Monday, January 25, 2010

Fixing the math: Fortitude, Reflex, Will

They start out all right, neither too easy nor too difficult to hit. But as the levels increase, they lag behind and never recover. Fortitude, Reflex and Will, also known in certain circles as NADs (non-AC defenses), are broken. Heroic characters barely notice it, Paragons start to suffer, and Epic heroes just have to assume that certain attacks will always hit them. Today I will talk about why this happens, just how bad it is, and how the official "feat patch" fails to solve the problem - and in the following post I will suggest a way to fix it!

The issue with NADs is similar to the one with attack bonuses and expertise, only worse. Essentially, attacks and defenses in 4E are assumed to increase at a rate of 1 point per level, but they don't quite. Over the course of 30 levels, a character's attacks fall behind by 4 points, compared to their expected values. (hence expertise). In the case of NADs, they also fall behind, but at different rates, depending on whether they are 'good' or 'bad' defenses:
  • A good defense is affected by a primary or secondary ability modifier. Since this ability is increased whenever possible (for a maximum of an additional +4 modifier at maximum level), the defense follows the same progression as attack bonuses, sharing the same 4 point gap . This is annoying, but not catastrophic.
  • A bad defense, on the other hand, depends on tertiary abilities, which only get increases at levels 11 and 21. As a consequence, the gap for these defenses reaches a whopping 7 points at level 30. This means that, at Epic Tier, a monster making an attack against a bad defense can hit a player character with a roll of 2 or more. Hit rates at Paragon aren't that extreme, but can easily be higher than 80%, which is also problematic. Every character in the game suffers from at least one bad defense (or two, if both primary and secondary abilities affect the same defense), so this is a critical problem.

Example 1: Basic scenario

I have built two sample characters to illustrate defense progression across levels. The first one, PC1 is an extreme (but still relatively common) worst-case scenario of a character with two bad defenses. Assuming that the character uses an ability score array of 18, 14, 11 (pre-racial modifiers), that he has a racial bonus to his primary ability and a +2 class bonus to his best defense, his starting NAD scores would be 17 for the best defense, and 11 and 10, respectively, for the second and third best. 1 point in the second-best defense comes either from a racial bonus to a tertiary ability, or from a racial bonus to a defense. This character could be a Battlerager Fighter, a Wand Wizard, or a Devoted Cleric, among others.

The second sample character, PC2, has well-balanced NADs, with only one bad defense and a starting ability array of 16, 16, 12, 12 (pre-racials). This character would have racial bonuses to both primary and secondary abilities, and a +2 class bonus to the best defense, for starting NAD scores of 16, 14, and 11 (from best to worst defense). This character could be a Whirling Barbarian or a Chaos Sorcerer, among others.

The following graphs show the NAD progression for PC1 and PC2 in the basic scenario (no defense-boosting feats). These values have been normalized (i.e. they are substracted the PC's level) for clarity. Two additional lines, "cap" and "auto-hit", are shown, representing the defense values where a skirmisher monster of equal level would hit on a 20+, or on a 2+, respectively. For more information on normalization, you can read this article. Enhancenment bonus from Neck slot items are added at levels 2, 7, 12, 17, 22 and 27. The detailed calculations can be followed on this spreadsheet.

We can calculate the average hit rates for monsters of equal level against these defenses, using the method described in the normalization article. They are the following:

As we can see, for PC 1 the worst defense moves into auto-hit territory at level 15. PC1's second defense and PC2's worst one, on the other hand, don't get that bad until level 23. Nevertheless, their values are worryingly low even before reaching this cap, with hit rates of 90% starting at levels 13 and 17, respectively.

As for the good defenses, they are acceptable but noticeably lower at epic tier, compared to their starting values.

Example 2 - NAD-boosting feats

Since the examples above assumed that no NAD-boosting feats were taken, now we are going to analyze how these feats mitigate the problem. There are eight feats in the game whose sole purpose is to provide a bonus to Fortitude, Reflex, and Will. Half of them are Paragon-Tier feats: Paragon Defenses, Great Fortitude, Lightning Reflexes, and Iron Will. The rest are Epic clones of the former, but with better bonuses: Robust Defenses, Epic Fortitude, Epic Will, and Epic Reflexes. It is unfortunate that they chose to duplicate feats, rather than having less of them, but with scaling bonuses, a la Weapon Focus.

A player who wants to close the NAD gap by taking these feats is presented two options: the cheap solution, and the expensive one. The cheap solution consist in taking Paragon Defenses at Paragon tier, and retraining to Robust defenses at Epic. This costs the player a single feat, but has a reduced effect - good defenses become a bit lower than they should, whereas the auto-hit cap in bad defenses is delayed a few levels but eventually appears again. For this reason, we will focus on the expensive solution: taking the full set of 3 feats for fortitude, reflex and will at paragon, and retraining them at epic.

For that hefty cost, one would assume that you could forget about NAD problems, but it turns out that you can't. The figures below show defenses for PC1 and PC2, assuming that they somehow take the three appropiate feats at level 11, and retrain at 21. (Actual PCs would have to wait until levels 11 and 22 for the third of these feats, but the graphs ignore this for simplicity).

And the corresponding hit rates:

This progression is definitely better, and the dreaded bugbear of auto-hit is gone. However, upon close examination, we can see that bad defenses are still terrible at Epic tier, with hit rates of 80% or worse. At such low values, the feat bonuses are underutilized: 80% is only a 15% improvement above the cap, instead of the theoretical 20% that a +4 bonus should net you. And this diminished improvement practically disappears when facing a higher-level monster or a soldier. For this reason, players might be better off giving up on bad defenses altogether. Clearly, this expensive solution is unsatisfactory.

Example 3 - The house rule.

Since this is already quite long, I will leave my suggestion for house rules for the following post. However, I'd like to show the graphs for these revised rules here, so that they can easily be compared with the current ones. Here they are:

Although some oscillations are inevitable, this is a very regular progression across tiers. A mechanism to ensure that bad defenses don't fall below a certain threshold has been added, so that they remain weak but can actually be missed at epic levels.

Next: The Fix!

1 comment: