How I Learned to Embrace Encumbrance

Encumbrance is a tricky issue – it promises realism / believability but tends to feel like an accounting exercise whose only effect is to give a penalty to players – and who wants to keep on calculating a penalty?

I place a lot of store in the realism camp – and if I'm going to have it for the sake of realism then I want some attempt at realistic results, not arbitrary penalties. This helps get over the first negative aspect of encumbrance – at least when you've calculated it you feel like that the penalty is deserved.

The next aspect is the ease of tracking the total weight characters are carrying – I've found that by splitting equipment into carried / with your horse / at home, and then further dividing each section into major / minor items (not tracking the weight of minor items unless you’re going over the top with them), and with a column in the list for weight then there’s only a small amount of adding to do, it’s easy to do when neatly arranged, and (importantly) I've found that players change what major items they’re carrying quite rarely in practice.

Next up is the feeling of being penalised, with no way round it except to leave stuff behind. By basing encumbrance on the amount you can lift, then you get a choice when you improve athletics (which you will do as that improves your damage bonus) - you can either improve your raw speed, or you can improve your power and thus reduce the encumbrance penalty on your speed.

Encumbrance In Practice
In the last session the players encountered a 5’ wide chasm across the corridor; all except the Dwarf could jump it, whereas he had to take off his armour and throw it across first. The jump distances and the effect of encumbrance all felt right, and the lack of rolling to see how far the PCs could jump felt right – it all made sense in the fiction of the game. Flairin did offer to jump across holding Kazem's armour but the Dwarf likes to be self-sufficient. He could even have jumped a 4’ chasm giving Kazem a piggy back – but if that had been sufficient somehow I think the offer would not have been accepted!

The Rule
Given the weight carried and the character’s Lift, look up the penalty on the table below.

 This is then applied to move/jump (see this post) - table reproduced below:

For example suppose you have STR +3, AG +2, Rank 4 athletics (Power 2, Speed 2) – so one rank short of Gold Medal Olympian ability – which gives you Lift 5 (600 lb), Run 5 (110 ft/rnd, max 10 mins) as per the char sheet calculations below.

Suppose you want to run carrying 110lb: 

The enc penalty is from the 100lb row and the Lift:5 column to get a penalty of -4, so you are reduced to Run 1, which is 72 ft/rnd.

This is tracked / calculated together with the Athletics skill on the character sheet as below – the encumbrance is just the extra column at the end. If there’s no penalty then just leave that section blank:

In practice it is very quick to update this when necessary, or look up a result for an ad-hoc situation such as "Can I jump the chasm holding that sack?". In total Athletics and Encumbrance take up one twelfth of the character sheet, which is a reasonable amount.

Originally this table was a single column and each +1/-1 lift moved you one row up/down. In play however this became another rule you had to remember, and it’s clearer as this table. For example, if you have a -12 penalty, then +1 lift makes it -8 (one row up) NOT -11, but it’s easy to forget that.

Speed or Power – which is best?

Players have a choice of where to put their points – into Speed or Power. In the example above, the athletics of 4 was split into Power 2, Speed 2 – what if it was a different split?

If instead you had Power 3, Speed 1 you’d get Lift 6, Run 4, Enc -3, so Run 1 again which is 72 ft/rnd.

However with Power 1, Speed 3 you’d get Lift 4, Run 6, Enc -6, so Run 0 which is only 64 ft/rnd.

So for any given weight there’s a sweet spot for power versus speed, and the heavier the weight the more it leans in favour of power.

If you ever have an encumbrance penalty of -6 or more then you improve your speed more by improving your power. That’s why I’ve shaded those cells in the table – that’s where a lack of power hampers you.

How does this measure up to real life?

I want a baseline of what effect carrying large weights has on people’s speed. Fortunately some nutters in Gawthorpe having been conducting experiments!

Every year (since 1964) they hold “The World Coal Carrying Championships” http://www.gawthorpemaypole.org.uk.

The event consists of Men’s, Women’s and Children’s races that take place on Easter Monday. Men carry 50kg of coal and women 20kg in weight.
Adult races start from the Royal Oak public house, Owl Lane, Ossett and continue for a distance of 1012 metres to the finish line at the Maypole Green in Gawthorpe village.
(Please note your time will be recorded when your sack of coal hits the green).

So that’s a weight of 110 pounds carried for 3320 feet. How fast can they do it?

