Saturday, September 14, 2013

Choke Points Revised

In an earlier post, I noted the tendency of attacks and defenses to hit choke points. However, the model I was using in order to address this tendency actually led to a higher standard deviation from the proper values than the actual 4E system.

Then I realized the issue that I was having, and have since fixed the math. To understand the issue at hand, let's create a model:

If we assume that attack bonuses and defenses are supposed to level up at a rate of 1/level, then by 30th level PCs will be at -2 to hit/defenses relative to the proper baseline, assuming normal rules (+1 feat bonus per tier, +6 enhancement bonus). To quantify the deviation from the baseline, we create a chart that shows the estimated values for each level, compared to the expected value (which is the level of the character):

Normal 4E rules:
I'm playing a bit fast and loose with the statistics terminology here, but "Variance" is what we're trying to minimize-that is, at any given level, we want to be as close to zero as possible. So, as we see, standard 4th edition rules gives a sum of Var of 38 over 30 entries. As an alternative, let's look at the revised method I've been using in my campaigns-that is, giving PCs a +1 bonus at 1st level, and a +1 bonus every three levels:


Level 1/2 level Ability Sum
Boon End Difference Var
1 0 0 0
1 0 0
2 1 0 1
1 0 0
3 1 0 1
2 0 0
4 2 0 2
2 0 0
5 2 0 2
2 -1 1
6 3 0 3
3 0 0
7 3 0 3
3 -1 1
8 4 1 5
3 0 0
9 4 1 5
4 0 0
10 5 1 6
4 0 0
11 5 1 6
4 -1 1
12 6 1 7
5 0 0
13 6 1 7
5 -1 1
14 7 2 9
5 0 0
15 7 2 9
6 0 0
16 8 2 10
6 0 0
17 8 2 10
6 -1 1
18 9 2 11
7 0 0
19 9 2 11
7 -1 1
20 10 2 12
7 -1 1
21 10 3 13
8 0 0
22 11 3 14
8 0 0
23 11 3 14
8 -1 1
24 12 3 15
9 0 0
25 12 3 15
9 -1 1
26 13 3 16
9 -1 1
27 13 3 16
10 -1 1
28 14 4 18
10 0 0
29 14 4 18
10 -1 1
30 15 4 19
11 0 0

As we see, the sum of the var in this instance is a mere 12-a vast improvement over base 4E in terms of avoiding chokepoints. On the other hand, perhaps the proper baseline is actually not advance +1 per level, but rather advance +1 per level -1; that is, you should have gained +29 by 30th level, rather than +30. The boon system in this case can be simply amended to be +1 every three levels, but the base 4E system cannot. On the other hand, consider what happens if the +2 bonus to ability scores that many epic destinies grant are considered "math fix" features, and we are operating under this "+29 by 30th level" system:


Level 1/2 level Ability Feat Item Sum Diff Var
1 0 0 1 1 2 2 4
2 1 0 1 1 3 2 4
3 1 0 1 1 3 1 1
4 2 0 1 1 4 1 1
5 2 0 1 1 4 0 0
6 3 0 1 2 6 1 1
7 3 0 1 2 6 0 0
8 4 1 1 2 8 1 1
9 4 1 1 2 8 0 0
10 5 1 1 2 9 0 0
11 5 1 2 3 11 1 1
12 6 1 2 3 12 1 1
13 6 1 2 3 12 0 0
14 7 2 2 3 14 1 1
15 7 2 2 3 14 0 0
16 8 2 2 4 16 1 1
17 8 2 2 4 16 0 0
18 9 2 2 4 17 0 0
19 9 2 2 4 17 -1 1
20 10 2 2 4 18 -1 1
21 10 4 3 5 22 2 4
22 11 4 3 5 23 2 4
23 11 4 3 5 23 1 1
24 12 4 3 5 24 1 1
25 12 4 3 5 24 0 0
26 13 4 3 6 26 1 1
27 13 4 3 6 26 0 0
28 14 5 3 6 28 1 1
29 14 5 3 6 28 0 0
30 15 5 3 6 29 0 0

We are then left with a variance of 30. Comparatively, a +1 every three level boon system, combined with the +2 to an ability score at 21st level gives us:


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

We are again given a variance of 12-far better than standard 4th edition rules.

