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.

Logarithmic Scales

Previously I've talked about the logarithmic scales that Explore uses for measurements. An example of a logarithmic scale is 1, 2, 4, 8, 16. This is a very useful system for scaling things up/down, in particular by choosing the scales carefully you get +1 on one scale gives you +1 on another scale. For example, +1 weight corresponds to +1 height and also +1 lift.

I've been working on tweaking the scales I use, which has required coming up with some new progressions. Anyone playing the game doesn't have to care how I came up with the numbers, but over at Gaming Ballistic, Douglas Cole has been talking about why he loves the GURPS logarithmic scale so I thought I should briefly discuss how I came up with my scale rather than any other version.

In fact one observation I have from playing Explore is that the players don't need to even think about the scale to play the game, it's just the underlying reason why the game fits together without any sharp corners to get snagged on.

Doubling Every N

The first approach to creating a logarithmic scale is one where it doubles every +N (e.g. 2, 3, 4, 6, 8, 12… doubles every +2).

The scale I choose then is:

N, N+1, N+2, … 2N-1
2N, 2(N+1), 2(N+2),… 2(2N-1),
4N, 4(N+1), 4(N+2),… 4(2N-1),

For example, for doubling every +4 the scale is:

4, 5, 6, 7,
8, 10, 12, 14,
16, 20, 24, 28,

You then extend this in the reverse direction to low values:

1, 1 1/4, 1 1/2, 1 3/4,
2, 2 1/2, 3, 3 1/2,

This has several good points:

• It has integers for high values, nice fractions for low values.
• Each scale contains all the earlier scales, so all include 1,2,4... and all scales apart from the first two include 10, 20, 40 etc.

The downside is that at high values the scale has values such as 1024, instead of easy to work with numbers such as 1000.

Tenfold Every N

The alternative approach is to a tenfold increase every +N (e.g. in GURPS you have 1, 1.5, 2, 3, 5, 7, 10, 15, 20 etc.).

With this approach, however, if N is large (i.e. there is a slow increase) you get a lot of decimals instead of nice fractions. In our earlier doubling every 4 scale, we would be x10 every +13. This gives:

10, 12, 14, 17, 20, 24, 29, 35, 41, 49, 59, 70, 84, 100

You can tidy this up a bit, e.g. round to nearest 5 or 10, but below 10 the values become nasty decimals. 

1, 1.2, 1.4, 1.7, 2, 2.5, 3, 3.5, 4, 5, 6, 7, 8.5, 10,
(10), 12, 14, 17, 20, 25, 30, 35, 40, 50, 60, 70, 85, 100

This isn't an issue in some games, but a slow increase like this is exactly what has proved to be necessary in Explore.

Combining The Approaches

The solution I'm favouring is to use the doubling scale until you get to a value which is 10x a previous value and then switch to the 10x scale. For example you can switch at 10, 20, 40, or 80. (Note you cannot switch until after the scale has only got 1/2 fractions, i.e. above 2=>20 in the example.)

1, 1 1/4, 1 1/2, 1 3/4,
2, 2 1/2, 3, 3 1/2,
4, 5, 6, 7,
8, 10, 12, 14,
16, 20,
and then switch to 10x...(20), 25, 30, 35,
40, 50, 60, 70,
80, 100, 120, 140,...

Swapping from feet to inches, pounds to ounces

When you get to small sizes it can be useful to switch to a smaller unit, such as from feet to inches, or pounds to ounces. All scales contain 16, and almost all contain 12. Hence you can start the scale using the small unit (e.g. inches), and when you get to one large unit (e.g. foot) you start again at 1.

For example, there are 16oz to 1lb, so we can have

1oz, 1 1/4 oz, 1 1/2 oz, 1 3/4 oz,
2 oz, 2 1/2 oz, 3 oz, 3 1/2 oz,
4 oz, 5 oz, 6 oz, 7 oz,
8 oz, 10 oz, 12 oz, 14 oz,
16oz = 1lb
… and then restart at 1 on the lb scale.
(1lb), 1 1/4lb, 1 1/2lb, 1 3/4lb,
2lb, 2 1/2lb, 3lb, 3 1/2lb,...

Sometimes you might have to move the join point to be higher up so that the fractions are units on the smaller scale e.g. to avoid having 1 1/8 feet.

Why Logarithmic Not Exponential?
The values in the scale increase exponentially, so why do we call the scale "Logarithmic"? It's because we're saying Dwarves are height -4 compared to a Human. So the scale height in feet => height rank is the act of taking the logarithm of the height. This makes it like logarithmic scales in science.