David Jones holds the record – he did it in an impressive 4:06 in 1991 and 1995, so that’s 3320/41 = 81 ft/rnd. 4 minutes is between a run (10 min) and a sprint (1 min) in my system, so I extrapolate that the record for 10 mins would be 72 ft/rnd, which is Run 1.

Astonishingly this is the same answer as my example above (almost as if I engineered it that way).

What is the formula behind the table?

The penalty is logarithmic, doubling every other row. The weight on the other hand doubles every four rows. That means the penalty is proportional to the Weight/Lift squared – which was the initial version of the rule. You could have a formula instead of a table - everyone would have a Carry value (approx. 1/10th the weight) and the penalty would be Weight/Carry squared. This would give a more fine grained result, but…

Why have a table instead of using the formula?

When you use the formula do this some values round up, some round down, and the effect of +1 speed or +1 power varies slightly. For example sometimes +1/+2/+3/+4 sometimes gives you a progression -8/-6/-4/-3 and sometimes -8/-5/-4/-3 and sometimes -8/-7/-4/-3. I like the outcomes of player choices to be clear, and the regularity of the table gives a clarity with observations such as “if your encumbrance penalty is -6 or worse then power is better than speed” is lost.

So in the end I opted for the table – you only have to look it up when the amount you’re carrying changes significantly, and you only fill in the values when you need them. The athletics and encumbrance tables fit onto one sheet of paper, and these are the only tables you need when updating your character sheet.

Why this formula?

The old version (the flawed one I referred to in the last post) was linear, not squared. That was simpler, and doesn't need a table, but the predictions it gives don't match with expectations. 

When I go for a run (or a walk) I can carry quite a bit before it starts to slow me down. Carrying more weight has a little more effect, and a little more, until it suddenly starts too feels too much, and then you find that it’s a real struggle. The straw that broke the camel's back?

The simplest way to model that is a squared rule, and it seems to give reasonable answers.

Simplifying for the Common Case

I omitted Encumbrance from my post on Athletics abilities in November because my old system had some flaws in it, so I’ve been working on a revised system (and playtesting it).

To recap, the rule for Athletics was that you put points into either Speed OR Power, these were adjusted by appropriate attributes and SIZE and HEIGHT, resulting in a bonus which you look up on a table to get a lift / run / jump capabilities.

Each +1 gives a percentage improvement, and it was scaled to give Olympian capabilities at +8.

In playtesting of the new encumbrance rules I discovered that athletics could be greatly simplified by a simple change in how the character sheet is laid out, so I’ll talk about that today and leave the Encumbrance rules until next time.

It's an application of a good general principle: things should be simplest for the most common case.

With athletics you get SIZE as a bonus on Lift, Survival and Kill, and HEIGHT-SIZE on Run and Jump. This means you end up with lots of boxes on the character sheet which are all zeros for humans!

Dwarves are also more complex than necessary - Dwarves are SIZE -2, HEIGHT -4, which would give them -2 in all categories. Except that in addition Dwarves get modifiers of +1 lift, +2 survival and kill, and -1 on Jump. So Dwarves have modifiers of -2 AND a +2 which cancel each other out. That's a lot of numbers for no gain.

Hence halfway through copying out character sheets to the new template I revised the template and started again!

Now I have a table (below) for races showing what the overall bonus is. There is no box on the character sheet for these bonuses, you just annotate the appropriate part of the character sheet with a bonus (just as you would for any other miscellaneous bonus). The top line (in italics) is the default, which gives you a starting point before any racial specific alterations. I've included 12' tall Giants as an example for a typical large humanoid monster, not because I've got Giant PCs (though there's no reason why you couldn't have a Giant campaign). You can see I'm being quite generous to Dwarves and Halflings.

Race	SIZE	HEIGHT	Survival	Kill	Lift	Move	Jump
			SZ	SZ	SZ	HT-SZ	HT-SZ
Halfling	-6	-10	-3	-3	-6	-4	-5
Dwarf	-2	-4			-1	-2	-3
Elf		+1				+1	+1
Giant	+10	+10	+10	+10	+10

So Humans don’t put anything at all onto their character sheet, and Dwarves simply put -1, -2, and -3 in the appropriate places. As with all simple things like this I wondered why I hadn't seen that in the first place!

