[DF] Suitable Dangerous Encounters

[Nymdok]

Originally Posted by tjbuege

Ok, you lost me. Where are you coming up with these percentages and numbers?

Well, I made a spreadsheet its on my website here is the short answer.

The slightly longer answer is that for a hit to land and do damge:

Your Attack Must succeed.
The Defenders defense must fail.
The Attackers Damage Rolled Must exceed the DR.

So for an attack to succeed,

(Attacker gets a Crit)+(Attacker gets a hit thats NOT a crit)(Defender Fails His defense) = Chance youll land a blow.

So for a 15 skill versus a 12 active defese its...

(Odds od a crit: 5 or less= 4.62) + (Attack Succeeds But is NOT a crit : 5<AttackRoll<=15 or [<=15] - [<=5] = )(Defense Fails - Not >=12 = 13 + : 25.93)
Odds of a Landed Blow = (4.62%)+(90.75%)(25.93%) = 28.15 or 28.2

Damage Greater than DR is the expectation value of each damge summed.

So for 1d versus DR4, only rolls of 5 or 6 will get by DR, each with 1/6 of a chance to show up.

5 - 4 = 1 * .166667 = .16667
6 - 4 = 2 * .166667 = .33333

Damage Expectation = .48

(The Damage Expectation)*(Odds of a Landed Blow) = The Average Damage we expect per turn.

Its a poor metric, but one of the few that we have :)

Nymdok

[Nymdok]

Original Enocounter edited....

Nymdok

[tjbuege]

Originally Posted by Nymdok

(Attacker gets a Crit)+(Attacker gets a hit thats NOT a crit)(Defender Fails His defense) = Chance youll land a blow.

Ok, I see where I went wrong. I've been putting together my own spreadsheet, but I forgot to take into account that with a crit hit, no defense! What you have makes sense to me now.

Originally Posted by Nymdok

So for 1d versus DR4, only rolls of 5 or 6 will get by DR, each with 1/6 of a chance to show up.

I get this, for 1d, 2d or 3d rolls. I can create a table with the permutations for each variation of the dice. But when it gets to 4d and up, it gets a bit tedious to calculate how many combinations of the dice equal a specific # or less. There must be some formula for figuring it out. Any suggestions, or are you just calculating for low dice damage?

For example, say you inflict damage of 10d+2 (that's 12-62 points damage) vs a DR of 25. What are your chances of rolling penetrating damage? By my calculations there are 60,466,176 possible combinations of 10 dice (6^10). That's beyond my patience of figuring it out the long way! :)

Thanks,
Tim

[tjbuege]

If you don't mind, let's see what I come up with for numbers with your examples:

Originally Posted by Nymdok

Guard in full Plate(DR7), With Spear(12:1d+2 Imp), Defense(BPD) = 0-9-9, HP:10.

Barbarian in Fur(DR1) with Bastard Sword(17:4d Cut), Defense(BPD)=0-12-9 (Includes ComRef), HP:22.

Cleric in Mail(DR 4:2) with Mace(14:2d+1 cr) and MedShield, Defense(BPD) = 12-12-10(Includes DB), HP:12.

Wizard in Robes (DR1) with Staff(14:1d+2), Defense(BPD)=0-12-9, HP:10.

Barbarian vs Guard (17:4d vs 9:DR7)

The Barbarian has 99.5% chance to hit, with 9.3% of that being critical hit. That means the Guard can defend against 90.3%. The Guard fails his defense 62.5% of the time. So, the Barbarian will land a blow, getting past the guard's defenses 65.7% of the time:

9.3% + 90.3% * 62.5% = 65.7%

Rolling 4d for damage, there are 1296 possible combinations of the dice with 1261 of them resulting in >7 total. So 97.3% of the time the Barbarian will do some damage. The average roll with 4d is 14, which would result in 7 damage. I'm not sure how to figure that into the average damage done.

Cleric vs Guard (14:2d+1 vs 9:DR7)

1.9% + 88.9% * 62.5% = 57.4%

The cleric will penetrate the DR 21 out of 36 times, or 58.3% of the time. Average roll with 2d+1 is 8, resulting in 1 damage.

Wizard vs Guard (14:1d+2 vs 9:DR7)

1.9% + 88.9% * 62.5% = 57.4%

The wizard will penetrate the DR only 1 time out of 6, or 16.7% of the time. The average roll with 1d+2 is 5.5, which is under the DR of 7. This bit of information does nothing to help me figure out how to consider average damage dealt.

But damage aside, I think my calculations for chances to land a blow are a bit different than yours. Is there something else I'm not considering?

