Exponential VS Linear ?

[Warp9]

I really like the Hero System. However, there is one issue which I feel has not been handled satisfactorily in the Game at this time. Part of the System works on a linear basis, and part of it works on an exponential basis, and I feel that the mixture of the two methods causes problems.

 

We’ve already argued about the question of “is Hero Linear or Exponential in scale?†This thread is not really about that. It is more about the question: “Should Hero be Linear, or Should it be Exponential?†(Not that anybody really cares )

 

I will start out with some my own thoughts on the matter. (This stuff is all IMO, of course)

 

Exponential (Logarithmic) VS Linear in Hero (From Warp9's perspective).

 

Combat Velocity (default method, the optional Velocity Table works in an Exponential Fashion), Damage Accumulation, Casual STR lift, Throwing, and Explosives all work in a linear fashion.

 

Whereas lifting, BODY rating (+1 BODY per X2 mass), fire arms damage, Non-Combat Velocity, and the size of holes made in a walls, all work in an exponential fashion.

 

This leads us to some problems:

 

If you rate objects at +1 BODY per X2 mass, and then let explosives increase damage at a linear rate we can get some strange situations. For example, we have a the Earth rated at 86 BODY (in line with +1 BODY per X2 Mass), but 200 sticks of dynamite can blow it up.

 

Linear velocity damage can also be a problem for the same reasons; a guy who does a Mach 3 move through on the Earth can also destroy it.

 

Casual Strength is based on cutting a character’s STR in half. Cutting your STR value in half would be great if STR was linear, but with an exponential standard, things change. A normal guy with a 10 STR can lift one-half as much with casual STR (5 Casual STR), but a strong Brick will only be able to lift one thousandth as much with his casual STR (100 STR vs 50 Casual STR). And an ant will actually be able to lift much more with his casual STR (-50 STR vs -25 Casual STR).

 

Damage also accumulates in a linear manner, a 1 point Killing NND (which does BODY) can totally destroy a planet sized object with a couple of hundred hits.

 

An all linear system would be OK; all exponential would be OK. Mixing the two approaches leads to trouble. Although I should say that I personally prefer an exponential approach.

[Warp9]

Re: Exponential VS Linear ?

 

More discussion of the 2 different approaches (Pros and Cons)

 

The Linear Approach.

 

Advantages:

 

It is very straight forward.

 

It allows for direct relationships between amount lifted and STR (1 point of STR = X amount of lift), or velocity and damage (1 hex per second = X damage) .

 

0 means 0, unlike an exponential system where 0 is just a base value.

 

Disadvantages:

 

Relationships between values can be a problem. In a linear system, a pixie with 2 STR is twice as strong as a pixie with 1 STR. But they are only separated by 1 point of STR. On the other hand, characters with very high STR may be separated by a wide range of points, and yet have almost the same strength percentage wise (1,000,000 vs 999,000 is 1,000 points of difference but the one is still 99.9% the same as the other).

 

If you want the system to handle a wide range of things from ants to Godzilla to Death-Stars you will end up with some really big numbers. Do you really want a Superman with a 94,752,035 STR ?

 

 

The Exponential (Logarithmic) Approach

 

Advantages:

 

It keeps numbers smaller. With a relatively small range of number you can rate a very large variety of things, which is especially nice if you want to have a “UNIVERSAL†system.

 

This method keeps relationships constant. In an exponential system, if character A has 5 more points of STR then he has double the ability. The relationship holds true if Character A has a -60 STR, and Character B has -65 STR. The relationship holds true if Character A has a 5 STR, and Character B has 0 STR. The relationship holds true if Character A has a 10 STR, and Character B has 5 STR.

The relationship holds true if Character A has a 1000 STR, and Character B has 995 STR.

 

Disadvantages:

 

It is less straight forward for people who may be used to thinking in a linear manner.