The Cat Test

“The Cat Test” is a test I devised for calibrating my game in homage to the infamous deadly house cat in AD&D. It's statted up in Monster Manual 2 with 1-5 hit points and can do a max of 5 hp damage per round! The test is what's the chance in combat of a starting fighter versus a house cat, and versus a tiger.

This has its origins in a fight in my game between a panther and a giant rat - the panther was wounded, and there was scepticism expressed about the giant rat's chances to survive in real life. Delta then had a post on the stats of different cats in AD&D, which prompted me to dream up this test to run on Explore to iron out the sizing rules.

The Fighter
First up is the fighter. Here's an average first level fighter:

Fighter Template
Skills: Melee: 3, Parry: 2, Athletics:2 (K1), Unarmed: 1, Thrown: 1, Survival: 14.
Arms & Armour: Sword (P2 A2 K2) Shield (P3) Chain [4] Steel Helm [2].
Combat: Melee: P17 A5 K3 [8/11/14/17 (20)]
FR39 XP44

The first line is the skills, the second is what arms and armour they've got, the third is the combat bonuses (just from adding up items on the first two lines, e.g. Melee 3 & A2 from sword give Melee A5) The last line is the fight rating and XP you gain if you kill it.

I've called it a template as from these stats you can quickly determine the stats for a fighter of any level, or any size (e.g. a giant fighter); also template seems appropriate as a fighter is just one particular choice of skills, you can make up your own templates.

Adding levels: Each level you get +1 on all skills you are trained in, and +1 on survival (which is not actually a skill). Which means the fighter gets +1 parry, +1 attack, +0.5 kill, +1 survival every level. So @3rd level they'd be Melee: P19 A7 K4 [8/12/15/19 (22)].

"Level" here is slightly misleading; you improve your skills incrementally as you gain XP - it's only saves that improve when you gain enough XP to make the next level. The Fighter template is just a predefined way of spending that XP on skills. 

Changing Size: Size is included in calculating combat stats; the effect of increasing it is to give a bonus on kill and all your saves (where +4 size is double the weight). So size +2 would make you Melee: P17 A5 K5 [10/13/16/19 (22)].

Note that changing size doesn't give you any attack or parry bonuses. On the one hand being smaller makes you harder to hit because you're a smaller target, but on the other hand being bigger makes it more difficult to get past your defences and land a blow. By matching increases in kill with increases in saves, changing the size of both combatants has absolutely no effect on the fight. Two giants fighting is the same as two humans fighting.

Being larger does make you easier to hit for missile attacks, but only in that it reduces the range penalty.

I've described the Fight Rating (FR) before - it's attack + parry + kill + the middle save. It's a measure of how good at fighting you are. Your rating increases by 3 every +1 level, by 2 every +1 size. From this you lookup how many XP defeating it earns you (it doubles every +6 FR). From this you can easily approximate how well two combatants will fare in a fight by comparing the ratios of their XP squared.

The Tiger
I'm going to assume a man sized tiger would fight about as well as a fighter, and claws and teeth and dodging being as good as sword (P2 A2 K2) & dagger (P1 A1 K1), with a tough hide giving the same as full leather [4].

Skills: Melee: 3, Parry: 2, Athletics:2 (K1), Survival: 14+7.
Arms & Armour: Sword & Dagger (P3 A3 K3) Full leather [4].
Melee: P15 A6 K:4. [6/9/12/15 (18)].
FR37 XP36

 So from this we get the stats for a Tiger by sizing it up:

Tiger: Size 7 (600lb), Height -8 (3'6''), Length 8 (10')
Melee: P15 A6 K:11. [13/16/19/22 (25)].
FR51 XP180

The Pussycat
I originally had the domestic cat as a down-sized tiger, but while the lion has prey up to twice its size, the prey of a domestic cat is much smaller than itself, so I've reduced its kill by 3:

Domestic Cat: Size -16 (10lb), Height -28 (10''), Length -20 (18'')
Melee: P15 A6 K-15. [-10/-7/-4/-1 (2)].
FR2 XP1

That's the stats for a tiger, but -23 size, -23 saves, -26 kill.

Cat vs Fighter
So here's the answer you've all been waiting for...

Domestic Cat (1XP) vs 1st level Fighter (44XP): 1:1936.
Tiger (180XP) vs 1st level Fighter (44XP): 17:1.

These are only a ballpark figure and it gets less accurate the more extreme the comparisons so I ran it through my combat simulator which comes up with accurate odds: 1:700 for the domestic cat, 12:1 for the tiger.

