Dwarf vs Zombies: A Series of Contrived Fights (Now with orcs!)

[FireLance]

Today, the 4th-level dwarf takes on two fights of two orcs each and two fights of three orcs each. Between several bad rolls for the orcs and several good rolls for the dwarf, the dwarf emerged quite decidedly victorious.

The first fight was over very quickly. The dwarf won initiative, killed one orc in the first round and the second orc in the next round without taking any damage.

The dwarf was unluckiest in the second fight. He won initative and killed one orc in the first round, but only killed the second orc with his fourth attack, after hitting with his second, but failing to kill it, and missing with his third. In addition the orc managed to score a critical hit on the dwarf for 14 points of damage, which was reduced to 12 because he managed to parry it. After this fight, the dwarf took a short rest and spent a d12 Hit Dice and a d8 Hit Dice, recovering all his lost hit points.

In the third fight, one orc managed to beat the dwarf's initiative but misssed him when it attacked. The dwarf killed it with his first attack and easily dodged the clumsy attacks of the other two orcs. Two good attack rolls and damage rolls and one Expertise Dice spent to Cleave later, the two remaining orcs were dead.

The last fight went pretty much the same as the third, except that the dwarf won initiative and killed the first orc before it managed to even make an attack roll. One of the other orcs managed to hit the dwarf for 6 points of damage when it attacked, but the dwarf again killed both the orcs in the next round, this time by rolling two critical hits.

All in all, the dwarf only lost 18 hit points over the course of the four fights. Of course, this was because the dwarf's good rolls cut down on the number of attack rolls the orcs managed to make against him, and the orcs' own bad luck meant that only two of the nine attacks actually hit. If the dwarf hadn't been so lucky, and the orcs hadn't been so unlucky, my guesstimate is that the orcs would have attacked him about fifteen times and hit about five times, dealing an average of about 42 points of damage, close to what the zombies dealt to the other dwarf. However, as with the previous fights, the balance seems a little off as the orc fights were actually supposed to be tougher.

 

[pemerton]

I determined that the orc's Rage trait is actually a poor option against the dwarf due to his high AC. The damage bonus is simply not worth the reduction in accuracy. The orcs will thus make normal attacks.

This seems true for a pretty wide range of ACs.

The orc's normal attack is +2 for an average of 8.5 hp.

The orc's rage attack is +2 with disadvantge for an average of 13.5 hp.

The damage multiple for rage is therefore 27/17. So anytime the disadvantage causes a reduction in the probability of hitting less than 17/27 (or about 2/3), rage isn't worth it.

The orc hits an AC of X with a d20 roll of (X-2) or better. That is, it's chance of hitting an AC of X is (23-X)/20.

Disadvantage requires meeting that probability twice in order to hit. So if (23-X)/20 is less than 17/27, the orc is better off not using rage. Solving for X:

(23-X)/20 < 17/27

23 - X < 340/27

X - 23 > -340/27

X > (23*27 - 340)/27

X > (621 - 340)/27

X > 281/27​

So AC 11 or higher makes rage not worthwhile. That's basically all PCs, isn't it?

I would have thought that after the Careful Shot/Twin Strike fiasco, WotC would have practised their expected damage calculations, but apparently not.

 

[slobo777]

So AC 11 or higher makes rage not worthwhile. That's basically all PCs, isn't it?

Except when the orc is suffering disadvantage anyway, in which case it should rage as there is no further penalty.

Taken like that, it's actually quite a nice design feature of orcs as a monster. PCs might think twice about trying to corner/restrict/attack whilst invisible etc versus an orc due to the risk of them taking more damage.

Edit: Though the theme that comes out with this style of fighting seems to have little relation to any previous incarnation of orcs . . .

 

[pemerton]

A follow-up calculation for orcs: when is it worthwhile using rage, if the orc has advantage on the attack (to cancel out the disadvantage)?

The chance of an orc hitting AC X is (23-X)/20. So the chance of missing AC X is (X-3)/20. Advantage reduces the miss chance to (X-3)^2/400. So, with advantage, the chance for the orc to hit an AC of X is (400 - (X-3)^2)/400. If this, divided by the normal hit chance, is greater than 27/17, then the orc is better off not raging, and instead benefitting from the increased hit chance from advantage. If this is less than 27/17, then the orc will increase its expected damage by raging (and simply letting the advantage cancel out the disadvantage). Solving for X:

(400 - (X-3)^2)/400)*20/(23-X) < 27/17

400 - (X-3)^2 < 20*27*(23-X)/17

6800 - 17(X^2 - 6*X +9) < 12420 - 540*X

17*X^2 - 642*X + 5773 > 0​

Solving for the break points:

X = (642 +/- SQR(642^2 - 4*17*5773))/34

X = (642 +/- SQR(19600))/34

X = (642 +/- 140)/34

X = 782/34 or 502/34​

So the break points are X > 32 or X < 15.

AC 32 is irrelevant here, as the chance to hit caps at 1/20 (and at that chance to hit, rage is no good even with advantage). So it seems that at all ACs of 15 and above, the orc is better of taking advantage of the advantage, but below that the orc is better off raging, and using the advantage to cancel the disadvantage.