 

It can also hide the real magnitude of a character’s abilities. If one follows the pattern of 2^(STR/5) for STR, then a 30 Hero STR would actually be equal to a 160 STR in a linear game. Although this problem can be mitigated by making the curve a little less steep, for example maybe STR could be based on 2^(STR/10), or even based on 2^(STR/15)

 

 

For a bit more discussion of Logarithmic/Exponential approach (as opposed to Linear), here are a couple of rpg.net threads which also touch on the issue:

 

http://forum.rpg.net/showthread.php?s=&threadid=9593&highlight=logarithmic

 

http://forum.rpg.net/showthread.php?s=&threadid=5333&perpage=40&highlight=logarithmic&pagenumber=2

[Onyxclaw]

Re: Exponential VS Linear ?

 

I have to admit the exponential scale was rather sonfusing during my first character creation. I kept thinking that 30 strength when a normal human has 8 was a little low for a dragon the size of an elephant. My GM kept telling me it was fine and well, after some games I believed him.

 

The benifit to hero being exponential, I think (these things are not my especiality) is that it allows for the creation of higher power characters (not necisarily higher point) without going into enormous numbers.

 

Like you said before, the numbers for stats are so much higher with a linear system.

 

Also with the linear system you have all of the small steps in between, which granted will add more variation. But which make calculating things like damage difficult.

 

I dunno...just my 2 cents

[Warp9]

Re: Exponential VS Linear ?

 

I have to admit the exponential scale was rather sonfusing during my first character creation. I kept thinking that 30 strength when a normal human has 8 was a little low for a dragon the size of an elephant. My GM kept telling me it was fine and well, after some games I believed him.

 

The benifit to hero being exponential, I think (these things are not my especiality) is that it allows for the creation of higher power characters (not necisarily higher point) without going into enormous numbers.

 

Like you said before, the numbers for stats are so much higher with a linear system.

 

Also with the linear system you have all of the small steps in between, which granted will add more variation. But which make calculating things like damage difficult.

 

I dunno...just my 2 cents

I sounds like we are on the same wavelength

 

Buy I'd also add that, while a linear scale may allow for more variation at higher levels, the exponential allows for more variation at lower power levels.

 

If you've got a linear scale where 10 STR is average, then there are only 9 points left to cover the entire range of "less than average STR" (from weak people, to mice, to ants).

[Fox1]

Re: Exponential VS Linear ?

 

For in play reasons, I changes the exponential part of HERO back when the first rulebook came out.

 

Instead of x2 per 5 points I'm x1.53779192 per 5 points.

 

Once that was fixed, I didn't worry about the other problems. I just don't go where the system breaks down at.

 

Pure exponential system would be too complex in play for even my tastes. It would also be more limiting than I'd want.

 

Pure Linear system would be unmanageable in play or would require scale shifts. Nah, not going there.

 

I'm happy with things as there are (the change I noted).

[Cancer]

Re: Exponential VS Linear ?

 

As a matter of principle, if you have to keep track of effects of vastly different magnitude -- which is approximately always true in superhero situations -- then doing it without the use of log scales is hopeless. (I prefer the word "logarithmic" to "exponential" to describe this kind of manipluation, but I also know that a lot of people -- my students, anyway -- consider "logarithm" to be either a direct invocation of Satan or an auto-sexual act of the vilest sort.)

 

When it comes time to compare grossly different values, well, an example: you start needing to keep track of how many zeros are in the brick's lift capacity versus anyone else's.

 

... but whether you realize it or not, counting zeros like that IS the first step toward a logarithmic scale. So accept the math, make your system work that way. Life ... well, actually, RPGs, but that's more important than life ... gets a lot easier.

[Hugh Neilson]

Re: Exponential VS Linear ?

 

Instead of x2 per 5 points I'm x1.53779192 per 5 points.

 

I'm curious to know the logic behind that particular, andvery precise-looking, scale.

[Onyxclaw]

Re: Exponential VS Linear ?

 

while a linear scale may allow for more variation at higher levels, the exponential allows for more variation at lower power levels.

 

If you've got a linear scale where 10 STR is average, then there are only 9 points left to cover the entire range of "less than average STR" (from weak people, to mice, to ants).