The Tiger seems about right, and is quite deadly.

I think the pussycat's chances are still massively overrated, but I'm glad that it's in the right ballpark. In reality it would turn and flee rather than engage in a fight, but what if it is demonically possessed? You could add rules such as it always loses initiative the first round (long weapon advantage), or other rules for a small creature against a large one, but fundamentally it has a chance to kill PCs as a consequence of allowing PCs to have a chance to slay a giant.

Another day I'll talk about how to make interesting differences between the big cats.

Roll to see how far you jump?

I've been examining how in different situations you want different methods for resolving character actions – in some cases it should be swingy results (e.g. attacks in combat), some cases bounded results (e.g. climbing), some cases predictable results (playing the lute). The final case on my list is "Character is seeing how their body performs, without any external interference whatsoever".

What I wrote was:

The canonical example is running – as a runner I know that all races are really against yourself, it is how you perform on the day. I also know that the variation between my time on a good day and on a bad day is very small in comparison to the overall time. A 5% slowdown is awful, and 10% would be an abysmal performance. There might be more variation in the distances and heights you can jump, but it is a similar situation, as is the amount of weight you can lift. These are all skills where your ability should be “you can run *this* fast, you can jump *this* far and *this* high, and lift *this* much”. For these skills as the Referee you should choose realistic values for obstacles in the game world, whilst incorporating an element of chance. For example you might note that to roll the boulder takes 100+d% lbs force (depending upon how smooth it is). When a character decides to push it, you roll and find it’s 183lbs, you can then see if the character can move it or not. By rolling for it when the situation arises, and not beforehand, you've introduced tension and uncertainty. Until the player decides to roll it, you don’t know any more than the players whether it’s possible. The cat remains both alive and dead until the box is opened.

The skills that fit into this category - running, jumping, lifting - all come under one skill in Explore: Athletics.

Power or Speed?

Evidently in the real world athletes who train for running have a very different physique from weight lifters – it seems unreasonable to have characters who excel in both.

My solution is that each rank you take in Athletics you either improve Power or improve Speed. By combining the two into a single skill it forces you to either specialise in one or the other, or split between the two at a much lower ability.

You always get half your athletics rank as a bonus to damage, regardless of whether you’re specialising in Power or Speed.

For example, here is an Elf with Athletics Rank 4 (cost 8), ST 1, who has split their 4 ranks into 1 rank power, 3 ranks speed.

This Elf has a kill bonus of +3 (i.e. +3 damage).The power (1) and speed (3) are used later to calculate lift, speed and jump when they become of interest. The Power also increases the character’s weight.

Note that to be rank 4 for power AND speed would require athletics rank 8, hence cost 128 points - 16 times as much as the 8 they spent so far!

I left in the combat section above it as that’s got the column headings. That section contains the skill "thrown" which is your accuracy at throwing, whereas Athletics gives you the kill bonus, i.e. how fast/far you can throw something.

Real World or Fantastical Ability?

As mentioned in the last post, I have tweaked the numbers for progressions. Previously +2 was doubling in weight, now it is +4; previously +7 was world record ability, now it’s +8 (rank 5, stat +3). This means ranks 1-5 are “real world ability”, ranks 6-10 are “fantastical ability”. You can cap athletic rank at 5 if you want a historical rather than a fantastical game.

Weight Lifting

For weight lifting, your bonus is Strength + Size + Power, which gives you a weight in pounds on the table below. This is a dead lift, i.e. pick something up of the ground just enough to move it.

	-3	-2	-1	0	1	2	3	4	5	6	7	8	9	10	11	12	13
Lift	140	160	200	250	350	400	500	600	700	800	900	1000	1200	1400	1600	2000	2500

Note +8 (+3 stat, +5 power) gives you a dead lift of 1000lbs (the current world record), and +4 equates to double the weight lifted (as per the weight of a character). The average value (250 lbs) seems reasonable.

As this is a game-design-post, not a how-to-play-the-game post, I'm talking through each of the athletics abilities separately. At the bottom of the post there’s the combined table for all abilities and the corresponding section on the character sheet. There is some complexity, but as players only have a two decisions to make (athletics rank, and the speed/power split), there's only one table, and the character sheet guides you through the process, so character generation and improving skills are quick, and my players appreciate having a description of their character’s abilities they can relate to.