Anyway, I think that the maths is complicated enough that it would be helpful for the Monster Manual entry to tell the GM when it is worth using rage, and when not: namely, never unless you have advantage, and even then only if the AC is less than 15.

Which is a bit dissapointing, really - rage is only good for charging those prone squishies. But it's no good against anyone in chain or heavier armour, even when they're prone or you've got the drop on them.

Rage might be better if it yielded advantage to opponents, rather than caused you to suffer disadvantage yourself.

 

[pemerton]

Except when the orc is suffering disadvantage anyway, in which case it should rage as there is no further penalty.

Taken like that, it's actually quite a nice design feature of orcs as a monster. PCs might think twice about trying to corner/restrict/attack whilst invisible etc versus an orc due to the risk of them taking more damage.

Edit: Though the theme that comes out with this style of fighting seems to have little relation to any previous incarnation of orcs . . .

I guess you could also have your drunk orcs rage and they're no worse off. But still less dangerous than a sober, non-raging orc, which is to say, not especially dangerous (but fairly swingy: if they do hit, it will be fairly hard).

I think this is a maths error. Between this, Glancing Blow, the ranger at-wills in the 4e PHB, and the initial problems with framing skill challenges, I'm starting to think that WotC doesn't have anyone on staff capable of doing high school maths!

 

[FireLance]

I think this is a maths error. Between this, Glancing Blow, the ranger at-wills in the 4e PHB, and the initial problems with framing skill challenges, I'm starting to think that WotC doesn't have anyone on staff capable of doing high school maths!

I don't think it's a question of ability. I think it's a question of importance. It may simply be that there is only an insignificant minority of gamers who put a premium on WotC's ability to get the math right. After all, I bet a lot more people prefer the quote "Never tell me the odds" to "They say a little knowledge is a dangerous thing, but it's not one half so bad as a lot of ignorance".

 

[pemerton]

I don't think it's a question of ability. I think it's a question of importance. It may simply be that there is only an insignificant minority of gamers who put a premium on WotC's ability to get the math right.

Maybe. But how is anyone's play experience enhanced by raging orcs being less dangerous?

 

[FireLance]

Maybe. But how is anyone's play experience enhanced by raging orcs being less dangerous?

My cynical answer is: so that many more gamers can boast that they took on raging orcs and beat them.

"But raging orcs are actually less dan-"
"Never tell me the odds!"

 

[slobo777]

Having just been at a workshop for the language I code in at work, I thought I'd look at adding some monte-carlo stats based on this. It's a different angle on the encounter balance issue, inspired by the OP.

Just for a sneak peak / starter, I considered what an "adventuring day" might look like for the Dwarf first-level character in the OP, if the whole adventure is basically running the gauntlet of a series of encounters with 1 Zombie per battle. Pretty boring adventure, right, but the design goal for the DM is to pick a number of Zombies that gives a fair daily challenge . . .

So the first check is to run as many encounters as the Dwarf can handle before he ends up on 9 or less hit points, and with no Hit Dice left. I ran this 1000 times to get an average.

Answer: typically 124 zombies . . . . whew!

It varies a lot, and the numbers are typically high - I think this is a consequence of the bad initiative rolls of the Zombies. They don't really make a good one-on-one challenge for individual combat encounters.

The second check is to run the 124 zombie gauntlet (possibly the dullest adventure ever!) with 1000 dwarves and count the survivors.

Answer: 731 out of 1000 dwarves survived the gauntlet.

This is bad. Put it down to swinginess of the one-on-one with zombies though. With that many encounters, and only exceptional bad luck where the dwarf is taking damage. Whatever the cause, this would be a very swingy adventuring day, and probably not the sort of thing to really plan.

More to come on another thread . . .

 

[Crazy Jerome]

It is probably mainly that the monsters stats and XP is still way out of whack, but when looking at expected outcomes, I'd note one caveat that was exemplified in our playtest this weekend: For a party, surprise, location, and lighting really makes a big difference.

We had 5 2nd level characters, dwarf fighter, hafling rogue, elven archer, elven wizard, and elven cleric. No one had survivor specialty.

A. 8 orcs ambushed the party and got complete surprise (bad luck by party combined with badly timed mistakes in plans). Toughest fight of the evening, with everyone down into single digits, and spells almost gone.

B. Party escapes back to cleared out kobold lair, holes up securely, but doesn't cover their tracks. 20 orcs investigate, decide to shoot them up when they leave the cave. Ambush is launched on unsuspecting party, but through incredible luck on spot and initiative, all five party members detect it in time to retreat into kobold cave. Upshot, after several rounds of sniping with cover on both sides, the orcs getting the worst of it, half the orcs drop over the cliff face on ropes to attack the cave mouth as their archer friends charge. With timely spells and tricks and a few lucky rolls, two rounds later the party is cleaning house.

Congruent with the topic thus far, however, I will note that in the first ambush, the dwarven fighter took on 4 orcs while the rest of the party fought the other 4. Despite some substandard rolls, he had 2 of them down and 1 injured by the time the rest of the party was able to help. Yet, if I'd had two more orcs in that first ambush, it might have been a TPK.