Christian said:
Thanks, KD. I'd done the math for the Con bonus above, but I didn't think about doing such an exacting analysis ...
Thanks.
Christian said:
The choice is more interesting for a Barbarian, whose d12 hit die makes the Con bonus a smaller percentage of total hit points. Although, since he will probably want to stay in medium armor ... for a front-line character who soaks lots of attacks, being on the low-end of AC for a primary fighter decreases the effect of the Dex bonus as well. (The proof of this is left as an exercise for the reader.
) But for a wizard or sorcerer, there's just no Con-test.
Actually, I think the Barbarian example is very interesting.
As you state, being on the low-end of AC decreases the effect of the DEX bonus.
Compare him to a Fighter with AC 4 higher. The Barbarian might take 35% hits, the Fighter takes 15% hits. So, +1 AC for the Barbarian drops his chance to be hit from 35% to 30% or a 14% drop in average damage. Adding +1 AC to the Fighter drops his chance to be hit from 15% to 10%, a 33% drop in average damage.
Then, compare the increase in hit points due to CON for the Barbarian. Hit points are increased by approximately 15% (CON 10 to 12), 13% (CON 12 to 14), and 12% (CON 14 to 16) respectively.
It appears that taking 14% less damage due to AC might, on the surface, be better than having 12% or 13% more hit points.
But, this can be a little misleading.
This is only in the case where the Barbarian takes his most of his hit points in damage within a combat. Let’s take examples of him taking 20, 40, 60, and 80 points of damage in a single combat and let’s say that he is 10th level with a CON of 12 and has average hit points of 80. The following chart shows how many hit points he has left after combat (in each of these 4 cases):
20 60
40 40
60 20
80 0
If you give him +2 to DEX or +1 more AC, he has the following hit points remaining (due to taking 14% less damage due to the increased AC):
20 63 (he only takes 17 points of damage on average since his +1 AC protects him 14% more)
40 46
60 28
80 11
Now instead, say that you gave him a 14 CON as opposed to the +1 increase in AC. Now, his hit points look like this in the four cases (since he has 10 more hit points or 90 total hit points):
20 70
40 50
60 30
80 10
So, in all of these cases except the last one, he has more hit points remaining after the combat. Basically, the extra CON effectively protects him more than the extra DEX whenever he is in a combat that does light or moderate damage to him. It is only in the extremely heavy combat situations where the AC might protect him more (it might not, depending on his opponents chance to hit since as levels increase, BAB increases more than AC).
The bottom line is that the extra CON is typically better for the higher hit point characters like Fighters and Barbarians as well as for Wizards and Sorcerers. It just is not as helpful for the high hit point characters, nor as noticeable that this is the case without doing the math.
One caveat on this. Special abilities and/or feats of opponents can quickly change the numbers here. For example, if your opponent has a Keen Flame Burst weapon (or is a Dragon or Giant doing 20 points of damage with a single melee attack), the extra 10 hit points might not protect you as much as the increase in AC since dropping 10% of the average damage of a mega-damage weapon can often be greater than the extra hit point per level if your opponent gets to attack you multiple times with the attack. But, I have found in practice that even dumb Fighters will attempt to avoid combat or decrease the number of opponents attacks when their opponents have mega-powerful attacks. So although mathematically, a mere 5 20 point attacks by an opponent will eat up the extra 10 hit points that CON would have supplied (due to having 1 AC less for a 10th level character), in practice most PCs do not just rush up and give their opponents those types of opportunities if they can avoid it. You get smacked hard once by a mega-attack, you tend to shout for the party spell casters to protect/heal you. IME.