Math behind PC defenses and to hit VS monsters ?

[Silverwave]

I'm looking for a post where someone made the math behind the pc and monster to hit and defense curve that make a lot of people thinking the system needs a fix (that Expertise and Epic reflexes/fort/will don't patch up well, wich I agree).

I do understand that monsters gains +1 to hit and defense every lvl (+29 at lvl 30), and that pc only get +25 in 30 lvls.
But I'm interested in more precise maths that could make me believe or deny that the system really needs a fix.

Is anyone made the math including all the modifiers (lvl, stat, magic, etc) and also include "misc" bonus granted by powers, CA, etc ?

I've been looking around for hours and didn't find what I'm really looking for.

Thanks.

 

[Nail]

I have, but pro'ly not in a form you'd like: xls spread sheet.

You needn't bother with "misc" (or "situational") modifiers, as they don't always apply, and vary quite a bit between games.

You do need make lots of assumptions:

#1) Magic Items: The best IMO, is to assume a +1 Atk, AC, & F-R-W by level 4, and then +1 to each every 5 levels after that. ...Or you can get a tad more complicated, and assume you get +1 atk by 2nd, a +1 AC by 3rd, and a +1 F-R-W by 4th. Either way.

#2) Ability Scores: +1 to the primary attack stat at all levels possible, +1 to a secondary stat at all levels possible (and assume the secondary stat increases a different defence than the primary stat). Then the 11th and 21st bumps to all, which means all other defences go up by 1 by 21st level.

#3) Race and Class: Assume a +1 defence in 2 of F-R-W.

.....an' that's a lot of assumptions.



Do it yourself, an' see what'cha get.

 

[KarinsDad]

I won't go into other defenses or into PC to hit since that has been done a lot, but I'll illustrate PC AC vs. monster to hit here. Comparing Light to Heavy armor at various levels, the armors get the following total boosts (not counting half levels, assuming acquiring +1 better magic armor at levels 3, 8, 13, 18, 23, and 28):

Light: 3 +1, 8 +3, 13 +4, 14 +5, 18 +6, 21 +7, 23 +8, 28 +10
Heavy: 3 +1, 8 +3, 13 +5, 18 +7, 23 +9, 28 +12
Heavy: 3 +1, 8 +2, 13 +3, 18 +7, 23 +8, 28 +12
Monster: 3 +1, 5+2, 7+3, 9+4, 11+5, 13+6, 15+7, 17+8, 19+9, 21+10, 23+11, 25 +12, 27 +13, 29 +14

The first Heavy here is the WotC corrected PHB II (or AV), the second Heavy here is the original PHB. The original PHB was terrible for Heavy armor by level 13 (the monster is +6, the PC is +3).

Monster to hit gains go up by +13 over 26 levels (over PC half level bonus). Light armor goes up by +10 in 27 levels, Heavy by +12. This does not take into account feats, powers, paragon path abilities, etc.

In response to your question, the concept is that monster hit points gain significantly at higher levels. When both the PC to hit drops percentage-wise to monster hit points and the PC damage drops percentage of monster hit points-wise, it takes longer to wipe out a monster. That makes the encounter last much longer.

The same is true conversely for AC here. If the AC does not keep up with the monster to hit (and obviously, it is very difficult to gain a +4 to AC for all classes by high Epic, a few classes can manage it), the PCs are behind the 8 ball in both offense and in defense. This means that they waste more actions and resources healing or giving additional saves or whatever than attacking which makes an encounter last even longer.

No doubt. PCs have more powers and synergies at higher levels to partially make up for this. But then again, so do monsters. At first level, a standard monster has similar hit points to a PC. At high level, a standard monster often has double as many hit points as a PC. Higher level Solos have 5 times as many hit points as PCs at first level. They can have 8 to 10 times as many hits points at high level. Many monsters have auras at high level. Very few monsters have auras at low level, etc. When the chance to hit decreases and the chance to get hit increases as one goes up levels, these extra monster hit points allow the monsters to last a long time. The PC synergy bonuses do not make up for this.

 

[Elric]

I won't go into other defenses or into PC to hit since that has been done a lot, but I'll illustrate PC AC vs. monster to hit here. Comparing Light to Heavy armor at various levels, the armors get the following total boosts (not counting half levels, assuming acquiring +1 better magic armor at levels 3, 8, 13, 18, 23, and 28):

Light: 3 +1, 8 +3, 13 +4, 14 +5, 18 +6, 21 +7, 23 +8, 28 +10
Heavy: 3 +1, 8 +3, 13 +5, 18 +7, 23 +9, 28 +12
Heavy: 3 +1, 8 +2, 13 +3, 18 +7, 23 +8, 28 +12
Monster: 3 +1, 5+2, 7+3, 9+4, 11+5, 13+6, 15+7, 17+8, 19+9, 21+10, 23+11, 25 +12, 27 +13, 29 +14

The first Heavy here is the WotC corrected PHB II (or AV), the second Heavy here is the original PHB. The original PHB was terrible for Heavy armor by level 13 (the monster is +6, the PC is +3).

Monster to hit gains go up by +13 over 26 levels (over PC half level bonus). Light armor goes up by +10 in 27 levels, Heavy by +12. This does not take into account feats, powers, paragon path abilities, etc.

You're missing Masterwork Light Armor in the above table. Light Armor goes up by +12 as well once you take that into account.

 

[Nail]

Many monsters have auras at high level. Very few monsters have auras at low level, etc.

...that may be, but one of my DMs manages to hit us with an "aura" monster almost every combat!

"Auras" turn out to be a contributing factor that I never concidered before playing. Since an aura isn't (necessarily) an attack, your defences (and marks!) don't matter, and they can quickly make life difficult - and hps scarce! - for all melee PCs.

 

[KarinsDad]

You're missing Masterwork Light Armor in the above table. Light Armor goes up by +12 as well once you take that into account.

You're right. My bad.

Light: 3 +1, 8 +3, 13 +4, 14 +5, 18 +7, 21 +8, 23 +9, 28 +12
Heavy: 3 +1, 8 +3, 13 +5, 18 +7, 23 +9, 28 +12
Heavy: 3 +1, 8 +2, 13 +3, 18 +7, 23 +8, 28 +12
Monster: 3 +1, 5+2, 7+3, 9+4, 11+5, 13+6, 15+7, 17+8, 19+9, 21+10, 23+11, 25 +12, 27 +13, 29 +14

So, AC is not really a major issue (+12 vs. +14). Good to know. I really zoned on that Light Armor.

Just PC to hit (+10 vs. +14) and PC non-AC defenses (+7 to +10 vs. +14).

 

[KarinsDad]

"Auras" turn out to be a contributing factor that I never concidered before playing. Since an aura isn't (necessarily) an attack, your defences (and marks!) don't matter, and they can quickly make life difficult - and hps scarce! - for all melee PCs.

The big two auras in the MM are Fire and Necrotic (Cold and Psychic secondary).

The big two ongoing in the MM are Poison and Fire (Acid and Necrotic secondary).

So, get yourself some good Fire and Poison gear, and possibly Necrotic and Acid gear in that order and you can pretty much ignore the rest.

 

[Silverwave]

Thx KarinsDad

Well, I was also looking for attack bonus and defense bonus, something like (it's just an example)

PC bonus to attack
1: +6 (+3 stat, +3 profiency)
2: +7 (+3 stat, +3 profiency, +1 ½lvl)
3: etc
...
30: etc

PC bonus to defenses (strong/average/poor)
1: 15 (+3 stat, +2 class) / 12 (+2 stat) / 10
2: 16 (+3 stat, +2 class, +1 ½lvl) / 12 (+2 stat, +1 ½lvl) / 11 (+1 ½lvl)
3: etc
...
30: etc

and the same for monsters.

It's just that there's so much post about fixing Expertise, etc, so I said : it's clear someone already made the math!