Running & Walking

Movement is calculated for four different types: Sprint (max 1 min), Run (max 10 mins), Jog (max 2 hrs), or Walk (all day).

Your bonus is Stat + Height – Size + Speed, which gives you feet / round looked up on the table below (a round is 6 seconds).

The stat is ST for sprinting, ST/AG for run, CO/AG for jog and CO for walk. (By ST/AG I mean the average of the two stats, rounded up.)
This means that different characters excel at different distances, and it is even possible for you to be no faster say at sprinting than running (though you cannot be worse).

It isn't affected by your height (as that doesn't seem to make much difference) but instead by your build (Height – Size) which gives Dwarves and Halflings a penalty, Elves a bonus.

The walk speed is also the number of miles per day (assuming you average 9hrs walking per day).

	-3	-2	-1	0	1	2	3	4	5	6	7	8	9	10	11	12	13
Sprint	64	72	80	90	100	110	120	130	140	150	160	180	200	220	240	260	280
Run	48	52	56	64	72	80	90	100	110	120	130	140	150	160	180	200	220
Jog	36	40	44	48	52	56	64	72	80	90	100	110	120	130	140	150	160
Walk	28	30	32	36	40	44	48	52	56	64	72	80	90	100	110	120	130

A bonus of +8 (+3 stat, +5 speed) corresponds fairly closely to world record performance: sprinting is 43.7s for 400m, running is 3:30 for the 1500m, jogging is 2:06 for the marathon.

I've gone for the rate of increase being halved compared to weight lifting (i.e. +8 is double) both as this gives more realistic values, and it fits with kinetic energy being proportional to velocity squared.

Average walk speed (36 ft/rnd) is 4.1 mph. With no rest at all, average walk in 24hrs would be 98 miles, so there probably needs to be some sort of limit here.
Note that each line is the same as the last, but shifted three cells. It was originally a single line, with Jog/Run/Sprint giving you a bonus of 3/6/9, but in practise having four lines in the table is easier to work from than having one long row with bonuses.

Jumping

Your bonus is ST/AG + Speed (for long jump) or AG + Speed (for high jump), which gives you feet on the table below.

You also gain a height bonus when jumping – if jumping to catch something you add your height, if diving onto or over something you add half your height.

For example, in the traditional high jump and long jump you get to add half your height. If you jumped up to grab hold of a ledge, or the long jump was to grab hold of the lip on the other side you'd add your full height.

Note that the physics of the height bonus work the same for both long jump and high jump, except that for the long jump that's strictly the "direct distance" from your centre of gravity to the target. This is only be important if the long jump distance is small compared to the height, hence:

At most you can double your long jump distance when adding this height bonus.

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

High Jump

8''

10''

1'

1' 3''

1' 6''

1' 9''

2'

2.5'

3'

3.5'

4'

5'

6'

7'

8'

10'

12'

Long Jump

3' 6''

4'

5'

6'

7'

8'

10'

12'

14'

16'

20'

25'

30'

35'

40'

50'

60'

The distance you jump is proportional to the square of your speed, so the rate of increase is double that of running, hence +4 doubles the distance you jump.

World records for high jump / long jump are 8ft and 29ft. Both of which when reduced by half height mean +8 should be 5' and 26', and the table gives 5' and 25'.

Swim

Your swim speed is just one quarter of your standard movement speed. This gives reasonably close values to the world records for the 100m (sprint) and 1500m (run) swims (there aren't records for the longer distances). I doubt the time it takes you to swim something will come up in play very often, but you can use it as e.g. you need to be able to swim at this speed to be able to swim across without being swept away.

All together

The Elf player now completes the athletics abilities section on the character sheet. They copy the Power 1, Speed 2 across from earlier and fill in the other details. Each row is just summed from left to right, then at the end you look up the value from the table below. Halfway there is a subtotals column (surrounded in bold) is so you don’t have to recalculate the full sum every time you go up a rank.

You look up the values off this table:

For example Run is 1 + 1 to give subtotal 2. Then you add Speed 3 to get 5. Run of 5 is 110' per round.

In practice the players never need to read through any rules, you just show them how to fill in this section the first time it’s needed and they soon pick it up. It also (importantly) isn't needed at character creation, but when it's first used.

Encumbrance?
The performances here take no account of encumbrance. I've been calculating this and applying a penalty to speed, but it needs revising, so I'll leave that for another day.