 

That's also true, but as it's set up even with the exponential scale there are still only 9 levels below 10 that are available, if of course you stop at zero.

Linear can go below zero, in which case there are plenty more (although odd to me) levels

 

I always felt it was odd to have negative strength...but it is allowd and they do include it on the strength chart...at least before I left for work today I remembered it being there, as I am still at work I can't verify that. So really in this case "10" seems more like a place holder rather than a liner limit. It simply represents the place on the curve/line where "adverage" lives.

 

personally I think they picked 10 because it was a round number =P but what do I know

[Guest Black Lotus]

Re: Exponential VS Linear ?

 

I support the idea that some elements of HERO must necessarily be linear in nature, and some must necessarily be exponential in nature, so that the system is thorough, yet streamlined in as many areas as possible.

 

This creates a few gaps and inconsistencies, but it's definitely a wingable situation, I think.

[Fox1]

Re: Exponential VS Linear ?

 

I'm curious to know the logic behind that particular' date=' andvery precise-looking, scale.[/quote']

 

It was determined based upon the campaign I run which is based on (some very significant changes, but based on) Marvel.

 

I basically had to match to the following range:

 

STR 10- Average human male in good condition

STR 25- Captain America

STR 90- 100 ton lifts

 

The STR 90 deserves it's own note, at the time the Marvel Universe stated that a few characters with 100 ton lifts hit with the force of a 500lb bomb.

 

In that edition a 500 lbs bomb did 27d6. A STR 90 haymaker also did 27d6.

 

That odd looking number got me there. So life was very good.

 

 

Since then they've changed the haymaker rules and I haven't decided what to do about that...

 

Jerks.

[Warp9]

Re: Exponential VS Linear ?

 

For in play reasons, I changes the exponential part of HERO back when the first rulebook came out.

 

Instead of x2 per 5 points I'm x1.53779192 per 5 points.

 

Once that was fixed, I didn't worry about the other problems. I just don't go where the system breaks down at.

 

 

 

Going with a +10 per X2 gives you almost the same result, and it's something that you can do in your head.

 

 

Pure exponential system would be too complex in play for even my tastes. It would also be more limiting than I'd want.

I'm not sure I follow you here (although tracking damage could be a pain if it was not done correctly).

 

I'd like to hear more of your thoughts on this matter.

[Fox1]

Re: Exponential VS Linear ?

 

Going with a +10 per X2 gives you almost the same result' date=' and it's something that you can do in your head..[/quote']

 

No it doesn't. I had target numbers to hit.

 

See my post above.

 

 

 

I'm not sure I follow you here (although tracking damage could be a pain if it was not done correctly).

 

Show me your method of doing exponential STR (say 1 50 ton lift) with move-through damage for 3", 15", 30", and Mach 3 of movement.

 

Keep in mind that KE = MV^2

 

Maybe it's easier than it first appears. Look up charts are not easy btw.

[Warp9]

Re: Exponential VS Linear ?

 

That's also true, but as it's set up even with the exponential scale there are still only 9 levels below 10 that are available, if of course you stop at zero.

To stop at 0 is a personal choice, rather than a limit of the STR progression itself.

 

Linear can go below zero, in which case there are plenty more (although odd to me) levels

I don't follow this, assuming a direct linear coorelation to STR value and STR lift we have

 

10 STR = 100 kg lift

9 STR = 90 kg lift

8 STR = 80 kg lift

. . .

3 STR = 30 kg lift

2 STR = 20 kg lift

1 STR = 10 kg lift

0 STR = 0 kg lift

Where do you go from there? I don't see how one could lift less than 0 pounds.

 

 

I always felt it was odd to have negative strength...but it is allowd and they do include it on the strength chart...at least before I left for work today I remembered it being there, as I am still at work I can't verify that. So really in this case "10" seems more like a place holder rather than a liner limit. It simply represents the place on the curve/line where "adverage" lives.

 

personally I think they picked 10 because it was a round number =P but what do I know

When dealing with an exponential/logarithmic curve, there is no reason not to go below 0, in fact 0 is the most logical standard average (rather than 10).

