12 December 2010

Granular Skill Checks, and Interpolation

I just read a discussion in the CBT forums (Thanks PiP!) about the "granularity" of skill rolls in Battletech. The basic problem is that skill level changes in the boardgame make a BIG difference in play, but if you are running A Time Of War (Battletech roleplaying) then you want may small changes so that characters can improve gradually in many small steps - as opposed to 3-steps to a Superman.

I'll keep this discussion about the Battletech RPG, but these comments should apply to any game where characters have skill levels that seem too granular. I originally posted this whole thing in the CBT forums, then UN-posted it because what I had was broken. Now it is fixed, but much longer, so I hope nobody minds that I'm linking back to myself.

One way of doing this would be to use a different random distribution for skill checks. The second editions of the Battletech roleplaying game (Mechwarrior) uses 2d6 rolls just like the boardgame, and all skill were very granular. The 3rd edition of the game made a switch to 2d10 "exploding" dice, which greatly reduced the granularity problem, but suffered because it was difficult to make meaningful improvement in character skills.

There are also various "house rules" for doing the same sort of thing, but these generally require changing other aspects of the game to balance out the change in probability distribution. For instance you might switch to a 2d10 or 4d6 to-hit roll. There is less granularity now, which is good for your RPG, but the game has changed! On this new scale a +1 or -2 modifier will have relatively less effect or results, potentially "breaking" the usual balance of the game. You might fix this by adjusting all these modifier, but you won't ever get the original balance back this way.

I have an alternate suggestion: Add a decimal point to the skill levels, and an extra 1d10 roll when rolling for a skill check. Differences between Battletech skill level are BIG changes, so the idea is to add steps in-between. For example, instead of Gunnery 5 and 4, some possible skill levels are 5.0, then 4,9, 4.8, 4.7, 4.6, 4.5, 4.4, 4.3, 4.2, 4.1 and finally 4.0. Likewise any skill level, just adding a fractional skill level to it. There is a word for this - "Interpolation". We can interpolate between whole number skill levels, filling in with smaller changes in probability.

To use this, calculate the target number (TN) normally adding the skill level and any modifiers, and round the final number down. Make the usual 2d6 roll;
if this is less than the TN, you fail;
if this is more than the TN, you succeed;
if you roll exactly the target number, then you must also roll the 1d10, read it as 0-9, and this must be equal or greater than the decimal in your skill to succeed (if the decimal is "0" then this always succeeds, no need to roll).

Example: Suppose the base gunnery skill is 3.6, and after various modifiers the target number to-hit is 8.6, which rounds to 8. You roll 2d6 and ...
On a 9 or better you hit,
On a 7 or less you miss,
On exactly 8, you roll 1d10 (0-9), and if this is a 6,7,8, or 9 then you hit, otherwise you miss.

With TN=9 probability of success would be 0.278, and TN=8 it would be 0.417. The effect of the decimal in the skill level and the 1d10 die roll is to interpolate, or smooth out, between those two probabilities. The final probability of success for a TN of 8.6 is 0.333.

This gives 10 steps of skill improvement to every 1 in the regular rules, which ought to be fine-grained enough to satisfy the pickiest Game Master. In fact it may be too fine, and you might want to restrict it to just 5 steps (.0, .2, .4, .6, .8) or even 2 (.0, .5). Further, you will need to adjust the experience needed for fractional skill improvements accordingly. If it cost 100 experience points to improve Gunnery skill from 5 to 4, then it should cost about 10 to improve from 5.0 to 4.9. Most GM's love to tinker with this sort of thing anyway, so I'll leave the application in your capable hands (or fangs, tentacles, whatever).

Now the really good news - interpolating skills does not "break" any other parts of the game by changing the probability distribution the game is designed on, it just smooths it out, so a +1 or -2 modifier still has the same effect it always did. There is nothing special about using 2d6 with this either, so you might easily apply this to any RPG with granular skills.

Here is a chart with the probabilities of success on a 2d6 skill check. The way I have set this up makes it look a bit like a wavy staircase:
Probability of success on 2d6 with standard skills
You could walk up those steps! And the granularity is obvious. This chart has target number up to 13 because I need to show the probability go all the way down to zero for the next chart. Now a chart showing the same for interpolated "Skills with a decimal":
Probability of success with interpolated skills
Nice and smooth. If you look really hard you might notice this is actually 11 straight line segments joined together. This method of interpolation really just connects the dots between probabilities for whole number skill levels.

Now we have wiped out the granularity problem, but at the cost of some extra dice rolls. If you don't want to roll so many extra dice, you could make a single 1d10 interpolation roll (after fire declaration) and apply it to all skill checks results for that turn. This will be weirdly granular, because it is like changing your skill level randomly from turn to turn, but it will average out to the same effect over the course of many rolls.

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3 comments:

Saxywolf said...

Nice.
Not that I play the RPG, but it seems like a really simple way to add in-between skill levels.

EastwoodDC said...

I don't play the RPG either, but our local group often play extended continuing campaigns* where pilots might have the chance to improve. I might try to talk the guys into trying this.

* currently the Sword and Dragon scenarios.

skiltao said...

I like how smooth that curve looks. And once you have those gradations in skill, it's not hard to slice difficulty modifiers equally fine. (Of course, half the reason to switch to another die is if you *want* to change the curve; for example, I remember MegaMek players complaining that extreme die rolls happen too often.)

Interpolation does make skill improvement slower and more expensive, but that was only half the complaint - adding steps between the bottom 5 skill levels does nothing to make the top 5 skill levels more useful. Well, I suppose that interpolating half-steps would let you compensate by setting your BT skill to half of your RPG skill, but I think your intent was to avoid extra modifications.

And I'm surprised how rarely these discussions acknowledge it, but there's another approach to all this: encourage players to spend XP for momentary bonuses. More "experienced" characters enjoy many small improvements, and everybody's permanent skills advance more slowly. (You just have to price it right.)

Players are always shocked to read "elite" characters (in the oldest scenario books, usually) rated with 4g/5p skill - I bet they're so low because the first edition RPG assumed they'd be using their XP (like "Edge" in modern parlance) to get out of tight scrapes.