Does this all matter?
Probably not!

Anyway I can now go back to talking about proper stuff. Next up is how much can you lift and how fast can you run - both of which incidentally use these scales - but which are also of some actual practical use!

Roll to see if you can climb the ladder?

This post is a follow on from what I said earlier about tracking / climbing / pick lock style skills – when the character attempts a complex multi-step task to solve a static multi-faceted problem:

You cannot role play through the resolution of this – sometimes the character will succeed, sometimes fail, depending upon the specific details of the task and the character’s strengths and weaknesses. If the task is simple compared to the character’s ability you would expect them to always succeed. Conversely, if the task is far beyond the character’s ability you would expect it to be impossible for them to succeed.

These two factors give some meaning, some sense of progress, to a character’s abilities; just like the warrior can now slay an Ogre, and the wizard can now cast that cool spell, there should be a feeling that you can now track the wolf when you previously couldn't. You want it not to be too narrow a gap between auto-success tasks and auto-fail tasks – if it is always “no roll” then everything is in effect predetermined by the referee. On the other hand, the random element should not be so large that novices regularly outperform experts. The random element here needs to be a reasonably narrow bell curve, and not open ended, so not the same resolution method used in combat. I’ll talk about the solution for Explore in an upcoming post.

The resolution system for a single attack in a combat is not a good fit for such situations. Single attacks in combat are extremely variable results, but as a combat comprises many such rolls, overall these combine to give much more predictable results. In combat situations, getting +1 onto all your skills means you're twice as likely to win a combat. Hence +1 on climbing needs to be a big improvement.

Some systems address this issue with a "take 10", which is a sticky plaster for the observation that the resolution mechanic used for combat isn't appropriate for the situation at hand. Others suggest only rolling "if your character is under stress". Although this sounds an attractive approach, under this system under non-stress situations everyone is equally capable at every task.

The solution I've developed is: roll a d6 and add your skill level, attempting to beat a score. Do this three times and count the number of successes.

No Successes: Complete failure. No retry. Possibly a bad consequence.

1 Success: Failure. Can retry.

2 Successes: Succeed.

3 Successes: Complete success. You completed it quickly and with panache. No more rolls needed for this skill today until you face a more difficult task.

Three Rolls are Better than One

It is true that if we’re rolling in non-stress situations then it should add interest to the game.

By rolling three times, you get a build up to the final result – a building sense of dread up to the third roll where you know you have to succeed or you fall.

Retries:

If you get a complete failure you cannot retry until you improve the skill.

If you get a failure you can retry, but it takes 10 times as long (1 rnd=>1 min=>10 min=>2 hrs=>all day). You can retry tomorrow but starting threshold is 10 times as long (up to max of 10 min).

Note that you will either get a success or a complete failure with only a few tries, so this process cannot go on for very many rolls, though it may take a long time in game time. 99% of the time it is decided in 5 attempts, but that represents spending all day at it.

For example, if you're trying to pick a lock whilst the count is at the banquet, then the first attempt takes 1 round. Your second attempt takes one minute. The third attempt is dodgy as it takes 10 minutes and there's a chance of a servant passing. It is also your last, as you  only have one hour until the banquet ends. You can come back tomorrow and try again, but the first attempt will take 1 minute this time.

Auto-Success Situations

Because the range of results is low, there are many situations where you don't roll as you're guaranteed to succeed. For example, you don’t have to roll every time you climb a ladder. When you do roll, it is because there is a chance of failure.

Chances of Success

The chances and how you improve are shown below:

Roll Needed	Complete Failure	Failure	Success	Complete Success
7	100%	0%	0%	0%
6	58%	35%	7%	0.5%
5	30%	44%	22%	4%
4	12%	38%	38%	13%
3	4%	22%	44%	30%
2	0.5%	7%	35%	58%
1	0%	0%	0%	100%

At the bottom you are unable to succeed at all. The +1 that gets you onto the first rung on the ladder gives you a stab at it (8% chance of success), but still 58% chance of complete failure. The next +1 makes you 26% likely to succeed, and now only 30% chance of complete failure. Another +3 makes you now 92% chance of success, and over half the time you get complete success, and failure is only a faint possibility (0.5%). Any better and you cannot fail.

The numbers in the table were generated using anydice.com which is a handy resource. For example, "output 3@3d6" gives the highest result of rolling 3d6.