Exponential power curves without exponential numbers

[Yakk]

I have been playing around with some engine maths to attempt to generate exponential power curves (as in e^kx, not as in anything above linear) in an RPG system without having to make the numbers grow exponentially.

One approach that is time tested is target numbers and modifiers to d20 checks: it is actually hyperbolic, but it approximates an exponential curve with a x1.1 multiplier each point. Sadly this.leads to wiff fests: I would rather have some kind of attrition rather than no effect be the baseline failure mode.

Another thought I have had is a damage vs DR system, possibly with random DR, and with both a replenishing pool and a non replenishing pool on the defensive side.

Is, attacker rolls their accuracy dice and damage dice. Defender rolls their dodge and soak. Then the defender rolls "fate" or "luck" dice to top off either of their defense rolls to beat the corresponding attack pool: defeat either one and you do not get hurt. The defender is allowed to double their current total if they take a grazing blow. Luck would not refresh easily, while dodge and soak would.

This could be exponential, in that attacks less than dodge/soak would be ignorable. Those less than twice would be no more than grazes, while bigger ones drain hard to refresh pools. I have not done a serious analysis yet.

Another thought would be risk: if the defender had to defeat each die of the attacker. Dice could explode. This results in big dice being exponentially better than small, as beating a 12 on smaller dice is tricky. This curve is bounded, with little control on how steep it is, other than how the exploding happens.

[Belial_the_Leveler]

No need to complicate things. Consider the following comparison of some very bare-bones fighters at 7th level, 14th level and 20th level.

Guy A deals 10 damage per attack, has +10 attack bonus, 20 armor, 2 attacks, and 100 hit points.

Guy B deals 20 damage per attack, has +20 attack bonus, 30 armor, 4 attacks and 200 hit points.

Guys C deals 35 damage per attack, has +30 attack bonus, 40 armor, 6 attacks and 300 hit points.


Guy A needs 200 rounds to kill guy B and 300 rounds to kill guy C.
Guy B needs 2 rounds to kill guy A and 75 rounds to kill guy C.
Guy C can kill two guys A per round and 1 guy B per round.


The numbers scale very linearly but the comparative power gives an exponential increase. And those numbers aren't arbitrary either - they are the numbers a decent fighter build will have at those levels.

[Yakk]

Yes, but almost all of that is from the attack defense bonus, which leads to wiff fest based combat instead of attrition based. The rest is a quadratic or cubic from linear damage and attack count and HP.

The fact that of fence outpaces defence also means that even level fights round counts go down. 35*6 is 210, so 1.5 rounds to self kill, vs 5 rounds to self kill at the first build.

The unmentioned iterative attack penalties can help make up for that, but now we have a subsystem that requires wasted rolls in even level fights (that will almost certainly miss) just to let you kill weak opponents faster.

And despite all those subsystems patched together, the attack bonus all by itself provides a pretty smooth exponential curve within +- 10 points of attack defense, but one that sucks in practice: auto hits and misses, or approaching both, is not interesting. We can throw yet another patch to avoid auto hits (like power attack), but at this point we are talking half a dozen or more subsystems that all interact in quirky ways just to pull off the games power curve!

[Belial_the_Leveler]

Mutants and Mastermind introduced the Power Level system. Said system says "You don't get a level and then you get your attack and defense based off it. You get an attack and defense and your level is calculated off that. So if your offense and defense are X, your level will be X"




Basically, an inversion of the normal system. Your level doesn't dictate your stats. Your stats dictate your level. So if your GM says "hey guys, we're gonna play at X level" then you will build characters with X defense and offense. You can't powergame numerically because if you get better numbers you'll be at a higher level. You also can't make a weak character by accident because if you do, you'll immediately see that his level is below the norm.

[Grod_The_Giant]

Mutants and Mastermind introduced the Power Level system.
It kind of goes both ways. Your Power Level (PL) limits almost all the numbers on your sheet, and you can find your PL by looking at the numbers on your sheet.

M&M also has exponential scaling in their ranks and measures table. For every additional rank of Strength, you can lift twice as much. +1 rank of speed, you run twice as fast. And so on; it gets used for almost everything. Doesn't touch combat power, though.

[IamL]

Mutants and Mastermind introduced the Power Level system. Said system says "You don't get a level and then you get your attack and defense based off it. You get an attack and defense and your level is calculated off that. So if your offense and defense are X, your level will be X"




Basically, an inversion of the normal system. Your level doesn't dictate your stats. Your stats dictate your level. So if your GM says "hey guys, we're gonna play at X level" then you will build characters with X defense and offense. You can't powergame numerically because if you get better numbers you'll be at a higher level. You also can't make a weak character by accident because if you do, you'll immediately see that his level is below the norm.

The only issue is when magic gets involved, then you have a lot of other things to calculate to determine power level.
And it still leaves a ton of other ways to powergame.

[Knaight]

M&M also has exponential scaling in their ranks and measures table. For every additional rank of Strength, you can lift twice as much. +1 rank of speed, you run twice as fast. And so on; it gets used for almost everything. Doesn't touch combat power, though.

Fudge uses something similar for scale. Scale zero is set to something (say, 75 kg for a human game, we will call this C), the mass scale connection is M=C(1.5^Scale). Speed is similar, though the connection is S=C(1.2^Scale). Of course, these are logarithmic power curves, which isn't what's being looked for here.

[Yakk]

The term "logarithmic curve" and "exponential curve" are often used interchangeably, as it depends on how you are looking at it. (is it the map from "real" value to scale, or the map from scale to "real" value, that is being named? One way is logarithmic, the other exponential.)

[Yitzi]

Your best bet is probably to require a number of dice equal to the defender's level minus the attacker's level plus 1, and they all have to succeed; if the attacker's level is higher, then you again roll a number equal to the difference plus 1, but only one of them has to succeed.