More hit points vs. Expertise isn't really the tradeoff you're looking at. It's more hit points and a higher to-hit bonus versus more AC. The AC and hit point conversion can be calculated as follows on a purely average damage basis (the easiest way, but not necessarily the most helpful).
Average damage taken per round= damage per hit x chance to hit +chance of a confirmed critical hitx average damagex(crit multiplier-1) The math is simpler if you ignore crits, however so we'll do that for now.
Increasing AC by 5 points generally reduces the chance to hit by 25% (excluding "need a 20 to hit" and "hit on a 2 anyway" scenarios). So the five points of AC reduce the average damage you take per round by 25%. It takes a 25% hit point increase in order to match that in the context of average damage per round from physical attack.
Evidence follows:
If A=average damage per round and R=number or rounds then you are down when A x R >= hp. Logically then, R >= HP/A
If you want R to be equal in the AC scenario and the hit point scenario, then HP2 will be the increase in hit points and:
(HP+HP2)/A >= HP/ (A-.25A) this can be written as (HP+HP2)/A >= HP/(3/4 A)
Therefore 3/4 (HP+HP2)/A >= HP/A
Therefore 3/4 (HP+HP2) >= HP
Therefore 3 HP+4 HP2 >= 4HP
Therefore 4 HP2 >= HP
Therefore it is superior when HP2 >= HP/4
My experience, on the other hand, suggests that the proper ratio of hit points' value to AC's value is not actually 5% hit point total per point of AC. So, what's wrong with the picture?
Well, to start with, our model ignores the sources of damage that don't deal with AC. There are actually quite a few. The 5 point increase in AC does not do anything to reduce damage from spells with saving throws (or with no saves). Fireball, ice storm, flaming sphere, magic missile, etc all ignore your AC. Hit points help against them; AC doesn't. These abilities are far more common than the reverse situation where AC actually reduces damage more significantly than the above math indicates (rend is probably the most common example (where the 5 points of AC will mathematically reduce average rend damage per round by roughly 45% in addition to the 25% reduction in damage from the attacks that produce the rend)). The AC also does not help much in touch attack situations which are far more often "a two hits anyway" situations and where a non-combat expertise AC increase won't apply. The AC also won't help against grapple situations. (Though it may help to prevent the grapple from being started).
A second problem is that our model here treats hit points as a non-renewable resource. In actual game situations, they're not. Combat healing spells can extend the lifespan of both the increased and the decreased AC character and render the high AC less necessary for survival than the above analysis might indicate. (Also note that, if you don't run out of healing in a day's adventuring, then the reduced AC hasn't hurt you).
The third problem, and probably the most significant one is that simple statistics are not actually as relevant to D&D combats as the kind of math I've seen called "discrete probability." This is illustrated very well by some well-known examples from the D&D minis game.
Let's take a character A with 60 hit points. How much of an increase in his effectiveness is produced by bumping his hit points to 65? The real answer is "much more than the <10% amount would indicate." Common damages in D&D minis fall into the 5, 10, 15, 20, and 30 point per swing ranges (That's pretty true in normal D&D too unless you get really mega-buffed and are power attacking for a lot, smite evil on a spirited charge, have a Zealot Pact kick in or are in another corner case situation). Minis that do 5 and 10 points of damage per swing are generally not dangerous enough to be the focus of the game (and, by the level you have 60 hit points in regular D&D, that's also true unless they have dangerous special abilities). Now is where the discrete probability comes in. How many 15 point swings does it take to drop/kill the 60 hit point character? 4. The 65 hit point character? 5. That's effectively a 25% increase in the number of swings it takes to drop the character. How about 20 damage swings? They go from 3 to 4--a 33% increase in survivability. How about 30 damage swings? They go from 2 to 3--a 50% increase in durability. That's a lot better than the 8.33% increase that it looks like using simple statistics and it demonstrates why minis with 65+ hit points are dramatically better than minis with <=60 hit points in the minis game.
Applying that logic to the rpg is more challenging than applying it to the minis game because the situations are far more varied. However, it's worth looking at the various effects of AC and hit points in the game. An ogre attacks at +8 for 2d8 +7 points of damage.
The 42 hit point character will take 3 average hits and be at -6. The 49 hit point character will take 3 average hits and be at 1hp. Well, 1 hp isn't a very good place to be if you're next to a creature that deals 16 points of damage a hit, but it's enough to drop a cure critical wounds spell on yourself and stay in the fight. It is also a pretty nice safety margin. If the ogre rolls just a bit hot on damage, the 42 hit point character is straight up dead. The 49 hit point character has room to take some significantly above average damage and still be alive (although negative). Though it's not as easy to model as the minis game, I think the extra 7 hit points winds up being significantly better than it sounds when you say "7 hit points" or just run the average damage analysis.
