Explain The Math to Me...

[Tequila Sunrise]

...as if I'm a casual player who doesn't think about weird stuff like math. What's all this talk about 'expected attacks & defenses'? For example, why shouldn't I add a magical sword's full enhancement bonus (+6) to my NPC's attack roll? Why's it so important to jack up my attack stat every four levels?

My math-head gamer friends make a big fuss about this stuff, but I'm too disinterested to understand on my own. Maybe a good analogy would help me understand!

 

[Dausuul]

...as if I'm a casual player who doesn't think about weird stuff like math. What's all this talk about 'expected attacks & defenses'? For example, why shouldn't I add a magical sword's full enhancement bonus (+6) to my NPC's attack roll? Why's it so important to jack up my attack stat every four levels?

My math-head gamer friends make a big fuss about this stuff, but I'm too disinterested to understand on my own. Maybe a good analogy would help me understand!

It's pretty straightforward. The game is designed around certain expectations, to keep everything balanced so that battles are tense and exciting and the PCs don't curbstomp the monsters or vice versa. If a PC's attack bonus falls behind what the game expects for that level, the PC will have a hard time hitting monsters at that level. If a monster or NPC's attack bonus is too high, the monster will hammer the party.

Regarding the +6 sword question: To make things easier for the DM, NPCs are designed with all their attack, damage, and stat modifiers already factored in. So, if your NPC is wielding a +6 sword, it's assumed that the NPC's "real" attack bonus is 6 points lower, along with her damage roll, etc.

 

[fba827]

...as if I'm a casual player who doesn't think about weird stuff like math. What's all this talk about 'expected attacks & defenses'? For example, why shouldn't I add a magical sword's full enhancement bonus (+6) to my NPC's attack roll? Why's it so important to jack up my attack stat every four levels?

My math-head gamer friends make a big fuss about this stuff, but I'm too disinterested to understand on my own. Maybe a good analogy would help me understand!

Monster(well, all NPCs) attacks and defenses are built relative to their level (example: the attack modifier against AC for an average monster is monster level + 5) <-- why? because it's quicker and easier for the DM to add the one modifier to level instead of figuring out feats and powers and enhancement bonuses.

For PCs, their attacks and defenses are based on attributes, half-level, items, powers, feats, etc. Notice how only a small fraction of this is level-dependant (and half-level at that) <-- why? because it allows more player controlled customization

Note that the modifier added to level for monsters is based on the expected progression for the PCs (aka why they chose "+5 for attack vs AC rather than +2 vs AC").

But if the player customization (or item availability or whatever in that formula) starts veering too far from expectation, then either monsters will be hitting way too easily (because the PC has lower defenses than expected) or the monsters will be frustratingly difficult to hit (because the PC has lower attack bonuses than expected).



Your comment about NPCs and their bonuses, since they follow the math for monsters, those expected bonuses are already added in to that static modifier that they got. It's only if you give them something above and beyond the expected amount do you need to add in the extra. Otherwise, you'll be adding in too much and making the NPC have a much better hit rate than it should (causing frustration to the PCs if they are the targets, or outshining the PCs if they are allied against a common foe)


Edit: Ninjaed

 

[Aulirophile]

Because if you do, your NPC will hit 30% more often then it is supposed to. An average even level monster will hit a reasonable PC defense on a 10+ (same as a PC). You're changing that to a 4+. If that doesn't seem like a ridiculous advantage, then I got nothing. It is the equivalent of putting them against a monster of level+6 in terms of accuracy and damage (since the +6 will also apply to damage, of course). If your NPC was also wearing magical armor your PCs would need 16+ to hit.

4e is built around certain assumptions. Here's an analogy for you: if you don't know how a car engine works, don't crack open the hood and start yanking stuff out. Sure someone who knows how a car engine works can often make things run better by opening the hood and changing some things around, but he knows how it works. You're just going to break something. 4e's math is the car engine. If you want to put in the effort to understand it, all well and good, but don't just start yanking on things.

 

[Obryn]

Because if you do, your NPC will hit 30% more often then it is supposed to. An average even level monster will hit a reasonable PC defense on a 10+ (same as a PC). You're changing that to a 4+. If that doesn't seem like a ridiculous advantage, then I got nothing. It is the equivalent of putting them against a monster of level+6 in terms of accuracy and damage (since the +6 will also apply to damage, of course). If your NPC was also wearing magical armor your PCs would need 16+ to hit.

It's arguably worse than that, even. They previously had 10 numbers on which they could hit. Now they have 16 of them. This is a 60% increase, not 30%! If they're of a higher level than the party - and odds are they will be, with a +6 weapon - it's entirely possible they'll hit on everything but a 1.

As for increasing your own attack stat...

Well, the monsters are going to be improving their defenses regardless of whether or not you increase your chances to-hit. If you care about hitting monsters, you should probably increase your main attack stat robotically, every level ending in 4 or 8.

