A crunchy problem

[Jasper]

I'm tinkering with mechanics for a science fiction game now; specifically the rules for warring starships, and the damage calculation for the guns.  Now, there are three different "inputs" that have to get into the calculation to produce a final damage rating: damage rating of the attacker, armor of defender, and a concentration/spread rating for the attacker that describes how much the attacking fire is affected by that armor.

I've come up with several options already, but I'm searching for the fastest kind of mechanic I can have -- i.e. the least handling time possible but which still produces reasonable results.  The exact distributations don't matter much, but the end result of the mechanic should be a damage rating within a certain range: from (Armor*Spread) to (Damage).

My options thus far are as such:

1. Damage - (Armor)d(Spread)

The main problem with this is that it employs many kinds of dice (a single kind would be preferable) and more importantly, by doing so really limits the range of Armor and Spread.

2. (Damage)d6, with each die capped at (Armor - Guns) -- that is, thrown out if higher than that value.

The problem with this is that it doesn't exactly follow the original formula, and the range on the damage is fairly limited (rolling more than 8 dice is not so good, since there will be a lot of shots to roll for).

If I were doing it on a computer, I would have an ideal situation and would make it look like #1:
Damage - RND(Armor * Spread) = Total Damage

Obviously, there are many possible variations, but in general working three inputs into a mechanic is messy; most games have two.  The only standard RPG mechanic that does take three is target numbers and successes (where you can vary number of dice, type of dice, and target number).  But that's not at all ideal because the total output will be so low (and never more than the number of dice rolled), which is a bit too granular.

Has anyone seen or thought up a mechanic that could fit my bill?

[Le Joueur]

...There are three different "inputs" that have to get into the calculation to produce a final damage rating: damage rating of the attacker, armor of defender, and a concentration/spread rating for the attacker that describes how much the attacking fire is affected by that armor.

...I'm searching for the fastest kind of mechanic I can have -- i.e. the least handling time possible but which still produces reasonable results.

My options thus far are as such:

1. Damage - (Armor)d(Spread)

2. (Damage)d6, with each die capped at (Armor - Guns)

[3.] ...On a computer, Damage - RND(Armor * Spread) = Total Damage

[4.] The only standard RPG mechanic that does take three is target numbers and successes (where you can vary number of dice, type of dice, and target number).  But that's not at all ideal because the total output will be so low (and never more than the number of dice rolled), which is a bit too granular.

I'd apply #4 a little differently.  Follow:

Damage = Number of die thrown (all the same type)

Armor = Target number

Spread = The number of 'of a kind' needed to be rolled.[/list:u]If Spread is one, then every die that exceeds the Armor is a hit. If spread it two, then every pair - exceeding the Armor - is counts as two hits (each 'one of a kind' is now a miss).

For example; say your Damage is 9d6 and you roll 4, 2, 6, 2, 1, 6, 3, 3, 2.
Armor 1 and Spread 1 = 8 Damage
Armor 1 and Spread 2 = 7 Damage
Armor 1 and Spread 3 = 3 Damage
Armor 1 and Spread 4 = 0 Damage
Armor 2 and Spread 1 = 5 Damage
Armor 2 and Spread 2 = 4 Damage
Armor 2 and Spread 3 = 0 Damage
Armor 3 and Spread 1 = 3 Damage
Armor 3 and Spread 2 = 2 Damage
Armor 3 and Spread 3 = 0 Damage[/list:u]Handling time is pretty quick:

[list=1][*]Roll Damage of dice
[*]Set aside all Armor or less
[*]Clump by number (suggests fewer-sided dice for fewer clumps)
[*]Set aside clumps smaller in number than Spread
[*]Count remaining dice for Total Damage[/list:o]Not the most elegant solution, but I hope it shakes loose some thoughts on other potential solutions.

Fang Langford

[szilard]

It's a bit hard to figure this without knowing how numbers might relate in size and what you might find to be useful outputs.

How many different ratings for Armor and Spread do you expect to have? If not many, then have a little chart for the intersection of each armor-spread combo (call it the Threshold). I expect this would likely be N(Armor*Spread) from what you said you were going for.

Then take the Damage rating and subtract the Threshold from it. You get a number. Roll that many dice. Or whatever.

I don't really get why you think the formula for what I call the Threshold should work, though. As you have it, increasing Spread always decreases damage - which is only true if the target is armored equally everywhere (which might be an assumption you are making).

Stuart

[Shreyas Sampat]

I seem to recall Walt, in some older thread, posting about a mechanic with a randomness dial.  This seems to correlate nicely with your Spread, and I think it can be tweaked to work with your other dials as well:

Set a randomness level, from 0 (totally stat-sensitive) to 9 (highly random).