Thanks,
Tim
Tim

[Ulzgoroth]

Originally Posted by tjbuege

Wizard vs Guard (14:1d+2 vs 9:DR7)

1.9% + 88.9% * 62.5% = 57.4%

The wizard will penetrate the DR only 1 time out of 6, or 16.7% of the time. The average roll with 1d+2 is 5.5, which is under the DR of 7. This bit of information does nothing to help me figure out how to consider average damage dealt.

Well, this one is dead easy. The others are doable, but this one you can do in your head.

Expectation (or average) damage = chance to hit * (average over possible damage rolls of injury resulting)

In this case, the possible damage rolls give 5 0s and one 1 for injury, so expected damage is chance to hit * 1/6.

[tjbuege]

Ok, I've thought about this, and I think I've answered my own question on how to figure average damage:

Assuming the Barbarian lands a blow, 1261 times out of 1296 will penetrate DR. Total damage for those 1261 times is 9093. 9093 / 1261 is 7.2 points average per hit. With the Cleric, 21 out of 36 blows will penetrate DR. Total damage for those 21 times is 50. 50 / 21 is 2.4 points average per hit. The Wizard is easy. He can only only 1 time out of 6, and will do 1 point damage average. So considering the chance to land the blow in the first place:

Barbarian = 65.7% * 7.2 = 4.7 points damage per turn
Cleric = 57.4% * 2.4 = 1.4 points damage per turn
Wizard = 57.4% * 1 = .5 points damage per turn

Does this make sense?

Thanks,
Tim

[tjbuege]

Originally Posted by Ulzgoroth

Well, this one is dead easy. The others are doable, but this one you can do in your head.

Expectation (or average) damage = chance to hit * (average over possible damage rolls of injury resulting)

In this case, the possible damage rolls give 5 0s and one 1 for injury, so expected damage is chance to hit * 1/6.

Aargh...right...let me see....(one moment)

[Nymdok]

Originally Posted by tjbuege

Barbarian vs Guard (17:4d vs 9:DR7)

....9.3% + 90.3% * 62.5% = 65.7%
... I'm not sure how to figure that into the average damage done.


But damage aside, I think my calculations for chances to land a blow are a bit different than yours. Is there something else I'm not considering?

Yes, One of the things I do, and sadly I didnt mention it in the post was I always deceptive attack down to 16 or 15. Ill edit it in the post :)

What that means is that 17 v 9 = 65.7
But since I DA down to 15 its 15v8 = 71.8

On a side note, looking for the difference led me to find yet another (Ugh!) error in the spreadsheet. One more bug down.

For the Damage, I brute forced it with a spread sheet.

The expectation value is the value times the odds it will show up.
Do that for each possibel Damge value, sum those results and thats your Expectaion Per Hit.
Your Expectation Per Hit times your Odds Of Landing a blow is your average Damage Dealt per turn.

So it reallly works out to 2d+1 - 7 damage

02-0 -
03-0 -
04-0 -
05-0 -
06-0 -
07-1 -16.6
08-2 -13.8
09-3 -11.11
10-4 - 8.33
11-5 - 5.55
12-6 - 2.77

Multiply each line and sum ...
(1* 16.6) + (2*13.8) + (3*11.11)..... = 1.5522

Multiply that expectation Value, by the Odds of hitting,
.89*1.5522 and youll get .89

Bettter

Nymdok

[tjbuege]

Ok, I think I have it right (this time). As you said, the Wizard is straightforward. 1 out of 6 times he inflicts 1 points of damage, so his final average damage is 1 * (1 / 6) or .17 points of damage. The Cleric will inflict damage 21 out of 36 times. The average damage over those 21 times is 2.67, so his final average damage is 2.67 * (21 / 36) or 1.56 points of damage. The Barbarian will cause damage 1261 out of 1296 times. Average damage over those 1261 times is 7.21, so his final average damage is 7.21 * (1261 / 1296) or 7.02.

Plugging those in, we get:

Barbarian = 65.7% * 7.02 = 4.61 points damage per turn
Cleric = 57.4% * 1.56 = .89 points damage per turn
Wizard = 57.4% * 1 = .5 points damage per turn

Does this finally add up correctly?

Tim

[tjbuege]

Originally Posted by Nymdok

...I always deceptive attack down to 16 or 15

Once I get this down correctly, I'm going to list all (or most of) the possible types of attacks and defenses, and have the odd all laid out right there on the spread sheet. Simply fill in the skills, damage amount, damage type and DR.