King's Blade and weapon balance issues

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Michebugio
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Re: King's Blade and weapon balance issues

Post by Michebugio » Wed Apr 09, 2014 7:57 pm

Yusei wrote:I'm curious about your methodology. I didn't try to compute the values analytically, but your results are very different from my simulations, so maybe I'm missing something.
Considering 3 dices, you construct the probability curve. In the first column you have the possible outcomes, in the second the relative chance:

3 0,46%
4 1,39%
5 2,78%
6 4,63%
7 6,94%
8 9,72%
9 11,57%
10 12,50%
11 12,50%
12 11,57%
13 9,72%
14 6,94%
15 4,63%
16 2,78%
17 1,39%
18 0,46%
total 100,00%


Let's consider TN 14. You can score it by just rolling the 3 dices getting 14 or more, and the odds are: 6.94%+4.63%+2.78%+1.39%+0.46%=16.20%. In this case the Feat dice doesn't count because even if you score an Eye (counts as zero), you still meet the TN. Or you can score it rolling 13 (9.72%) AND rolling 1 or more on the Feat dice (11 out of 12 = 91.67%, since the only number lower than 1 is the Eye), so this case is 9.72%*91.67%=8.91%. Or you can score it rolling 12 (11.57%) AND rolling 2 or more on the Feat dice (10 out of 12 = 83.33%), so this case is 11.57%*83.33%=9.64%. And so on. Then you sum up all the partial results: 16.20% plus 8.91% plus 9.64% plus... and you finally obtain 69.48%.

I hope it was clear... :geek:

Evening
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Re: King's Blade and weapon balance issues

Post by Evening » Thu Apr 10, 2014 6:53 am

I have a same but different way of doing it. Like your method, this takes in account that 11 = 0 and 12 is auto success.

A --- B --- C --- D
18 - 12 -- 1 -- 12
17 - 12 -- 3 -- 36
16 - 12 -- 6 -- 72
15 - 12 -- 10 - 120
14 - 12 -- 15 - 180
13 - 11 -- 21 - 231
12 - 10 -- 25 - 250
11 -- 9 --- 27 - 243
10 -- 8 --- 27 - 216
9 -- 7 --- 25 - 175
8 --- 6 --- 21 - 126
7 --- 5 --- 15 - 75
6 --- 4 --- 10 - 40
5 --- 3 --- 6 -- 18
4 --- 2 --- 3 --- 6
3 --- 1 --- 1 --- 1

Column A = sum of 3d6
Column B = the number of d12 results that when added to the 3d6 number in Column A, the result is 14 or greater.
Column C = the number of dice combinations using 3d6 that will result in the number in Column A.
Column D = the product of B x C. This is the total number of successful d12 results that by default or when added to that particular 3d6 sum provides a 14 or greater result.

Add up Column C. This is the total of all the possible 3d6 combinations for Column A. The answer is 216.

12 x 216 = 2592, the total number of 1d12 + 3d6 dice combinations.

Add up Column D. This is the actual number of '14 or greater' successes out of the 2592 possible combinations. The answer is 1801.

Divide the number of successes by the total number of possible successes.

1801/2592 = 0.6948 or 69.48%

Therefore, a skill rank 3 against a TN14 is successful 69.48% of the time.
Don't start arguments over who has a better grasp of hiking and boating or someone might just bring down the banhammer.

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Yepesnopes
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Re: King's Blade and weapon balance issues

Post by Yepesnopes » Thu Apr 10, 2014 7:33 am

Michebugio wrote: So I ran three simulations with the same Woodman using an axe, a sword and a spear against an Orc Guard (armor 2D+4). Results seem to support my thesis: the axe Woodman has a victory rating of 60%, the sword Woodman has 68% and the spear Woodman has 72%. And 12% difference in rating just because of two different weapons is A LOT, in my opinion.
I then tried the same with a Beorning and the results are similar, but less evident (I guess it's due to higher damage output of the Beorning over the Woodman): 82% for the axe Beorning, 84% for the sword Beorning and 88% for the spear Beorning.

I'm getting convinced that this issue should really get some fixing.
I have never developed a rpg, I wonder if when you do, you check these maths. It indeed seems this "issue" needs some fixing, but on the other hand if the developers did the maths, may be they had something in mind.

I will start doing some numbers to find more balance between the weapons.

