This does mean that I'll have two charts -- one you have to derive your own values for -- rather than two formulas. It takes up more space, but it's likely easier on the casual dwarf-tosser when they suddenly feel like throwing someone, and it's not as though the hardcore guy who throws a character every session can't just copy it down for quick reference.

What's Next

For the second part, I'll be creating the actual rules that use the numbers I generated her, possibly simplify this whole beast a bit more, and get my GM's reaction (and maybe even some playtesting) on the experiment. That'll either be next month or the month after, depending on our group's gaming schedule.

As far as my own reaction to this, I think this is far too convoluted to be a good set of rules. I don't mind the steps taken in the middle -- I like monkeying around with algebra and sometimes you have to for an RPG -- but I'm currently displeased with the result. I wouldn't be surprised if I end up simplifying this further for the second part. But I'd like to hear what you think.

As a final note on this project, I was willing to bet money that after I put this column up, someone would point out D&D rules for exactly what I was trying to do. No one has taken me up on that.

I'd like to point out to everyone that the Master Plan Podcast is up. I'd also like to apologize for not having a column out last month. Between changing jobs, the holidays, and other little things, last month's column ended up getting left by the wayside.

That's enough for now. Catch you next time, Masterminds.

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