 

Although I admit that going from D&D to a game where that average is 0 would probably throw a great number of people.

[Warp9]

Re: Exponential VS Linear ?

 

Show me your method of doing exponential STR (say 1 50 ton lift) with move-through damage for 3", 15", 30", and Mach 3 of movement.

 

Keep in mind that KE = MV^2

 

Maybe it's easier than it first appears. Look up charts are not easy btw.

 

Refer to the optional velocity chart FREd page 292-293 it already covers all those things. (and it's all based on KE = MV^2)

 

For example, It says that a Mach 3 Character has a velocity factor (VF) of 17. Move through is STR + VF d6

 

So, by that optional velocity chart, a guy with 55 STR (which is the standard book value for 50 ton lift) would do 11 + 17 or 28d6 on a Mach 3 move through.

 

Assuming 4 SPD (the chart works on Velocity per Turn, not velocity per phase).

 

3" = 12" per Turn = 11d6 from STR + 1 VF = 12d6

15" = 60" per turn = 11 + 4 VF = 15d6

30" = 120" per turn = 11 + 6 VF = 17d6

 

and we've already covered the Mach 3 thing.

[Fox1]

Re: Exponential VS Linear ?

 

Refer to the optional velocity chart FREd page 292-293 it already covers all those things. (and it's all based on KE = MV^2)

 

For example, It says that a Mach 3 Character has a velocity factor (VF) of 17. Move through is STR + VF d6

 

So, by that optional velocity chart, a guy with 55 STR (which is the standard book value for 50 ton lift) would do 11 + 17 or 28d6 on a Mach 3 move through.

 

Assuming 4 SPD (the chart works on Velocity per Turn, not velocity per phase).

 

3" = 12" per Turn = 11d6 from STR + 1 VF = 12d6

15" = 60" per turn = 11 + 4 VF = 15d6

30" = 120" per turn = 11 + 6 VF = 17d6

 

and we've already covered the Mach 3 thing.

 

As I said, a chart is not to my mind simple.

 

What's the math for VF?

 

I will also note that I don't in practical gaming terms like the result of what you posted.

 

Frankly I know the current rules have screwed the pooch in realism. However I like how it all fits together with the current damage values.

[Warp9]

Re: Exponential VS Linear ?

 

As I said, a chart is not to my mind simple.

Ah you like to keep things simple, that's why you went from X2 for 5 points to x1.53779192 per 5 points. That 2nd one is sooo much easier to do in your head

 

What's the math for VF?

The math is based on the KE formule +1 DC per X2 KE, which seems to be to be the standard progression in HERO.

 

For your progression you'd have to change the chart/formula to represtent 1DC per x1.53779192 KE, it would fit with your game then.

[Fox1]

Re: Exponential VS Linear ?

 

Ah you like to keep things simple' date=' that's why you went from X2 for 5 points to x1.53779192 per 5 points. That 2nd one is sooo much easier to do in your head [/quote']

 

I don't mind charts during character creation.

 

Don't like them in the middle of HERO combat.

[Warp9]

Re: Exponential VS Linear ?

 

I don't mind charts during character creation.

 

Don't like them in the middle of HERO combat.

Either way it seems to me that you might have to refer to the chart if you didn't have the data.

 

But I'm pretty good at powers of 2, and I could fairly easily figure VF without the chart.

 

There no way I'm going to do powers of 1.53779192 in my head.

[Fox1]

Re: Exponential VS Linear ?

 

Either way it seems to me that you might have to refer to the chart if you didn't have the data.

 

But I'm pretty good at powers of 2, and I could fairly easily figure VF without the chart.

 

There no way I'm going to do powers of 1.53779192 in my head.

 

Pity, cause I'd need to do it for my game.

 

And again, I don't like the result. The mixed EXP and linear scale is just more fun and comic book like.

[Warp9]

Re: Exponential VS Linear ?

 

And I'll add to my previous statement, if flight (and other movement) were done in exponential terms, then figuring Velocity Factor would be easy.