Thanks for posting this
Yepes

BobusX
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Re: King's Blade and weapon balance issues

Post by BobusX » Thu Apr 10, 2014 7:59 am

I get the definite feeling with TOR that in depth mathematical analysis of their probability curves were not high priority over mechanical bonuses that just "felt right." The changes that rewards/virtues like King's Blade make to the math are not obvious on a surface level (at least for me), but they can be drastic when looked at deeper.

Michebugio
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Re: King's Blade and weapon balance issues

Post by Michebugio » Thu Apr 10, 2014 8:27 am

Yepesnopes wrote:I have never developed a rpg, I wonder if when you do, you check these maths. It indeed seems this "issue" needs some fixing, but on the other hand if the developers did the maths, may be they had something in mind.
BobusX wrote:I get the definite feeling with TOR that in depth mathematical analysis of their probability curves were not high priority over mechanical bonuses that just "felt right." The changes that rewards/virtues like King's Blade make to the math are not obvious on a surface level (at least for me), but they can be drastic when looked at deeper.
I think that you always have to check the maths when developing a RPG, at least a good one. Don't get me wrong: PLAYERS shoudn't do the maths, all LMs hate when they do. They should just focus on choices and roleplay. Also LMs should keep the maths to a minimum, and focus on narration instead. But in the development stage, well, you pretty much NEED a good mathematical analysis to support your game.

Of course, some % point of difference between one choice and another are never an issue. But when you go into the 10%, 20% of different outcomes comparing two theoretically equivalent choices, that's an issue, albeit still a small one.

Maybe you won't notice it on a surface level, as Bobus said, and be happy with that. Maybe you'll definitely feel that one character is somehow more powerful than others, without going into mathematical analysis, and it can be still fine for you. And finally in some (hopefully rare) cases, you notice that something is undoubtedly broken and you can scrap it or try to fix it (in my last game session, King's Blade effects were pretty obvious, even without doing the maths). It depends on your style.

I'm a bit of a perfectionist and a rule tinkerer (some of you have already noticed), so I like to give solid mathematical coherence to the rules, where it's missing. Without wasting too much time on it over the fun, of course. But a great deal (if not the most part) of RPGs fun is making players CHOOSE, and additional fun is when the choice isn't obvious, or straightforward, or way more convenient than the others.

Corvo
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Re: King's Blade and weapon balance issues

Post by Corvo » Thu Apr 10, 2014 10:56 am

Hi Michebugio,

As Rich wrote, that issue was already explored in other threads. On my part, I didn't answered not because I'm dismissing it: it's my kid son that keep using Bewilder + Seize Victim on me preventing me from writing articulate answers :D
There are weeks-old threads that I need to answer :(

That said...
1-I completely agree with you about the mathematic issue in games: it's place is in the designing stage, players and masters should concentrate on the narrative. A bad mechanic goes in the way of immersion.

2-I think the balancing between spears and swords is fairly good: spears are better against low armour guys (rank and file troop), while swords are better against the high armour guys (fewer, but more important enemies).
It's the axe that is screwed. Going from 1/12 to 2/12 chance to crit is huge. How to mend it? I don't yet know.
The fact that "break shield" is the worst of the called shots just rub salt in the wounds. I'm wondering if adding a second special effect to the axes: "if you roll a 10, the enemy is unbalanced by the blow: next round he cannot attack" (a bit like the enemy having rolled with the blow). But it's inelegant and lacks symmetry with the others rules.
Just thinking out loud...

3-the King's Blade is overpowered. Period. You tested it with 3dices, but we know it get even more powerful once the user's skill increase. Luckily I got no hobbit in my game, so I don't need to tackle the issue yet.

Michebugio
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Re: King's Blade and weapon balance issues

Post by Michebugio » Thu Apr 10, 2014 12:39 pm

I’ve thought a lot on how to correct the issues above, but any solution that implies changing the base weapon stats is neither simple to develop, nor effective in terms of results.

So as a first step I tried instead to evaluate from the same statistical perspective as above the performance of a house rule that I developed to make combat “deadlier” (and, somehow, to increase armor importance): the rule is that in addition to the Piercing Strike chance of Edge, every Extraordinary Success (2 or more Tengwars) on an attack roll is a Piercing Strike (but instead of dealing Weapon Damage + 2xDamage score, it only deals Weapon Damage + 1xDamage score, like a Great Success). It’s like a soft version of King’s Blade ability.