Now, on to the most important part: The choice: 5 points of AC or 7 hit points is a false choice. When creating the character, you don't really have a choice between 7 hit points and 5 points of AC. The real choice is between losing the 4 stat points from somewhere that includes 2 points of Con and not qualifying for Expertise. You could, for instance, run a character with 14 str, 10 dex, 14, con, 14 int, 14 wis, 10 cha. There you are losing bonus spells and DCs at certain levels in return for the ability to take Expertise. You could, alternately, go 14 str, 12 dex, 14 con, 10 int, 15 wis, and 8 cha and have the DCs and one point of AC all the time in return for a charisma penalty. There are any number of ways you could arrange your 28 points. The key question is this: Is expertise worth it?
In order to answer that question, you can't look at it as 5 points of AC. It isn't. It is a feat that can give up to 5 points of AC that apply only when attacking in melee and then only when you take a penalty of up to 5 points on your attack rolls. Thus it carries an opportunity cost (another feat), is situational (only when attacking), and comes at a price in terms of your damage output.
Opportunity Cost: Since we were looking at a hit point to AC ratio in the value part, let's look at the one core feat that gives more hit points: Toughness. This is generally acknowledged to be a very weak feat, but if we take the opportunity cost you lay out (sacrifice 2 points of Con), it's interesting to note that the hit point increase reaches 10--nearly the number necessary to offset a non-situational 5 point increase in AC that didn't come with penalties in an analysis that over-estimates the value of AC (25% of 42 would be 10.5). Obviously, that is only true at level 7, but it does give a rough picture of the value of that feat slot plus the con sacrifice. If Improved Toughness were available, that plus the two points of Con would blow Expertise away even in the analysis most favorable to Expertise.
Situational: How often are you going to be able to make it apply? Now, given the design of the character, you will be attacking a lot, but I'd guess that you'll spend at least something like one out of four combat actions casting a spell. Remember, as you weigh its value that it won't be 5 points of AC at those times.
The cost: Taking an attack penalty is serious business. Sometimes it won't matter because you still hit on a 2 (if you're attacking an ooze, for instance) or only hit on a 20 (but there shouldn't be many of those times for you). In general, however, as the math above indicates, it will result in a 25% reduction in your average damage per round as well as a 25% reduction in your opponent's average damage per round. (For whatever significance average damage per round has).
Slowing down the fight like that can be a good deal. If you have a cleric healing you up, maybe he is able to keep his healing in pace with the damage when you're using Expertise but would not be able to otherwise. (However, you ARE the cleric, so that won't really apply for you). If you have an archer or a wizard who can dish out the damage as long as nobody gets in his face, maybe the extra round or two that buys you is enough for your ally to kill the monster. (However, that doesn't sound like your party either). If your allies have withdrawn and are spending a round or two healing before returning to the fray, maybe slowing down the combat means that you're able to stand there and keep the monster off their backs instead of having to retreat yourself. It is also possible that the your damage much more consistently than your opponent so by slowing down the combat, you will eventually win the encounter. (The probability of actually hitting comes in here--if you can reduce the opponent's chance to hit enough while keeping your own accuracy at an acceptable level, you may well be able to get the hits you need in before your opponent gets the hits s/he needs--even if your average damage per round figures are identical. Of course, your opponent could also get lucky and just blow you out of the water too).
However, all of those tactics can be a challenge to pull off. After all, why won't the monster just go around you and finish off the cleric who is healing you, the archer/wizard dealing out the damage, or the dangerous opponents who are healing each other. Why will the enemies attack the high AC character if they can take down your more offensively oriented allies more quickly? (There's a reason that "take down the wizard first!" is a tried and true D&D battle tactic). In order to make Expertise work for you in those situations, you either need terrain that forces your opponents to deal with you because your position prevents them from getting to your allies (a narrow corridor is a good example of this), or an AoO that is likely enough to hit and deals enough damage that it's not worth the risk. A lot of times, Expertise reduces the AoO's likelihood to hit below the range where your AoO is scary.
All told, I don't think Expertise is a very good option for your character in general--certainly not when you consider the opportunity costs.
YokoburiKinura said:
Okay, here's a small question in relation to 'more hp vs. expertise' - Is it better to have, say, a 26 AC and 42 hp in a round, or a 21 AC and 49 hp? Are hp more valuable overall than AC? And how is this changed if we're playing under 'armor with damage reduction' or 'damage conversion' variants in UA?
![:]](http://www.enworld.org/forum/images/smilies/devious.png "Devious :]")
