Why exponential progression doesn't work for damage

[Sean Waters]

I have always liked the idea of exponential progression for damage/defences/BODY. It has a certain attraction: you can create truly awesome characters without ludicrous numbers of points, and it fits with the Hero ethos of simulating a wide range of genres: you can do Indiana Jones and you can do Superman. Moreover strength has always had an exponential progression.

 

I was chatting away on a couple of other threads recently and began to understand a problem with exponential progression that I just can't see an answer to.

 

Assuming, for instance, doubling the thickness of a wall adds +1 BODY (which Hero says you can when blowing holes in walls) that leads to the conclusion - right or wrong - that you are doing double the damage with +1 BODY, or each +1DC doubles the damage. Actually, to confuse me, some materials are +1 for doubling thickness and +2 for others. Ah well. The principle holds.

 

There's a problem with this.

 

If you hit a 4 DEF wooden wall, and do 7 BODY damage, you blow a hole in it 32 mm deep. If you do 8 BODY the hole is 64mm deep and if you do 13 BODY it is 2 metres deep. 13 BODY is 9 points over the DEF of the material

 

Now if you do that 13 BODY with 3 seperate attacks, each 4 points over the DEF of the material (i.e. 3x8BODY damage) you get a hole 64mm x 3 deep, or a little less than 20cm deep.

 

This is a perfect example of exponential damage: one big hit is far far more effective than lots of little ones - EVEN IF YOU IGNORE DEFENCE.

 

The same doesn't apply to the BODY stat of characters: that works on purely linear lines (so to speak). Each hit that exceeds defences reduces the total and it doesn't matter if it is one big hit or lots of little ones.

 

Frankly it would be difficult to manage accurate exponential BODY damage against characters - it can be done, but it is not straightforward, and would make costing BODY a nightmare.

 

Given this difficulty, I don't think we can model damage/defence/BODY exponetially - mixing linear and exponential is just plain confusing - and if we don't do it in one part of the system, we shouldn't do it elsewhere.

 

Thoughts?

[Hugh Neilson]

Re: Why exponential progression doesn't work for damage

 

My theory is not to look too close at the underlying math if the game is working.

 

That said, if one assumes +1 BOD = Duble Damage, then no matter how high your character's BOD, two hits that each inflict BOD should reduce him to "dead or dying".

 

Assume he has 100 BOD (that was expensive!). If the 100'th BOD doubles the previous 99 (ie +1 BOD = 2x as durable), and he is hit by an attack which inflicts 1 BOD, he has 99 left. 99 is as much as that +1, so another hit that inflicts 1 BOD should take away the remaining 99.

 

Mathematically sound, but not great for gameplay, since the same applies to a character with 10 BOD, or with 2 BOD.

[Fox1]

Re: Why exponential progression doesn't work for damage

 

Given this difficulty' date=' I don't think we can model damage/defence/BODY exponetially - mixing linear and exponential is just plain confusing - and if we don't do it in one part of the system, we shouldn't do it elsewhere.[/quote']

 

You worry too much, or rather are applying a correct worry to the wrong game.

 

HERO isn't designed to represent reality, it was originally designed to represent comic books using a fun and crunchy game system that is still rather easy to play. That's why it mixes linear and exp systems the way it does, it matches comic books.

 

You can reduce the problems by controlling your range of character/object construction, but the underlying concept will always be there. It's up to you if it bothers you or not.

 

If you can't put it out of mind, I'd suggest taking a look at JAGS (http://www.jagsrpg.org/), its a HERO like free product that attempted to correct some of the more glaring issues.

[Sean Waters]

Re: Why exponential progression doesn't work for damage

 

You worry too much' date=' or rather are applying a correct worry to the wrong game.[/quote']

 

No, mate, I don't worry enough

 

 

If you can't put it out of mind' date=' I'd suggest taking a look at JAGS http://www.jagsrpg.org/, its a HERO like free product that attempted to correct some of the more glaring issues.[/quote']

 

What a splendid link: I'd recommend anyone reading this has a look.

[Mister E]

Re: Why exponential progression doesn't work for damage

 

It's all very squirmy.

[Sean Waters]

Re: Why exponential progression doesn't work for damage

 

It's all very squirmy.

 

I'd have a lie down until it stops being squirmy then, if I were you

[Marco]

Re: Why exponential progression doesn't work for damage

 

Hi there,

 

If you're looking for a link where we discussed exactly this, there's an editorial on the site here: http://www.jagsrpg.org/index.php?name=PNphpBB2&file=viewtopic&t=4

 

I also want to say that despite having written JAGS and seen the linear/exponential nature of Hero as an issue, I think Hero (especially 5th Ed) is a phenomenal game and it certainly isn't broken in any way (individual preferences may be a different matter, of course).