 

[KarinsDad]

Well, I was also looking for attack bonus and defense bonus, something like (it's just an example)

PC bonus to attack
1: +6 (+3 stat, +3 profiency)
2: +7 (+3 stat, +3 profiency, +1 ½lvl)
3: etc
...
30: etc

PC bonus to defenses (strong/average/poor)
1: 15 (+3 stat, +2 class) / 12 (+2 stat) / 10
2: 16 (+3 stat, +2 class, +1 ½lvl) / 12 (+2 stat, +1 ½lvl) / 11 (+1 ½lvl)
3: etc
...
30: etc

and the same for monsters.

It's just that there's so much post about fixing Expertise, etc, so I said : it's clear someone already made the math!

Easy enough to do:

Same level creature to hit number against: high defense (taken every time plus starting stat 18 plus 2 class), medium defense (taken every other time plus starting stat 14 plus 1 class), low defense (never taken plus starting stat 10 plus 0 class): assuming item gain at levels 3, 8, 13, 18, 23, 28 and not using feats or race bonus and creature is Level +4 against the defense (most monsters average level +3 to level +5 except the Brute)

 1 11 8 5
 2 11 8 5
 3 11 8 5
 4 11 8 5
 5 10 7 4
 6 10 7 4
 7  9 6 3
 8 11 7 4
 9 10 6 3
10 10 6 3
11  9 6 2
12  9 6 2
13  9 6 2
14 10 6 2
15  9 5 1
16  9 5 1
17  8 4 0
18  9 5 1
19  9 5 1
20  8 4 0
21  8 4 0
22  8 4 0
23  8 4 0
24  8 4 0
25  7 3 -1
26  7 3 -1
27  6 2 -2
28  8 3 -1
29  7 2 -2
30  7 2 -2

Obviously, the 1, 0, -1, and -2 are all 2s because a 1 misses, but it does illustrate how much a player has to add with feats or whatever to a weak defense to get it even to a 3.

The best defense drops 4, the worse defense drops 7.

I won't bother doing it for offense. It's the inverse of the first column (i.e. the PC's chance to hit increases by the same amount that the monster's chance to hit decreases). So if the PC could hit with an 11 at level 1, he can hit with a 15 at level 30 (not counting feats, paragon path abilities, powers, etc.).

Note: I did this with a spreadsheet, so it should be accurate.


One other major note: This is with a same level creature. Imagine how much easier it is for an elite or a solo or higher level creatures to hit.

The math is seriously flawed, even for a PC's best defense.

 

[WalterKovacs]

Based on that, it does seem that the various defense boosting feats are enough to keep the defenses for the stats you boost at each level to keep comparable to starting defenses. The dump stated defense is probably going to be bad no matter what [you can get I guess +9 total with item bonuses added to the various feats. That gets you to 7. If it's reflex, a heavy shield gets it to 9. Presumably you'd start with a stat higher than 10 in your worst save (either 18's in your primary/secondary after racial, and 12 in one stat for a different save, or you have 18/16 with a 14 in a tertiary, so that can get you an extra +1 or 2, which could get you up to an 11, plus there are classes like paladin that would give you +1 across the board to saves, even the worst one.] Ultimately, with taking all the feats, and an investment in items, plus not completely dump statting at the start, you can get close to a 50/50 against same level enemies with your worst defense. Your best defense can be kept decent with minimal upkeep (about a feat per tier) and can be made really high if you invest.

In the AC situation, the paragon feats for armor specialization (or shield specialization) closes the gap to +13 vs. +14, so it seemed that AC, at least, had it's math worked out early (with the masterwork), and they used the Adventurer's Vault to clean it up (as they hadn't factored in some of the intermediate stages, just the big picture "at 30, the difference between start and now, with the feat, is a drop of 1".

The PHBII feats seem to fall in line with the masterwork/armor specialization 'math fixes' in the PHB and Adventurer's vault [the item bonuses to non-AC defenses in Ad Vault probably being a math fix before PHBII, meaning they can tbe combined to get ahead of the curve on good defenses, or can turn the worst defense into one that is non-trivial to hit.