Roll a d10. As long as you keep rolling less than or equal to the randomness level, roll it again. Count how many rolls you make before failing to roll the randomness level or less. (Don't count the final roll that exceeded the randomness.) Note that there's no point in actually rolling if the randomness is 0; the number will just be zero.

Now roll any 50-50 chance, to determine whether the number you just got is added to or subtracted from your skill level. Do the addition or subtraction, and compare the result with whatever the target is.

So,  this randomness roll represents the effects of Spread.
Unfortunately, this is open-ended, which doesn't fit your stipulations, but maybe it gives you something to think about.

[Jasper]

Szilard,

For the damage input, the range is fairly broad, going anywhere from 1 to about 30.  Armor and Spread both can range somewhere from 1 to 6, though a little more range (up to 8 say) would be preferred.  I am also indeed assuming that ships have equal amount of armor everywhere -- it's just not that detailed of a simulation.

Four Willows,

I could indeed make something potentially useful out of that, perhaps like:

Damage - (d6 rolls until one exceeds Armor, results summed)  with an absolute cap on the number of dice rolled equal to Spread.

It's a very cute mechanic, and one I'd like to use at some point, but the handling time is a bit higher, it's unfamiliar (not necessarily all that bad, I know), and the aesthetic -- of slowly accumulating damage with many rolls -- isn't as great as some of my other alternatives.  A cool idea though.  Thanks to both you and Fang for giving me things to mull over.


I have tentatively settled on a mechanic for now, and although it wasn't a clear pick, it fits the bill in all areas, and I needed to just choose something to work with.  It's definitely kind of weird, and unfamiliar though:

Damage - Armor(d6) w/ each die cutoff (that is, thrown out) at Spread.

Thus, if you have Damage 10, Armor 3 and Spread 4, you'd roll 3d6 for armor.  Say you get: 2, 4, 5.  The four and five are both equal to or higher than Spread 4, so they get thrown out, leaving you with jut a 2.  Subtract from 10 for final damage of 8.


It's "weird" for three reasons: it's atypical for the defender to be rolling dice on an armor resist type roll without the attacker rolling anything; my "cut-off" mechanic is unfamiliar (at least I've never seen it before, IIRC); and cut-off has a somewhat strange distribution (diminishing returns on better -- that is lower -- Spread).  I kind of like trying out new and strange mechanics, just to get out of the old mold, and see how it works though.  In addition, I think the player interaction and pacing/handling time will actually be better with this than a more traditional scheme where the attacker rolls damage:

Usually, the attacker rolls to hit, hits, and then grabs a heap of dice to cackle of maniacally before tossing them and counting up the results while the defender can do nothing but passively (and perhaps hopelessly) look on and await his (ship's) doom.  It's a rather one sided process, and in the case of less mature players, might be more likely to allow boredom or resentment (by the person getting attacked) to come up.

My system, on the other hand, while hardly being a magical way to dispell pettiness, does at least involve both players more actively throughout the whole process, which in my mind is a Good Thing.  The pacing of play is also a lot better, since with two people things can go really quick: attacker determines a hit and says so, calling out damage at the same time; defender, already ready, rolls his handful of dice; just as they land, attacker relates the Spread; defender throws out dice and counts the rest; then subtrats from original damage, and marks it on his sheet.  Very smooth, if I may say so :)   Do those seem like real selling points to people? (Of course, only a test run will really tell.)

Cheers.

[contracycle]

Another offering... I made this comment on another issue and eit was not taken up.  There are analogies with the armour penetration scenario:

Light, when acting as a wave, has both amplitude and frequency. Frequency determines colour; amplitude is proportional to energy at a given frequency. At the very least, this permits another layer of distinction: Bright and Dim.

Another angle which might be exploited is the photoelectric effect, one of the "particle" properties. Light will knock electorns off atoms if it is above a certain minimum frequency, depending on the matrial. The number of electrons affected is proportional to the amplitude/intensity, and the velocity with which they are ejected is proportional to frequency.

Hence, you end up with an array; the colours are arranged by severity of effect by frequency from Red (lowest) to Violet (highest), and are governed by qualifiers inidicating Brightness (quantity of effect). Coloour (frequency) is a minumum value; if you don't have sufficient frequency ("blue enough") no amount of Brightness will help. If you have exceeded the minimum colour, both Brightness and more blue will increase the effect (differently).

[szilard]

Another quick question:

Is Spread based on weapon type? Degree of success on the to-hit roll? or both?

Stuart

[simon_hibbs]

The way I see it there are three fixed factors here, and one random one.

1. The force with which the weapon strikes it's target. That's likely to be pretty fixed for most weapons, for which reliability of effect is generaly a high priority design goal.