 

It would be very much like Growth VS STR. It is not hard figure out how much STR it takes to lift somebody with 50 points of Growth, even though both happen in exponential terms.

 

If flight were exponential then VF would probably equal points in flight / 5 (to match with +1 DC per 5 points).

[Warp9]

Re: Exponential VS Linear ?

 

Pity, cause I'd need to do it for my game.

 

And again, I don't like the result. The mixed EXP and linear scale is just more fun and comic book like.

Comic Like? You mean like where 200 sticks of dynamite can destroy the Earth?

[Fox1]

Re: Exponential VS Linear ?

 

Comic Like? You mean like where 200 sticks of dynamite can destroy the Earth?

 

I'm not responsible for all the silly rules Steve Long wrote in his book.

 

I still use the standard EXP progression for dynamite from the old days, with my own progression number and starting point of course.

[Mister E]

Re: Exponential VS Linear ?

 

As far as game play is concerned, there really isn't that much of a problem, no matter how you look at the system...

 

That said, the exponential aspect of the game works really well, and I like it. But the game has left many unanswered questions. For instance:

 

If the quality of STR doubles every 5 points. And we use that as a model for ever other stat, (except for BODY, which doubles every 1 point), consider the significance of that on the INT attribute. If we were to universally assume that the average INT of humans is 8... unless I'm mistaken, that would equate to an I.Q. of 100. From that, it's simple enough to come to the conclusion that an INT of 13 (8+5) equates to an I.Q. of 200.

 

Now, in the real world, an I.Q. of 200 is fairly significant. But in checking out my new copy of Dark Champions, I note that the Army Ranger Package Deal states it requires characters to have a 13 INT in order to qualify for the package. Okay, I don't want to be insulting to anyone who's served in the Army Rangers, but I've met a dozen or so, and being a genius is definately not a requirement.

 

What follows is a little off subject...

 

It bugs me when I see players build characters with what I consider to be "casual" stat-inflation, that totally disregards the meaning of the vallue of a particular stat... especially when those characters are writen up in suppliment books, and especially when it involves the insideous secret DEX arms race. I will use "the Champions," from the Champions genre book, as an example:

 

Defender: 25 DEX

Ironclad: 20 DEX

Nighthawk: 25 DEX

Sapphire: 23 DEX

Witchcraft: 20 DEX

 

CON is the other stat that gets inflated, so that the heroes don't get stunned too often, and practically for no other reason:

 

Defender: 30 CON

Ironclad: 30 CON

Nighthawk: 20 CON

Sapphire: 23 CON

Witchcraft: 18 CON

 

Okay, I'm done with that...

 

As far as Casual STR is concerned, I think modifying it as a house rule, might be an exciting solution. Would you say that applying only half your strength constitutes casual application of strength? In that case, anything you do at -5 your STR would be an effortless action. I could probably be persuaded to go with "one-quarter" strength, and -10 STR, instead. Especially considered that one-quarter seems a lot more casual than one-half.

 

As far as 200 sticks of Dynamite blowing up the Earth is concerned... This is broken. For every +1d6 of damage, the amount of dymamite should rightly be doubled, (unless there is some sort of synergistic property of dynamite, I am unfamiliar with). This could just as easily be corrected with a house ruling.

[Warp9]

Re: Exponential VS Linear ?

 

I'm not responsible for all the silly rules Steve Long wrote in his book.

 

I still use the standard EXP progression for dynamite from the old days, with my own progression number and starting point of course.

OK then, how about this?

 

You mean "Comic Like" as in where a guy can destroy the Earth by smashing into it at Mach 3? (And you can't blame Steve Long for that one)

[Fox1]

Re: Exponential VS Linear ?

 

OK then, how about this?

 

You mean "Comic Like" as in where a guy can destroy the Earth by smashing into it at Mach 3? (And you can't blame Steve Long for that one)

 

As I said, I know places where the system is broke. I don't go to those places.

 

Edit: in this case however the system isn't as broke as it looks.