-O

 

[Dice4Hire]

As other posters have said, the game was intended to be balanced on a knife's edge, where even a +2 to hit (CA) or a -2 to hit (marked) was a significant bonus or penalty.

This is one reason a lot of the open-ended bonuses and penalties (usually tied to str, wis, or some stat) have been errataed to static bonuses as the characters could get up to +/-7 or more and it was too strong. This was a problem on the player end of the spectrum, with stacking and such.

On the monster end was the 'feat taxes' where the designers (and many players) thought the characters were falling too far behind the monsters attack and defense scores, and thus feats were used to plug the 'perceive' gap.

Of course, where your players/group are with that is totally up to you.

 

[Tequila Sunrise]

Thanks, all. I recently realized how shockingly many gamers don't understand basic design math. Even forum-goers who feel qualified to give advice about bonuses and numbers.

One poster suggested I allow a player to add an armor's enhancement bonus to his thrall's AC, which appears to be RAW legit, but could get horribly broken.

An average even level monster will hit a reasonable PC defense on a 10+ (same as a PC). You're changing that to a 4+. If that doesn't seem like a ridiculous advantage, then I got nothing. It is the equivalent of putting them against a monster of level+6 in terms of accuracy and damage (since the +6 will also apply to damage, of course). If your NPC was also wearing magical armor your PCs would need 16+ to hit.

I think talking in terms of numbers on the d20 is helpful to non math-heads.

Can anyone think of an anology to illustrate the difference between 'base 1st level bonuses' (10 + armor bonus, Dex/Int) and the contributors to the +1/level math (masterwork armor, stat boosts, enhancement bonuses, etc.)?

Like "your PC's foundation may be higher or lower than other foundations, but everybody should build their skyscraper at the same rate. this way everyone on their roofs can play catch with each other." But better.

 

[KarinsDad]

Because if you do, your NPC will hit 30% more often then it is supposed to. An average even level monster will hit a reasonable PC defense on a 10+ (same as a PC). You're changing that to a 4+. If that doesn't seem like a ridiculous advantage, then I got nothing.

Actually, I think that it's no big deal.

If I look at the PC Essentials Thief in our group, he gets Combat Advantage nearly every single round, melee or ranged attack.

That's +2 for his entire career.


There is nothing wrong with blowing off WotC's rules about not adding item bonuses to monsters.

Yes, I know this sounds radical, but the math allows for it. It's just a slightly tougher encounter.

Let's take a +1 level weapon for a monster at level 1 through 5 or so.

The monster had a 50% chance to hit a given PC for 8.5 damage per round (d8+4). Now, it has a 55% chance to hit a given PC for 9.5 damage per round.

It's dpr goes from 4.425 to 5.35 or less than 1 extra damage per round. Fighting one on one against a first level PC, that typically means that it will take the PC down in 5 rounds instead of 6 (less dramatic for PCs higher than first level). At most, this is as if the monster were 1 level higher than normal. So, the DM takes that into account. When calculating XP, he assigns the monster one more level, the players get the bonus XP and the players get the magic weapon when they win.

Win win. More XP and the magic weapon isn't just found lying in a hole somewhere. The players feel like they accomplished something real by taking out the monster and getting its magic weapon.


For higher level monsters, the calculations become a little more complex, but no matter how powerful of an item that the DM gives the monster, it is never as potent as throwing an additional monster into the mix.

A 25th level monster with a +6 weapon is never as potent as two 25th level monsters. If the two monsters hit 50% of the time, that's 100% normal damage. The one monster only hits 80% of the time for normal damage +6.


The same does not apply for defensive items. If you want to give the monsters a defensive item boost, that's ok. But, I would make it half item round up (i.e. +1 item gives +1, +5 item gives +3, etc.). It makes the monster harder to hit, but not impossible to hit.

Rule of thumb for XP increase is: half item round up added to the level of the monster for XP for weapons, third item round down added to the level of the monster for XP for defensive item.


This approach makes more sense than WotC's approach, but the DM has to be cognizant that the monster is a bit tougher and hence, has to boost the encounter XP to compensate.

 

[renau1g]

Well in the DMG there are rules for using magic items for the monsters.

Magic Items: A monster equipped with magic items can use the powers those items grant.
Enhancement Bonuses: A monster benefits from an enhancement bonus to attack rolls, defenses, or AC only if that bonus is higher than its magic threshold, as shown on the table below.

A monster’s magic threshold is an abstract representation of its equipment, power, and general effectiveness against characters of its level. If you give
the monster a magic item that grants a bonus to attack rolls and damage rolls or to defenses, subtract the magic threshold from that bonus before you apply it. For example, if you give that 8th-level ogre savage a +2 magic greatclub, you add only a +1 bonus to its attack rolls and damage rolls, since its magic threshold is +1.

DMG pg. 175

It follows with some warning that the monsters are balanced usually as is so avoid adding in equipment to all monsters. I think certain monsters, especially Elites, could benefit from some items, especially their powers.