 

Finally: Hi Brian

 

-Marco

[Sean Waters]

Re: Why exponential progression doesn't work for damage

 

Hi there,

 

If you're looking for a link where we discussed exactly this, there's an editorial on the site here: http://www.jagsrpg.org/index.php?name=PNphpBB2&file=viewtopic&t=4

 

I also want to say that despite having written JAGS and seen the linear/exponential nature of Hero as an issue, I think Hero (especially 5th Ed) is a phenomenal game and it certainly isn't broken in any way (individual preferences may be a different matter, of course).

 

Finally: Hi Brian

 

-Marco

 

You wrote it?

 

You hero!

[Warp9]

Re: Why exponential progression doesn't work for damage

 

My theory is not to look too coose at the undelrying math if the game is working.

 

That said, if one assumes +1 BOD = Duble Damage, then no matter how high your character's BOD, two hits that each inflict BOD should reduce him to "dead or dying".

 

Assume he has 100 BOD (that was expensive!). If the 100'th BOD doubles the previous 99 (ie +1 BOD = 2x as durable), and he is hit by an attack which inflicts 1 BOD, he has 99 left. 99 is as much as that +1, so another hit that inflicts 1 BOD should take away the remaining 99.

 

Mathematically sound, but npt great for gameplay, since the same applies to a character with 10 BOD, or with 2 BOD.

I blieve that you are a bit confused about exponential progression.

 

Do you really think that, on an exponential scale 100 BODY - 1 BODY = 99 BODY ?

 

Imagine that we subtracted the weight that a 5 STR character could lift from the weight that a 500 STR charater could lift. Do you really think that this would be equal to the weight that a 495 STR Character could lift?

 

(500 STR Lift - 5 STR Lift) is NOT equal to 495 STR Lift.

 

(100 BODY - 1 BODY) is not equal to 99 BODY (assuming an exponential scale)

[Sean Waters]

Re: Why exponential progression doesn't work for damage

 

Damage in Hero (despite what I said earlier) is kinda exponential in that we use defences that deduct from the total damage, so, in the example above, against a 4DEF piece of wood, no amount of attacks will have any noticeable effect if the damage is LESS than 5 Body, and once it exceeds that, the damage delivered is steep at first then tails off: 5 BODY damage does 1 BODY - infinitely more than 0, 6 does 2 - twice as much as 5, 7 does three - only half again as much as 6, and so on. High damage, to an extent, works on a law of diminishing returns, once you hit the magic threshold of Damage =DEF.

 

As for STR being an exponential lift and damage being a linear increase, well, yes but...

 

Fist off the damage you can do with a punch is only partly related to strength - more importantly it is also related to how fast you can move your hand, your body mass, and how efficiently you can throw that mass behind the fist, so, arguably, this is not inconsistent.

 

Who am I kidding? Read the discussion posted on the link above - it makes some excellent points. I think you should be able to do more damage hitting someone with a battleship than a fist, even if you are strong enough to lift the weight, if for no other reason than physics: a battleship is a big lever, allowing you to apply your strength more efficiently.

 

Mind you if we wanted to apply physics, we wouldn't be picking up battleships in the first place, would we? Leverage works two ways, and no piece of hull metal is going to be strong enough to support the whole thing.

 

Oh I don't know. It's all too complicated....

[Sean Waters]

Re: Why exponential progression doesn't work for damage

 

If Body was exponential, a BODY of 10 would require 1024 points of damage to erode, and damage of 10 (BODY) would do 1024 damage, whereas damage of 5 (Body) would do 32, so you'd need 32 hits at 5 (BODY) damage to destroy 10 BODY worth of material/character, instead of the 2 it takes at present.

 

I know whjat I mean, but you can see why I'm not a teacher, can't you?

[Warp9]

Re: Why exponential progression doesn't work for damage

 

I have always liked the idea of exponential progression for damage/defences/BODY. It has a certain attraction: you can create truly awesome characters without ludicrous numbers of points, and it fits with the Hero ethos of simulating a wide range of genres: you can do Indiana Jones and you can do Superman. Moreover strength has always had an exponential progression.

 

I was chatting away on a couple of other threads recently and began to understand a problem with exponential progression that I just can't see an answer to.

 

Assuming, for instance, doubling the thickness of a wall adds +1 BODY (which Hero says you can when blowing holes in walls) that leads to the conclusion - right or wrong - that you are doing double the damage with +1 BODY, or each +1DC doubles the damage. Actually, to confuse me, some materials are +1 for doubling thickness and +2 for others. Ah well. The principle holds.

 

There's a problem with this.

 

If you hit a 4 DEF wooden wall, and do 7 BODY damage, you blow a hole in it 32 mm deep. If you do 8 BODY the hole is 64mm deep and if you do 13 BODY it is 2 metres deep. 13 BODY is 9 points over the DEF of the material

 

Now if you do that 13 BODY with 3 seperate attacks, each 4 points over the DEF of the material (i.e. 3x8BODY damage) you get a hole 64mm x 3 deep, or a little less than 20cm deep.