So, what's the takeaway? Well, first of all, getting a new weapon every 5 levels is a lot less work than every three levels. Other than that, "epic" weapons being +6 corresponds with pre-4E rules, so perhaps there were legacy issues at work. My general math fix is as follows:

1.) Decide if you're using a +29 over 30 levels system or a +30 over 30 levels system.

2.) If using a +29 system, award a +1 bonus to attack rolls, damage rolls, and all defenses for every three levels; either do this through changes to the item system, or in the form of boons. (More info on heavy armor is discussed in a bit).

3.) Prohibit feat bonuses to attack rolls, damage rolls, and to defenses. It's up to the DM whether or not to allow Superior Will as a feat that gives no feat bonus to will or the like (I tend to think it's a bit too powerful of a feat, personally, but that's outside the scope of this post).

4.) Figure out how you're going to handle armor. The numbers used for attack under the basic system do not quite fit the numbers for AC, because rather than getting feat bonuses at a rate of 1/tier, characters instead get Masterwork bonuses (and potentially a feat bonus in the form of Armor Specialization). If characters get +1 AC per three levels, this value essentially includes the masterwork bonus-as thus, there's no need to include separate masterwork armor.

However, heavy armor characters obviously need a bigger boost. There are a few ways of handling this:

1.) Heavy Armor increases at a rate of +1/2 level, instead of at a rate of +1/3 level. If this bonus is staggered-such that the bonus is (Level-1)/2+1, you'll actually end up with a character with an AC that is exactly equal to the baseline, assuming you're using a +30 model, since you are literally increasing your AC by 1 per level.

2.) Heavy armor increases at a rate of +1/3 level, and also at a rate of +1/6 per level. This rate gives a higher variance, but more closely approximates non-heavy armor classes.

3.) Heavy Armor increases at a rate of +1/3 level, and also at a rate of +1/7 per level. This is the rate you should use if you do not consider epic destiny bonuses to be math fix, but on the other hand, it's a great deal clumsier than the other two methods.

A few other considerations:

1.) Some common magical items (Circlet of Indomitability, etc) give bonuses. Consider whether these are "math fix" items for the purposes of your campaign, and if not, if having them is appropriate.

2.) Epic Fortitude, Epic Reflex, and Epic Will are game changers in this regard. Here's my fix:
  Remove Epic Fortitude, Epic Reflex, and Epic Will from the game:
Great Fortitude now allows you to use a +2 bonus in place of your strength or constitution modifier when determining fortitude; this bonus increases to +4 at paragon, and +6 at epic.
Lightning Reflexes now allows you to use a +2 bonus in place of your dexterity or constitution modifier when determining reflex; this bonus increases to +4 at paragon and +6 at epic.
Iron Will now allows you to use a +2 bonus in place of your wisdom or charisma modifier when determining Will; this bonus increases to +4 at paragon and +6 at epic.

You may note that this system is similar to Perico's (author of the blog Square Fireballs), though using feats instead of items.

3.) The biggest difficulty in implementing the system described above is that it requires a total revamp of how weapons, armor, and neck slot items work. In particular, weapon changes require a change in critical hit dice. Other issues include the fact that armor, weapon, and neck slot features may be dependent upon enhancement bonus; therefore, a 12th level item in standard 4E goes from having a +3 effectiveness on special effects to having +4 or +5 effectiveness. I'm still working out these issues myself. For most "casual" campaigns, it's much simpler to simply stay with the baseline 4E model.


2 comments:

  1. I prefer to discreetly fix any balance issues from behind the screen, sometimes even on the fly, by adjusting the monsters' accuracy and defense. That also helps me deal with the very occasional player who optimizes his character more than his fellows.
    I nonetheless appreciate your very thoughtful and careful analysis of the mathematics and logic of the Fourth Edition system.

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