DR or AC

[valadil]

Tonight at game we had the chance to pick armor that was +1 AC or +1 DR. Supposedly our resident power gamer who wasn't there that night had determined that 1 point of AC mitigates just as much damage as 1 point of DR. He wasn't there to ask though, so I'm wondering if anyone here can show me the math.

I'm too sleepy for any definitive conclusions, but I feel like they'll give you different values depending on the kind of damage being dealt. For what it's worth, I'm considering a range of 20 attacks, where the d20 ranges from 1 to 20. I am not taking botches or natural twenties into consideration - for now it's just head math and my head is a very sleepy place right now. Also, this is 4th edition, if it matters.

If you take 10 per hit and get hit on a d20 roll of 10, you expect to take 100 damage over 20 dice. Increasing DR or AC will mitigate 10 damage.

So what if we get hit on a 10 and take 20 damage per hit? Increasing AC drops one hit, so you're looking at 180 over 20 attacks, but DR would leave you taking

But what if we're getting hit on a 10, taking 1 damage per hit? The +1 AC guy takes 9, but the +1 DR guy takes nothing.

Also keep in mind that as the target number for the d20 goes up, DR will protect against less and less. If you need a 19 or 20 to hit, DR will only affect 10% of your rolls.

Conversely, if you need a 2 or higher to hit, DR affects rolls that aren't 1s.

Does this even matter or does it just balance out in the end?

[Eloel]

AC, job done :)

[VerdugoExplode]

It doesn't matter at the end. When a monster has +30 something to hit it takes a good chunk of cheese to get your AC to comparable levels. On the same note if they do 2d8+24 points of damage a hit having dr 3/- isn't going to feel like it's making much of a difference either. The best strategy is to kill the enemy as quickly as possible.

[GoodbyeSoberDay]

AC is generally all-or-nothing, whereas DR/- is at least moderately useful in any amount. So if you've made a conscious effort to pump AC, I'd go with more AC, and if you haven't, I'd go with DR. There isn't really much math to do, considering it mostly has to do with the particulars. Speaking of which, what's your party level/composition?

[Kantolin]

Personally, although this may not be true if your group is hyper-optimized, I'd rather have a point of AC over even multiple points of DR. Every hit you can negate counts, while I've never found DR to be terribly relevant compared to the damage the enemies deal at the levels you tend to get it (At level 10, for example, DR seems to become fairly meh for your buck).

[Crow]

I've found DR to be more useful over the lifetime of a character. As was stated before, AC is all or nothing. If you're not going to max it out, you will probably be better with DR.

A lot of it depends on the playstyle of your group too. We have ironman sessions where characters are expected to face multiple encounters without much time for slow down. In this situation, every point of DR is pure gold. The enemies will be getting to take more swings than you will. If your group fights once and then retreats so the wizard can re-memorize his spells, then you'll be better with AC.

[valadil]

Speaking of which, what's your party level/composition?

It wasn't a static group. Some friends were bringing me up to speed for Living Realms.

We had a dragonborn pally of tempus 1 (me), human fighter 1, human? bard 1, eladrin cleric 2, and a warforged barbarian 3.

I ended up going with the point of AC. It was on dwarven armor. I'm not sure why but when we got the armor we could pick a point of DR or a point of AC. I figured I want my armor to be my source of AC and if I picked up a source for DR later it wouldn't stack with the armor anyway.

But I still don't know how to attack the probability for DR or AC preventing more damage. I feel like there's probably a magic value somewhere such that more damage than that and AC is better but if the average damage is below that, DR is better. With enough calculation I could probably find that value, but I have no idea how to find what the average expected damage is in 4th ed.

I'm more concerned with how you'd attack the problem than whether AC or DR is optimal.

[Baron Corm]

It doesn't matter at the end. When a monster has +30 something to hit it takes a good chunk of cheese to get your AC to comparable levels. On the same note if they do 2d8+24 points of damage a hit having dr 3/- isn't going to feel like it's making much of a difference either. The best strategy is to kill the enemy as quickly as possible.

I think this answered your question already. High damage and low attack makes AC better, high attack and low damage makes DR better. Medium they're about equal, as you showed in your first post. When both are high, DR wins out, because the AC does nothing. When both are low, AC wins out, because the attack will do nothing. If the attack does damage on a miss however, the DR still wins.

[Eloel]

I'll put some MATH here, so
BEWARE THE MATH!!
%defenseOfAC = (ACBonus / (20 - rollNeededToHitWithNoBonus)) * 100
%defenseOfDR = (DRBonus / averageDamageWithoutDRBonus) * 100

See which % is bigger for yourself, and you're good.

[Douglas]

It depends on how much AC and DR you already have. Each point of AC is more valuable than the last, unless your opponents already need a 20 to hit you. Each point of DR is more valuable than the last unless you already have enough to negate all hits completely. Whichever one you are already focusing on is the one you should continue to focus on more.