Friday, April 30, 2010

Character survivability across levels

After defining the concept of character survivability (and providing a tool for calculating it), I think it's time to explore its applications. Today I'll study the S (survivability) values of three different characters, representative of each party role: a defender, a controller, and a striker/leader (since both roles share similar amounts of HP and defenses). I'll compare their progression across the 30 levels of the game, examining survivability for individual defenses as well as overall survivability.

I'd like to find out whether the relative resilience of each role remains stable throughout tiers, or it presents large variability due to scaling differences. Also, I want to analyze absolute survivability values, and their implications on combat length - having defined the metric as the number of turns until a PC is killed by a monster of the same level, these numbers should provide a very rough estimation (i.e. before accounting for healing and stunned monsters) of the maximum duration of an encounter of the PC's level. The minimum duration, of course, would be dependant on the party DPR... but that is a story for another day. Let's proceed with the experiment.

The sample characters.

One requirement of this study is to have a set of sample characters whose survivability values could be representative of their role. Since defensive statistics can vary considerably, even for a given class/race combination, depending on the choice of feats and items, this is no trivial task. In order to keep complexity at a manageable level, we will make the following assumptions:

- Each character starts at level 1 with average defensive stats for their role.
- It is assumed that the character takes the feats and ability increases necesary to keep AC stable as they level up. Other than that, no survivability-boosting feats or items are considered. Any actual PC who invests in survivability should show values above these, particularly at higher levels.
- The leader role and striker role are considered equivalent from a survivability point of view. From now on, when I mention the "striker" character, it applies to either role.

This is how we assigned values for each statistic:

Hit Points
- Defender: 30 + 6 per level above the first. This assumes a starting Con of 15
- Striker: 24 + 5 per level above the first. This assumes a starting Con of 12
- Controller: 22 + 4 per level above the first. This assumes a starting Con of 12.

For simplicity, any posible increases in Constitution haven't been taken into account. The impact should be minimal, relative to total amounts of HP.

- Defender: Normalized AC of 18, equivalent to AC 19 (scale + shield) at level 1.
- Striker: Normalized AC of 15, equivalent to AC of 16 (chain, or leather and +4 starting ability modifier) at level 1.
- Controller: Normalized AC of 15, equivalent to AC of 16 (chain, or leather and +4 starting ability modifier) at level 1.

It is impossible to keep normalized AC completely stable across levels, but the deviations are usually minor. I have opted for using constant values because these variations depend more on the choice of heavy or light armor than on actual role, and are usually compensated over a character's whole career.

Non-AC Defenses

For Fortitude, Reflex and Will, I decided to make a small abstraction, and consider only "good defenses" and "bad defenses", regardless of how they were allocated. I have also considered them role-independent, so all three characters show the same progression. The progression itself was taken from the values generated for the character PC2 in this article. PC 2 is a character with 2 "good" defenses, and we defined it as follows:

"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."

Only the best and worst defense for PC2 have been used (as "good" and "bad" values, respectively), discarding the middle one. For the overall survivability of our three characters, we will make two calculations: one assuming they have two good defenses, and another assuming they have two bad ones. This introduces a small error, since the best defense of a character tends to be slightly higher if it is the only good one but, again, the gain in simplicity outweights the loss in accuracy.

The results

This graph shows the Survivability progression for attacks against AC:

This is where the greatest differences among roles show up. As we can see, the values for defenders roughly double those for controllers. As for strikers they start out very close to controllers, but slowly overtake them as the difference in HP grows more important over levels, capping at around 20% more at level 30.

Also interesting is the fact that absolute survivability values experiment considerable growth, more than doubling between level 1 and 30. This is in spite of the fact that the monster hit rates remain constant - the relation between PC hit points and monster damage becoming more and more favorable to the PCs.

The following figures show S for "good" and "bad" non-AC defenses:

Since non-AC defenses don't vary depending on role, the relative S values here are much closer, reflecting only the HP diferences of each role. Keep in mind that normalized defenses are actually diminishing as the character levels up (specially for the bad defense), but overall survivability still grows because of the unbalance between PC hit points and monster damage. Nevertheless, this growth is not as pronounced as AC survivability, and values at maximum level end up slightly below double those of level 1. Also of note is the fact that defenders are much more vulnerable against NAD attacks than against AC attacks, whereas strikers and controllers find their AC roughly equivalent to their good NADs. Bad defenses, as expected, are terrible for all characters, though it is interesting to see that their S values remain more or less constant, rather than getting worse as the characters level up.

Finally, we can average the values shown above to figure out the overall survivability of each character. As we can see, the differences between the builds with 2 good NADs and 1 good NAD aren't actually very significant, with regards to overall survivability. This can be explained by the fact that having an additional good NAD will only come up on 1/6 of attacks. Nevertheless, these figures hide other negative consequences of bad NADs, such as the higher variability among encounters (increasing the chance that enemies auto-hit you), as well as a huge vulnerability to attacks that inflict status effects (as opposed to raw damage, which is what S measures).

It is also possible that the coefficients used to average overall S (1/3 for AC, 1/6 for other defenses) need to be adjusted at paragon and epic tiers, since there seems to be a greater amount of NAD attacks for monsters of these tiers. However, since I lack solid data on that matter, I'll stick with my original approximation until I find some statistical analysis of the different monster manuals.


The relative resilience of the different roles is more or less as could be expected, with defenders being twice as tough, and controllers falling slightly behind strikers. However, we must remember that these are just baseline values - for real builds, non-defenders tend to have a lot more potential for improvement, specially for AC, so the gap with a defender should be much narrower if a player decides to invest in resilience. On the other hand, the temporary hit point gaining of some defenders are more rare among other roles, and would grant them an edge. The same could be said of damage resistance. I'll try to talk about this in a future post.

As for the implications of survivability on encounter length, we find that a group of same-level monsters will need more than twice the amount of time to kill a level 30 party, compared to one of level 1. That is, if the level 1 PCs can expect the monsters to defeat them after 6 or 7 turns of combat, the level 30 ones would live for more than a dozen turns. That is, of course, assuming that the PCs just stand around doing nothing - in an actual encounter, PCs will get healed, and monsters will gradually die, so the real time before the defeat should be significantly higher.

We can also apply these results to analyze the effect of focused monster attacks on a single character. Using the standard of 5 characters per party, the monster group would be able to knock out a level 1 non-defender in a single round, whereas the defender would survive for another round. At epic tier, the non-defender would endure 2 whole rounds of punishment, and the defender more than 3.


  1. I've started to see more of this in the latter parts of the paragon tier. Unless a monster cheats moderately or more, the PCs really aren't in danger of dying or even dropping to zero. Even when they do drop to zero, the fight is typically wrapping up with just a few mobs left to defeat.

    For example, last night I had a fight with 6 PCs against Baldraan the Flayer (I think this is V6 or V7 in the Demon Queen's Enclave module). The PCs had two relatively new players in the game so were not effective. The fighter tank wasn't really locking up anything appropriately. There was a lack of focus fire on the field and no controller (The current one had switched to a sorc). With all of these negatives associated with the fight, the fighter was the only one near death. I believe that another player was bloodied. None of the other characters were bloodied after several rounds. Partly that was the healing put out by the leader but partly it was the low monster damage to total party health.

    I do imagine this stabilizing as the party daily and encounter abilities are now set at 3 each.

  2. Well, the damage boost to monsters after Monster Manual 3 should shake things a bit! I think the change is for the better, though it forces me to revise all the math in these articles... which I'll get to as soon as I know the new formulas.