The Mathematical Model of the d20 System

[Wulf Ratbane]

I disagree that these are problematic.
I've never had a problem with the fighters having things easy in fights.
Easily hitting the hulking beast that is literally the broad side of a barn, only with giant teeth and a boatload of HP is a feature, not a bug.
Swatting down mooks by the dozen is a feature, not a bug.
Making the wizard's eyes get as big as saucers and go "Damn! That was impressive!! But can you do THIS!!??!!??" is a feature, not a bug.
Throwing in foes with an AC that requires a decent roll from the fighter and forces the wizard to come up with an idea better than hit it with a stick is not a problem whenever desired.
I like all of the above and would not look well on a rule that infringed upon them.

That misses the point of the "sweet spot" entirely.

The "sweet spot feel" is determined by the ratio of successes to failures. Always succeeding and/or always failing, such as occurs when the d20 is overwhelmed by the bonuses involved, throws out that ratio. The sweet spot is that very specific feeling that is generated by exactly the right ratio of success, failure, risk, reward-- making or missing a roll by "just this much."

One could sum up the entirely of your post as, "I don't think there's such a thing as a sweet spot."

And that's fine.

You're also saying that you enjoy the game of absolutes. That's also fine-- but a matter of taste.

You're also pretty much saying that you're perfectly content to play d20 without the d20, letting the fighters always succeed at the things they are good at, always letting the wizards succeed at the things they are good at, and vice versa for failures. You've described a very different but nevertheless viable game where the only determining factor is in describing the "right" decision that is in character.

That is exactly what happens in high level play. The entire feel and philosophy of the game changes.

Which is exactly what I was addressing (ie, "Why does the sweet spot end where it does?")

 

[occam]

The version of the original joke I heard went something like this:
A gambler approached a mathematics professor looking for a way to beat the horse races. The mathematician worked on it for several months, with the gambler constantly calling for updates and preliminary results, but the mathematician wouldn't give any information until his work was done. Finally, he called the gambler and said, "I have worked out the system you wanted. The outcomes are predictable in the aggregate, and we will both be rich."

The gambeler said, "Fantastic! Tell me, how does it work?"

The mathematician said, "First of all, assume the horses are spherical..."

Here's how I heard it:

The king called in an engineer, a mathematician, and a physicist, and told them, "My subjects are having a hard time making enough to eat. I need you to find a way to milk a cow more efficiently. Come back in a week."

A week later, the engineer is brought before the king. "Sire, I looked and looked, through every book I had, and nowhere could I find the specifications for building a cow-milking machine. I'm sorry, I have failed you."*

"Fine," says the king, "bring in the mathematician." The mathematician arrives, and says, "Sire, I have not devised a way to milk a cow more efficiently. However," he says, triumphantly, "I have proven that, given the existence of a cow, it can be milked."

The king glares at him, and says, "Take him away! Bring me the physicist!" The physicist comes before the king, and excitedly proclaims, "Sire, I have solved your problem! I have found a way to milk a cow more efficiently!" "Please, tell me how," says the king. The physicist says, "First, we assume the case of a spherical cow..."

I don't have any comment on the thread topic, I've just always liked this joke.

* I should point out that this is how a physicist tells the joke; others may tell it somewhat differently.

 

[occam]

The "sweet spot feel" is determined by the ratio of successes to failures. Always succeeding and/or always failing, such as occurs when the d20 is overwhelmed by the bonuses involved, throws out that ratio.

I think to be more specific, the problem is caused by the d20 being overwhelmed by the variation in bonuses involved. I.e., if the fighter has a +25 attack bonus and the wizard has a +20, that's OK. If the fighter has a +25 and the wizard has a +10, that's a problem. It seems that reducing the variation, not the absolute scale, is what 4e is trying to do to extend the sweet spot.

I guess I did have something to say on this topic.

 

[BryonD]

One could sum up the entirely of your post as, "I don't think there's such a thing as a sweet spot."

And that's fine.

I would certainly say that I am significantly less hung up on the sweet spot than you are. But I think it is a big overstatement to go from my wider tolerance to what it fun is to a rejection of a sweet spot at all.

You're also saying that you enjoy the game of absolutes. That's also fine-- but a matter of taste.

No, exactly the opposite, I'm saying I like a wider range of greys.

You're also pretty much saying that you're perfectly content to play d20 without the d20, letting the fighters always succeed at the things they are good at, always letting the wizards succeed at the things they are good at, and vice versa for failures.

No, again, I'm saying that the DM controls when the D20 is the controlling factor and when the bonuses and targets are the controlling factor. The majority of the time the bonuses and targets are the controlling portion. You are ignoring what I said in my very first post in this thread.

I don't think that is a problem with D20. As long as the targets and bonuses are roughly ok, it works.

It was you that moved the focus of conversation to extremes. I simply responded to your subsequent examples of irrelevance. And when the DM chooses to allow those fringe irrelevance episodes to happen, it is because the DM wants them for the kind of fun that brings.

You've described a very different but nevertheless viable game where the only determining factor is in describing the "right" decision that is in character.

No. I've described a game where the blend of luck control and "right" choice control is a tool that may be adjusted by a good DM.

Which is exactly what I was addressing (ie, "Why does the sweet spot end where it does?")

And I think the clear point here is that there is not at all a "right" answer to that question.

I don't find the "sweet spot feel" to be established on a roll by roll basis. To me it is much more important how encounters and even strings of encounters flow. And if the fighter never gets that bit of "miss only on a one" then the game is going to be outside the sweet spot because being that level of badass is part of it. But it is way off to say that defines the game. They remain an exception. So trying to use those exceptions to define the total game feel is very wrong. But just because they are the exception doesn't mean I would look well on removing them. It is a package deal.

I like having my cake and eating it too.

 

[Wulf Ratbane]

I think to be more specific, the problem is caused by the d20 being overwhelmed by the variation in bonuses involved. I.e., if the fighter has a +25 attack bonus and the wizard has a +20, that's OK. If the fighter has a +25 and the wizard has a +10, that's a problem. It seems that reducing the variation, not the absolute scale, is what 4e is trying to do to extend the sweet spot.

I guess I did have something to say on this topic.

And well said. That's exactly right.

Bryon's point (if I read him correctly) is that there needs to be cases where +25 vs. +10 still occur. That's not "sweet spot" feel, but it's a different "good feel" that the current game emulates that needs to be preserved.

Haven't really thought about it too much except to say I'm probably closer to Bryon's point of view than 4e's. I'm definitely not a fan of all classes running together into a pasty mush.

I think 3e's problems in this regard are closer to this:

1) Too many ways to accumulate bonuses make the gap appear faster (ie, bonus stacking issues)

2) Players have way too much control over their ability to accumulate those bonuses.

I'd fix one, if not both, of those things, before I'd move to a 1/2 level +X flat scale for all classes.

a) I'd remove certain types of bonuses and/or how they stack;
b) I'd drastically curtail player control/customization vis-a-vis Item Creation.

 

[Wulf Ratbane]

No. I've described a game where the blend of luck control and "right" choice control is a tool that may be adjusted by a good DM.

I know you're gonna have a field day with this, but here goes:

That's bad design.

Even bad DMs have a reasonable expectation that the game should just "work."

A good portion of 4e adopters are in that camp for exactly that reason.

 

[Nifft]

I know you're gonna have a field day with this, but here goes:

That's bad design.

Even bad DMs have a reasonable expectation that the game should just "work."

A good portion of 4e adopters are in that camp for exactly that reason.

Even some of us who are occasionally considered "good DMs" like the idea of doing the work we want to do, rather than doing the work the game designers decided they didn't want to do.

A lazy bastard, -- N

 

[Wulf Ratbane]

Even some of us who are occasionally considered "good DMs" like the idea of doing the work we want to do, rather than doing the work the game designers decided they didn't want to do.

A lazy bastard, -- N

But math is HARD.

 

[Nifft]

But math is HARD.

"Let's go shopping!" [/barbie]

"Dreamhouse now comes with with FREE Quori!", -- N

 

[arscott]

As for the WotC's EL/CR/XP system, the whole thing works out something like this:

In order to gain a level, a character must earn [current level * 1000] xp (on top of the xp he has already gained at previous levels)

Defeating a creature with a CR equal to your level yeilds [current level * 300] xp (divided by the number of characters in the party)

There is no underlying math behind CR assignment. A creature is assigned a CR based on the best guess of its designer.

Creatures with fractional CRs are considered to be a threat equivalent to that fraction of a single CR 1 creature, and grant xp accordingly (That is, three CR 1/3 creatures are a equal to one CR 1 creature).

For Whole-number CRs, two creatures of a given CR are considered to be equivalent to a single creature of [CR + 2], and grant xp accordingly (That is, two CR 1 creatures are equal to one CR 3 creature)

The method listed above in can be extended to Creatures whose CR is within seven of a character's level. after that, the creature doesn't grant XP at all. (So, if two CR 1 creatures are equal to a CR 3 creature, then four CR 1 creatures is a CR 5 creature, eight is a CR 7. But no EL 9 encounter ((that is, an encounter equivalent to a CR 9 creature)) can be built using only CR 1 creatures.)