 

This is a perfect example of exponential damage: one big hit is far far more effective than lots of little ones - EVEN IF YOU IGNORE DEFENCE.

 

The same doesn't apply to the BODY stat of characters: that works on purely linear lines (so to speak). Each hit that exceeds defences reduces the total and it doesn't matter if it is one big hit or lots of little ones.

 

Frankly it would be difficult to manage accurate exponential BODY damage against characters - it can be done, but it is not straightforward, and would make costing BODY a nightmare.

 

Given this difficulty, I don't think we can model damage/defence/BODY exponetially - mixing linear and exponential is just plain confusing - and if we don't do it in one part of the system, we shouldn't do it elsewhere.

 

Thoughts?

I believe that there are plenty of ways to do exponential damage.

 

Now I'll admit that they are probably not as straightforward to most people as a linear scale would be. But doing things in a consistently exponential manner would fix a number of problems.

 

Probably the easiest method I know of would be do go to doing wounds.

 

You could compare the damage of the attack to the character's BODY.

 

If the damage was below a given level there would be no impact.

At some threshold you'd get a superficial wound,

And at a level beyond that, you'd get a light wound,

And as the power of the attack went up, the level of wounds would go up, until you reach a point where the target will be blown apart.

 

As for adding up damage, that would work as follows: 2 Superficial Wounds = a Light Wound.

 

4 Superfical Wounds (or 2 Light Wounds) = a Moderate Wound

 

 

If you don't like the wound method, there are other methods as well. . . .

 

You could come up with a linear percentage, based on an exponential compare between Attack and BODY.

 

If the attack was too weak it would do 0%

At some value of power it would do 1%

Each extra point of damage over the 1% limit would double the percentage done.

 

 

Lets say that 10 damage does 1%

11 damage would do 2%

12 damage would do 4%

13 damage would do 8%

14 damage would do 16%

15 damage would do 32%

16 damage would do 64%

17 damage would be a Kill (128%)

[The Souljourner]

Re: Why exponential progression doesn't work for damage

 

The exponential-ness of some of Hero's rules is actually one thing I *don't* like. Doubling a wall's thickness only adds a single body point? How the heck does that work? Let's assume we have a 1m thick wall of metal. It has 17 body. A 2m thick wall has 19 body.

 

So by that rationale, it's better to build two walls right next to each other than one big thick wall, since the two walls would have almost double the body of the single wall. That's just too wacky for me.

 

A material should have a certain amount of body per thickness, and leave it at that.. it's makes a heck of a lot more sense, IMO.

 

-Nate

[Fox1]

Re: Why exponential progression doesn't work for damage

 

Finally: Hi Brian

 

-Marco

 

Hi Marco!

 

Long time no see. Sorry I dragged you into the den of scum and villainy known as the HERO boards. I hope everything is going well for you.

 

Btw, was it just my browser or are some of the links on your webpage not showing stuff? The FAQ for example.

[Sean Waters]

Re: Why exponential progression doesn't work for damage

 

.....Sorry I dragged you into the den of scum and villainy known as the HERO boards.......

 

Hoy! I resemble that remark

 

Do feel free to drag more in like this one though. Stunning work on JAGS.

[Dr. Anomaly]

Re: Why exponential progression doesn't work for damage

 

Sorry I dragged you into the den of scum and villainy known as the HERO boards.

I hope that's said in jest.

[Sean Waters]

Re: Why exponential progression doesn't work for damage

 

I believe that there are plenty of ways to do exponential damage.

 

Now I'll admit that they are probably not as straightforward to most people as a linear scale would be. But doing things in a consistently exponential manner would fix a number of problems.

 

Probably the easiest method I know of would be do go to doing wounds.

 

You could compare the damage of the attack to the character's BODY.

 

If the damage was below a given level there would be no impact.

At some threshold you'd get a superficial wound,

And at a level beyond that, you'd get a light wound,

And as the power of the attack went up, the level of wounds would go up, until you reach a point where the target will be blown apart.

 

As for adding up damage, that would work as follows: 2 Superficial Wounds = a Light Wound.

 

4 Superfical Wounds (or 2 Light Wounds) = a Moderate Wound

 

 

If you don't like the wound method, there are other methods as well. . . .

 

You could come up with a linear percentage, based on an exponential compare between Attack and BODY.

 

If the attack was too weak it would do 0%

At some value of power it would do 1%

Each extra point of damage over the 1% limit would double the percentage done.

 

 

Lets say that 10 damage does 1%

11 damage would do 2%

12 damage would do 4%

13 damage would do 8%

14 damage would do 16%

15 damage would do 32%

16 damage would do 64%

17 damage would be a Kill (128%)

 

 

 

Oooh, I like the wounds thing. That works well for me. I'm going to have to think about that.....

