Linear vs Logarithmic Scaling

[ajackson]

One of the basic problems with Hero is that it's a bit confused about whether it's a linear system or an exponential system. This means you have weird effects such as the fact that a blow that can reliably get body through on 30 Def (31d) is 4 million times more powerful than a blow that can reliably get stun through (9d), or that if Superman puts on a bulletproof vest, it will actually meaningfully protect him from Doomsday. The AP problem, from the Advantages thread, also acts like this.

There are ways of dealing with this sort of problem in a logarithmic system, but they tend to be either quite complex or fairly arbitrary (e.g. Def simply doesn't stack). The other option is to switch over to a true linear system -- armor that's twice as thick gives twice the Def, etc. Most likely, lifting ability should be set to Str^3/10.

That works nicely for street level characters, but hits problems at the other end: 50 Str is only 12.5 tons lift. If you want Superman at 100 kilotons of lift, he needs a Str of 1,000. That's both difficult to manage in a game (rolling 200d is a pain) and means that Superman has gobs of points available for other purposes; sacrificing 1d of damage for +1 OCV is easily worth it at those levels.

A method which has been used to good effect in other games is some form of Scale advantage. We can just set Justice League scale at x16 and then Superman has a nice manageable 62 Str. If for some reason Superman gets into an interaction with Joe Thug down the street (x1 Scale), Joe Thug's damage is divided by 16 vs Superman (4d6/16 isn't going to do much), Superman's damage is multiplied by 16 (and he probably pulls his punch to less than 1d). This also lets you just stat things like ants as negative scale characters. Scale would normally be a campaign setting, but could be purchased individually; based on analysis of points spent on powers, it's probably worth about 120 points per x2 (so Justice League scale is worth 480 points). Reduced scale probably shouldn't be used by PCs; just buy your powers at very low levels.

This doesn't deal with Superman occasionally deciding to push around the moon, but current rules don't deal with that either.

I'm not at all sure if this is a good idea, but I'm throwing it out there for consideration.

[Sean Waters]

Hero has always walked a poorly defined middle route, but somehow still worked. Personally I'd like to see an exponential system, but I really can see how that would upset a large number of people and yet I cannot imagine a truly linear system that works any better.

Not sure what my point is, but I'd think that Hero would work better as an exponential system than a linear one. Pretty sure linear=unplayable.

Or we could continue along that narrow but strangely attractive middle route...

[Vondy]

Hero has always walked a poorly defined middle route, but somehow still worked. Personally I'd like to see an exponential system, but I really can see how that would upset a large number of people and yet I cannot imagine a truly linear system that works any better.

Not sure what my point is, but I'd think that Hero would work better as an exponential system than a linear one. Pretty sure linear=unplayable.

Or we could continue along that narrow but strangely attractive middle route...

I think the problem is literalism. Hero is a system that abstracts. The strength chart provides a literal exponential measure, and some body measures are exponential, but attempts to apply that measure to other parts of the system clearly demonstrate that large parts of the system doesn't live by it. This is a big misconception on a lot of people's parts - that hero is exponential. Its not. Its abstract. That's why I'm not married to the strength chart, which is genre specific. The system works just as well if another strength chart is in place, or you disregard the body values objects and throw on an artisitically slapdash version of your own, or if you use a different non-combat multiple. The problem isn't "the exponential system," but the fact that the exponents that are in the system are excellent for one genre, but restrict granularity for several others. When I'm running supers I love it. When I run other genres, which has been my bread and butter of late, I start to grumble because the exponents (specifically strength and ncm movement) force a scale that doesn't provide much granularity. That's why I think we should have an optional strength chart for heroic games. It doesn't break the system, but makes it more flexible and lets me set a broader range without changing any actual mechanics.

