D&D 4E The Quadratic Problem—Speculations on 4e

[The Shadow]

Fair enough-- I refuse to have a discussion with a useless pedant who insists that "exponentially" must mean, "Involving the constant e" as opposed to, "Involving an exponent."

Excuse me? The standard definition of 'exponential' has nothing to do with 'e'. An exponential function is one in which you have terms like a^x, where a is a constant.

A quadratic function is not and cannot be an exponential one. An exponential curve will rise faster than any quadratic, regardless of the value of a.

If you have a problem with using the term "exponential" more colloquially to describe the power curve of D&D-- take it up with Bruce Cordell.

If Bruce Cordell uses the term that way, he doesn't know the way mathematical terms are used. To point that out isn't pedantry, it's literacy.

 

[drothgery]

Algebra days? I managed to duck algebra in high school and graduate without it. I have no idea what you wrote.

That's actually possible?!?! I mean, ducking calculus, or even Trig, okay. But I can't imagine giving a high school diploma to someone that hasn't passed first-year algebra or its equivalent. I mean, you can't do high-school level science without algebra.

 

[Charwoman Gene]

I have no problem with colloquial use of exponential as "Growing Fast".

It's inconsistent colloquialism that irks me. You used quadratic, a non-colloquial term, with Exponential used colloquially.

 

[hectorse]

I think your version is flawed.

Not only are they increasing the cushion constant K, but they are also putting power(1st) higher than 3rd edition, effectively giving 1st level PC's more power, but their stats advancing more linearly.

You should take that into account in your graph.

Plus, you should do discrete samplings instead of a continous one. You get more powerful by the level, as you never gain +0.323515 in BAB

One could argue that you can linearize the exponential growth expected and calculate the most desirable linear growth.

Linear growth is what I think we should expect: the more linearity we have, the less "OMG I went up a level and now everything is an INitiave tournament".

So what I would do, is do it backwards. From a desired linear growth, calculate the tangential exponential function that gives me the best approach, then discretisice it and transform it to game languaje.

Then we would have things like, 6th level is kind of overpowerful, but it fixes itself in 7th fast enough for people to not notice it.

I also noted that 3rd edition "sweet spot" is in the more linear part of the exponential.

 

[Wulf Ratbane]

I think your version is flawed.

Not only are they increasing the cushion constant K, but they are also putting power(1st) higher than 3rd edition, effectively giving 1st level PC's more power, but their stats advancing por linearly.

You should take that into account in your graph.

Unless I misunderstand you, it's accounted for in the equation. It's hard to see at the low end of the graph, as all the lines run together, but both the 2nd and 3rd series baselines at 1st level start above the 3e curve.

I can't, of course, put in the exact baseline shift since we don't know what it is yet (other than a pretty vague "4th is the new 1st.") I can say that none of my curves start at 4x power compared to 3e, but it's easy enough to tinker around with. I can see, perhaps, starting the PCs with 4HD, but I don't know how you'd reasonably make the Fighter 4x as effective on offense as he is now. Making him hit twice as often and twice as hard, I suppose-- but I am not sure that's reasonable. (Not IMC, at least.)

Plus, you should do discrete samplings instead of a continous one. You get more powerful by the level, as you never gain +0.323515 in BAB

True, but I'm most interested in looking at the smooth curve, not a series of discrete points.

 

[BryonD]

One point WotC has made is that first level characters are now more heroic.
This means that a and b are larger factors in your equations now.
As a and b get larger the impact of mdx^2 becomes less important.

The degree of this change remains to be seen.

 

[BryonD]

If you set A and B = 4 and m and d = 2/3 then over 30 levels the power only increases by 235%. Which I would consider to be far to little. So it seems this problem can be overcome.

 

[Wulf Ratbane]

One point WotC has made is that first level characters are now more heroic.
This means that a and b are larger factors in your equations now.

Exactly so. That's why I have used the values I used in series 2, 3, and 4.

It's also important to remember that (I think) m and d are ratios in relation to b and a; and for our purposes a and b are in relation to 3e.

For example, if we start the PCs with 4 HD, and they continue to get 1 HD with each increase in level, then we could say that a=4 and d=.25.

Offense is much harder to pin down. I can't believe that fighters will hit twice as often or twice as hard (but hey, they might...); or that wizards will begin the game at caster level 4. It's impossible to say at this point.

One possible clue is the new power sources: arcane, divine, and martial. We can agree that a wizard without spells is effectively neutralized, even if not killed. Assuming that the wizard generates his offense through his arcane power, the arcane power source becomes another expendable staying power, an alternative to hit points. We might be able to assume much the same about martial power, which might allow the fighter to hit twice as often and twice as hard, but through an expendable resource analogous to arcane or divine power.

As a and b get larger the impact of mdx^2 becomes less important.

I believe that as a and b get larger, m and d must become smaller fractions. (Character advancement, x, is already as granular as it can be: integers.)

When m and d are too small (that is, your increase feels like too small a portion of what you started with), levelling up starts to feel insignificant. I think there's a practical limit to how large a and b can get and still have m and d large enough to make levelling up feel like a win.

 

[BryonD]

When m and d are too small (that is, your increase feels like too small a portion of what you started with), levelling up starts to feel insignificant. I think there's a practical limit to how large a and b can get and still have m and d large enough to make levelling up feel like a win.

Exactly.

So it is "just" a matter of finding the golden ratios.

 

[Umbran]

Fair enough-- I refuse to have a discussion with a useless pedant...

Wulf, the name calling is not acceptable. I don't care how good the content in the rest of the thread is - I'm going to have to ask you to not post in it again. Please e-mail me if you want to discuss this.