[Fox1]

Re: Why exponential progression doesn't work for damage

 

Hoy! I resemble that remark

 

Do feel free to drag more in like this one though. Stunning work on JAGS.

 

Marco is one of the best.

 

An excellent designer, and a good solid person.

[Sean Waters]

Re: Why exponential progression doesn't work for damage

 

The exponential-ness of some of Hero's rules is actually one thing I *don't* like. Doubling a wall's thickness only adds a single body point? How the heck does that work? Let's assume we have a 1m thick wall of metal. It has 17 body. A 2m thick wall has 19 body.

 

So by that rationale, it's better to build two walls right next to each other than one big thick wall, since the two walls would have almost double the body of the single wall. That's just too wacky for me.

 

A material should have a certain amount of body per thickness, and leave it at that.. it's makes a heck of a lot more sense, IMO.

 

-Nate

 

I was at the Bovington Tank Museum the other day http://www.tankmuseum.org/ , and one of the things on display was laminate armour. Apparently building armour in layers of different materials does make it harder to penetrate than simply having a solid lump. Go figure. Well, you don't have to figure, I suppose: there is a reason for it, but I'll let Wikipedia explain:

 

http://en.wikipedia.org/wiki/Chobham_armour

 

The problem with damage application is in applying defences more than once: that can seriously erode damage. Mind you if you are applying damage in properly exponential terms, as well as to BODY, an attack that gets through the first wall might not suffer that much attenuation by the time it hits the second. It is that (apparent) mixing of linear and exponential systems that causes me confusion.

[Fox1]

Re: Why exponential progression doesn't work for damage

 

I hope that's said in jest.

 

Of course it was.

 

These boards with but rare exception are one of the better examples on the Internet.

 

Is that damning with faint praise?

[Marco]

Re: Why exponential progression doesn't work for damage

 

Hi Marco!

 

Long time no see. Sorry I dragged you into the den of scum and villainy known as the HERO boards. I hope everything is going well for you.

 

Btw, was it just my browser or are some of the links on your webpage not showing stuff? The FAQ for example.

 

 

We moved from the old site to a new one and I haven't moved the FAQ yet--so no, it's not your browser--and we haven't done Web links either. All our work is going into the upcoming JAGS Wonderland due out Halloween

 

Sean: thanks for the compliments. Let me know what you think when you've looked at it more

 

-Marco

[Dr. Anomaly]

Re: Why exponential progression doesn't work for damage

 

Of course it was.

 

These boards with but rare exception are one of the better examples on the Internet.

 

Is that damning with faint praise?

Just checking.

 

Or maybe it's praising with faint damns?

[Warp9]

Re: Why exponential progression doesn't work for damage

 

Hi there,

 

If you're looking for a link where we discussed exactly this, there's an editorial on the site here: http://www.jagsrpg.org/index.php?name=PNphpBB2&file=viewtopic&t=4

 

I also want to say that despite having written JAGS and seen the linear/exponential nature of Hero as an issue, I think Hero (especially 5th Ed) is a phenomenal game and it certainly isn't broken in any way (individual preferences may be a different matter, of course).

 

Finally: Hi Brian

 

-Marco

I do have a couple of comments about your editorial. . . .

 

Many superhero games assume that a character's lift is out of linear proportion to his damage (that is, a guy who can lift several tons doesn't do that much more damage than a guy who can lift a few hundred pounds).

 

There are a few problems with the assumption that "a character's lift is out of linear proportion to his damage" given that a 1000 STR Character can destroy the Earth with a single punch in HERO.

[ajackson]

Re: Why exponential progression doesn't work for damage

 

The problem with exponential progression isn't with damage -- it's with x2 mass -> +1 Body.

 

If anything, a realistic x2 Mass should be -1DC from all attacks (so if two people are 1000x mass and striking with 1000x the force, the +10DC from 1000x force, and the -10DC for 1000x mass, exactly balance out, and you wind up with identical results to operating at regular scale).

 

If you want to have mechanics which are closer to standard Hero mechanics, x2 mass should be +1 Def (hardened), plus an additional +2 stun only defense. Body should not change (there are legitimate concept reasons for Body to be increased, but they're basically the excuses one uses for damage reduction -- high Body implies that you can be injured by small attacks, but it takes a really big attack to oneshot you).

[Marco]

Re: Why exponential progression doesn't work for damage

 

There are a few problems with the assumption that "a character's lift is out of linear proportion to his damage" given that a 1000 STR Character can destroy the Earth with a single punch in HERO.

 

I'm not sure where you're seeing the problem specifically--is the problem that the earth is as easy to destroy as 50 separate people? Or are you saying that the statement itself wrong--or, did you agree with it

 

-Marco