[Killer Shrike]

I think the problem is literalism. Hero is a system that abstracts. The strength chart provides a literal exponential measure, and some body measures are exponential, but attempts to apply that measure to other parts of the system clearly demonstrate that large parts of the system doesn't live by it. This is a big misconception on a lot of people's parts - that hero is exponential. Its not. Its abstract. That's why I'm not married to the strength chart, which is genre specific. The system works just as well if another strength chart is in place, or you disregard the body values objects and throw on an artisitically slapdash version of your own, or if you use a different non-combat multiple. The problem isn't "the exponential system," but the fact that the exponents that are in the system are excellent for one genre, but restrict granularity for several others. When I'm running supers I love it. When I run other genres, which has been my bread and butter of late, I start to grumble because the exponents (specifically strength and ncm movement) force a scale that doesn't provide much granularity. That's why I think we should have an optional strength chart for heroic games. It doesn't break the system, but makes it more flexible and lets me set a broader range without changing any actual mechanics.

Agreed entirely.

Ive said for a while now that the problem with STR isnt necessarily the COST, the problem is the damn STR chart assigning flat weights to specific increments of STR which therefore requires STR to have much higher values than any other characteristic -- all the rest of which have no such hard measurement of what specific values mean.

Where things get weird / illogical / and sometimes dumb are the areas were some arbitrary measurement is asserted against abstract values. Its done haphazardly and incompletely. Unfortunately most people like thinking in concretes so they latch on to those fixed stakes in the ground and try to project outwards from there into the large areas of abstractness.

As long as the system stays loosely coupled to real measurements things remain relative rather than fixed and the game can scale a lot better.

[megaplayboy]

well, there's a variety of ways you could scale things.
1. hybrid linear/exponential: linear up to X threshhold then exponential, X varying according to genre.
2. pure exponential: this would be almost completely unworkable at the lower level
3. pure linear: this would be unworkable at any level above heroic
4. genre contextual scaling: IOW, the amount you can lift and amount of damage you can do/bounce varies according to genre/scale.
On the one hand, this would work beautifully for high level and low level gaming, and players wouldn't wince at the dice counts. On the other hand, static objects which exist in each setting would have to somehow remain consistent.

Let's say, for example, that we decide to have a "realistic" setting, a "heroic" setting, an "epic heroic" setting, a "superheroic" setting, "epic superheroic" setting, and "cosmic" setting--that would be six different scales.

In the first, let's say lifting capacity doubles every 20 points of STR. In the second, every 15 points. In the third, every 10. In a superheroic setting, every 5 points. In epic, 4x every 5 points, in cosmic, 16x.

A 30 STR in setting one can lift 200 kilos, and do the kind of damage one might expect a football player to be capable of.
A 30 STR in setting 2 can lift about 270 kilos.
Setting 3, 400 kilos.
Setting 4, 1.6 tons.
Setting 5, 25 tons.
Setting 6, 6.4 kilotons.

Dunno. Probably too radical a change for most folks.

I like exponential lift progression, personally, though perhaps it could be spaced out for the heroic genres, as suggested above.

[Toadmaster]

One of the basic problems with Hero is that it's a bit confused about whether it's a linear system or an exponential system. This means you have weird effects such as the fact that a blow that can reliably get body through on 30 Def (31d) is 4 million times more powerful than a blow that can reliably get stun through (9d), or that if Superman puts on a bulletproof vest, it will actually meaningfully protect him from Doomsday. The AP problem, from the Advantages thread, also acts like this.

There are ways of dealing with this sort of problem in a logarithmic system, but they tend to be either quite complex or fairly arbitrary (e.g. Def simply doesn't stack). The other option is to switch over to a true linear system -- armor that's twice as thick gives twice the Def, etc. Most likely, lifting ability should be set to Str^3/10.

That works nicely for street level characters, but hits problems at the other end: 50 Str is only 12.5 tons lift. If you want Superman at 100 kilotons of lift, he needs a Str of 1,000. That's both difficult to manage in a game (rolling 200d is a pain) and means that Superman has gobs of points available for other purposes; sacrificing 1d of damage for +1 OCV is easily worth it at those levels.

A method which has been used to good effect in other games is some form of Scale advantage. We can just set Justice League scale at x16 and then Superman has a nice manageable 62 Str. If for some reason Superman gets into an interaction with Joe Thug down the street (x1 Scale), Joe Thug's damage is divided by 16 vs Superman (4d6/16 isn't going to do much), Superman's damage is multiplied by 16 (and he probably pulls his punch to less than 1d). This also lets you just stat things like ants as negative scale characters. Scale would normally be a campaign setting, but could be purchased individually; based on analysis of points spent on powers, it's probably worth about 120 points per x2 (so Justice League scale is worth 480 points). Reduced scale probably shouldn't be used by PCs; just buy your powers at very low levels.