This rule has the additional effect of increasing the Piercing Strike chance as the Weapon Skill of the attacker increases (which seems also logical, btw: an expert warrior knows better than a novice where to hit to incapacitate his enemy). The question is: does it increase the chance too much? Or does it increase the chance with too much disparity between different kinds of weapons?

The following are the statistical results of my evaluation. The total, average chances to deal a Wound of ANY character with a Weapon Skill between 2 and 6, against ANY monster with any armor between 1D and 4D, using the “extraordinary success is a piercing strike” house rule are these:

- Axes (G Edge, 18 Injury TN): 14.27%
- Swords (10 Edge, 16 Injury TN): 15.26%
- Spears (9 Edge, 14 Injury TN): 15.12%

Well, I was lucky. It seems way more balanced, using the rule. It’s an increase of about 6% to the average chance to score a Wound for Swords and a 5% for Spears, but almost a 9% for Axes, which on average makes them now comparable to the other weapons (though still a tad inferior).

Looking more in depth, I split the above chances into separate chances for each armor category:

- Axes (G Edge, 18 Injury): 19.29% vs 1D, 17.58% vs 2D, 12.87% vs 3D, 7.33% vs 4D
- Swords (10 Edge, 16 Injury TN): 21.52% vs 1D, 20.51% vs 2D, 12.93% vs 3D, 6.10% vs 4D
- Spears (9 Edge, 14 Injury TN): 25.07% vs 1D, 20.57% vs 2D, 10.80% vs 3D, 4.05% vs 4D

As you can see, we have a nice rationale. Against lightly armored foes the Spears are the weapons to go with, while on the other side Axes are the best weapons to bypass heavy armor (by the way, as I wrote in my previous post, I see this as quite the contrary of real combat). In all cases Swords are a nice and well-rounded choice, performing well against all kinds of armor while never being the predominant choice.

I’ll playtest the house rule some more, but from these preliminary considerations it seems the right way to go. It may also be a step towards making heavy mail a viable choice, since our players would want to be more protected now: increased Wound chance and decreased Endurance damage (Extraordinary success has now the same damage of a Great success) mean becoming WEARY later, and increasing the chance to end combat scoring a Wound rather than dropping to zero Endurance. Which makes heavily armored characters a bit more favored.

Elfcrusher, it would be fantastic if you added this house rule to your simulator so we could also see how it performs! :)

Glorelendil
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Re: King's Blade and weapon balance issues

Post by Glorelendil » Thu Apr 10, 2014 2:20 pm

Michebugio wrote: Elfcrusher, it would be fantastic if you added this house rule to your simulator so we could also see how it performs! :)
Done. Knock yourself out.

Caveat Emptor: monsters get it, too. :-)
The Munchkin Formerly Known as Elfcrusher
Journey Computer | Combat Simulator | Bestiary | Weapon Calculator

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Yepesnopes
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Re: King's Blade and weapon balance issues

Post by Yepesnopes » Thu Apr 10, 2014 2:24 pm

Keep us posted if you further play test the rules. It seems that this house rule may solve two problems at once (King's blade imbalance and weapons imbalance), and it may be turns armours more valuable. In any case it has to be tested in game, with enemies and so on.

Very interesting.

Yepes

P.S: How it would affect the game if instead of "every Extraordinary Success on an attack roll is a Piercing Strike dealing weapon damage + 1xdamage score" would be
"every Extraordinary Success on an attack roll may be turned into a Piercing Strike dealing weapon damage + 1xdamage score or the usual Weapon Damage + 2xDamage score"

Glorelendil
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Re: King's Blade and weapon balance issues

Post by Glorelendil » Thu Apr 10, 2014 2:32 pm

Yepesnopes wrote: P.S: How it would affect the game if instead of "every Extraordinary Success on an attack roll is a Piercing Strike dealing weapon damage + 1xdamage score" would be
"every Extraordinary Success on an attack roll may be turned into a Piercing Strike dealing weapon damage + 1xdamage score or the usual Weapon Damage + 2xDamage score"
Do you mean it's the player's choice?

EDIT: By the way, in my simulator if you check both Michebugio's rule and Woodclaw's rule (stance determines max # of extra successes) they may not combine elegantly.
The Munchkin Formerly Known as Elfcrusher
Journey Computer | Combat Simulator | Bestiary | Weapon Calculator

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