2. The Spread of the weapon (or inversely, it's Penetration).

3. The durability of the target's armour.

4. The exact position and angle of the strike, the underlying structure of the target at that point, and any unforeseen circumstances that modify the previous assumptions.

This is somewhat different from your typical fantasy game where we're modeling sword blows - in that case the force with which the weapon is wielded and it's effectiveness are far more variable depending on the offensive move being made, the part of the weapon that contacts the enemy, etc. In most modern and futuristic weapons, a lot of engineering effort is expended to eliminate chance from the equasion as much as possible. Even so, unforseeable circumstances still come up all the time.

So what's realy happening is we've got four factors, one of which is random. That no help at all! I think the best compromise is to pick one factor and randomise that, leaving the others as fixed values. This achieves two things :

1. We only have one random roll to worry about.

2. The other two factors are fixed, so we can make a calculation based on them once, producing a fixed value for that weapon against that target. All subsequent instances of that weapon hitting that target can re-use the value we calculated the frist time, saving us a lot of time and brain cells.

Since Armour and Spread are obviously very closely related values, both relating to armour, I'd make those two the fixed values. In fact your formula combines them by multiplication, so we realy have no choice but to make them the fixed value and randomise damage. This gives us a formula something like this :

DamageD6 - (Armour * Spread) = Final Damage


Simon Hibbs

[Jasper]

Nice analogy there, Contracycle.  I like it, though I'm not sure quite what to do with it :-)  It seems more complicated than the scenario itself....

Simon,

Spot on in seeing that we really have four values, one of which is random.  I saw that early on, but knew it would be a mess, so did just what you suggest by making on of the others random instead.

Your final suggestion is not a bad one, but what you suggest a standard goal of engineering is actually another goal of mine for this syste; one which I think I neglected to make clear.  I would (ideally) like the randomness of the situation to correlate to armor, so that if you attack a ship with no armor, the amount of damage you do will be constant (or have very little variation).

This is partially so that armor means a little more, partially a general aesthetic choice (i.e. in keeping with the high-tech theme, as you discussed), and also with the thought that the attacker has already rolled to hit, and to see his shot totally fizzle down to one or two points, just by luck, even with no armor to oppose him, is anti-climactic, if you know what I mean.

I don't mean to keep coming up with new objections every time someone proposes something ("Well...no, that's not what I want either! bleh!"), and apologies if it seems so.  This was in fact a major issue that I had considered with several early options.   All ideas are, of course, gratefully considered though, since if nothing else they will give me something to think about, and perhaps roll together into something appropriate.  

PS. Just wrote up all the combat rules today -- still with the tentative mechanic I outlined.  Now campaing rules!

[simon_hibbs]

I would (ideally) like the randomness of the situation to correlate to armor, so that if you attack a ship with no armor, the amount of damage you do will be constant (or have very little variation).

This is partially so that armor means a little more, partially a general aesthetic choice (i.e. in keeping with the high-tech theme, as you discussed), and also with the thought that the attacker has already rolled to hit, and to see his shot totally fizzle down to one or two points, just by luck, even with no armor to oppose him, is anti-climactic, if you know what I mean.

Although perhaps realistic? "A hit! Excelent, what damage did we do? Ah - we blew up the storage pod containing their entire ship's supply of toilet paper - prepare to launch another salvo!"

Something else occured to me. Presumably it's preferable that your armour modifier value (spread) is usualy 1, so that for most weapons there is no calculation necessery. For this to be true, this means most weapons will be highly penetrative, with a few weapons having higher spread values. I don't think fractional spread values are a good idea, as this makes for complex maths.

Conversely, the alternative situation is if most weapons are not very penetrative, and some few weapons have specialist 'armour penetrating' properties. in which case  Penetration value works better (1 for most weapons, higher for weapons better at punching through armour). In this situation the target's armour value is then divided by the weapon's penetration rating.

Just a comment.


Simon Hibbs

[Jasper]

Well, most of the ships which I've designedf so far have a medium to large number of guns, which is what spread originally came from: not so much the spread of any given weapon, but the spread of all the ship's firepower in total -- you don't roll to-hit for individual guns, but for the entire ship (or entire banks of weapons anyway).  I realize the realism problems with this (spread should be tied to how well you rolled to hit), but in the interests of time and cinematism, I decided to just let to-hit and damage be separate.

So, as I was saying, most ships do indeed have about the same penetrative power, but it's rather low.  A smaller number of ships have much higher values -- the ones with just one big ol' gun each.

Division would possibly work, but is one of the things I try to avoid if possible in any mechanic because many people simply dislike it, and also because it introduces issues of rounding and break points.