This doesn't deal with Superman occasionally deciding to push around the moon, but current rules don't deal with that either.

I'm not at all sure if this is a good idea, but I'm throwing it out there for consideration.

I like this idea, its silly that you can have a human fighter in FH that can lift 1.2 tons, but the Hulk needs hundreds of points in strength because in issue #187 the Hulk lifted an aircraft carrier and whopped some bad guy in the noggin with it.

Another issue with exponents is often reality has some exponential aspects too. As an example if you double the velocity of something you square the energy, but if you double the weight you only double the energy. Armor that is twice as thick is more than twice as strong. Real figures are nice to help people get their head around something in the game but they also can become anchors, its always good to know when to let go.

[Kdansky]

JAGS does exactly that. People should stop naming their products "Just Another X Y"...

I've seen so many JA... or YA... (yet another), it's not even funny.

[Warp9]

2. pure exponential: this would be almost completely unworkable at the lower level
3. pure linear: this would be unworkable at any level above heroic

I disagree with statement 2.

And I'd add the following to your 3rd point: IMO a pure linear system is fairly unworkable at both very low, and very high power levels.

Looking at statement 2:

Pure exponential can work just fine for lower power levels, especially if one changes the rate at which doubling occurs.

Assuming that an olympic level weight lifter can lift 4 X what a normal person can, and assuming a base of 10 STR which doubles per + 15 points of STR, an olympic weightlifter would have a STR of 40. And, in such a system, 25 STR would be double the STR of a character with a 10 STR. This set up would actually allow for more granularity at lower levels than a liner base 10 STR system. In the linear system based on 10, a 20 STR would be double 10 STR, rather than the 25 STR in my suggested exponential system.

And in terms of low level linear systems, IMO they only work well at a very limited range. Things that are too small or too big don't work very well in such a system. For example, even a linear system where an average human has 100 STR will not really allow for you to model a game based around ultra-small creatures (such as ants) very well. If you didn't use decimal points, then it would seem that all ultra-weak creatures would have exactly the same STR score (probably 1 or 0). On the other hand, in an exponential system, a big ant could have a much different STR than a small ant (they might have -50 STR and -60 STR).

[Warp9]

This doesn't deal with Superman occasionally deciding to push around the moon, but current rules don't deal with that either.

A 400 Hero STR would allow one to lift the whole Earth.

[Toadmaster]

A 400 Hero STR would allow one to lift the whole Earth.

But what would he stand on?

[GamePhil]

But what would he stand on?

His 5" of Flight.

[ajackson]

A 400 Hero STR would allow one to lift the whole Earth.

Yes, but Superman doesn't push the earth around regularly; his routinely available Strength is in the 100-150 range.

[Sean Waters]

Strength is far from the only exponential aspect of Hero. Consider the +5=double rule. Consider the fact that doubling someone or something's mass or thickness adds +1 BODY, or +2 or whatever - a set amount anyway. It is these occasional, tantalising glimpses of an exponential world that make things so intruiging. OTOH REALLY being exponential about it all is quite difficult to pull off. The original DC Heroes (IIRC) made an admirable stab at it, but even that was not truly exponential: in such a system , any difference in characteristics of powers of more than a unit would be the difference between success and failure: it tends to be a far blunter instrument.

[Warp9]

Yes, but Superman doesn't push the earth around regularly; his routinely available Strength is in the 100-150 range.

But that was not the point.

The suggestion was that the rules didn't deal with being able to push the moon around, my point was that they can deal with it.

[Warp9]

The original DC Heroes (IIRC) made an admirable stab at it, but even that was not truly exponential: in such a system , any difference in characteristics of powers of more than a unit would be the difference between success and failure: it tends to be a far blunter instrument.

IMO part of the design consideration of DC Heroes was that two characters like Batman and Superman could hang out together.

It was not so much that Superman didn't have massive levels of power---he did. But the assumption was made that a massive difference in power level would not have as big an impact on success and failure as you and I might think that it would.