A look at Melee Combat. WARNING LOTS OF MATH!

[cloakblade]

So I've been sitting on this long mathematical wall for a bit and thought I'd share it with you. So I present a mathematical examination of the Unarmed Combat and Melee Combat dynamic.

2 Warnings before you start.
1: This is a huge wall of text and math there is no good way of simplifying it. I will try and show all my work either in the text or at the bottom.
2: This is an examination of mid to high level combat I don't even bother looking at numbers that are under 1 million LP in combat skills.

It is true and will probably always be true that Melee Combat requires Unarmed Combat skills too. Many argue that because of this it is silly to go anything other than 100% Unarmed Combat. Although it maybe easier and safer to simply go 100% Unarmed Combat (especially early on) the shear power that Melee Combat can provide is undeniable. There are several things to take into account when arguing this and these will be my 2 main points to look at: Attack & Defense Bar Size; Delta in relation to maneuvers.

Now onward to the math:
The amount of LP it takes to get to any amount of skill can be defined as: All the LP is scaled by 100 as all skill ups are scaled by 100 also.
s(x) = 0.5 (x + 0.5)^2 -1.125
The inverse is the more important formula for us as it will allow us to observe how high you can increase your Unarmed Combat Skill depending on how much LP you have:
u(x) = sqrt(2x + 2.25) - 0.5
Now lets look at a Melee Combat character who has decided to go 50:50. And see how some numbers play out with him. His formula is as follows:
m(x) = sqrt(x + 2.25) - 0.5

The first thing that is often looked at when talking about which is superior between Melee Combat and Unarmed Combat is Delta. Delta is a multiplier used to find out how effect many maneuvers are. The formula to find out what your delta is as follows sqrt(Your UA/Their UA). Using this formula we can see what the average delta for the Unarmed Combatant is 1.189 and the average delta for the Melee Combatant is 0.8498 (see bottom for math). This isn't the worst thing the Melee fighter could have seen its only about a 30% difference between the two.

The next thing we look at is defense bars. The size of your defense bar is determined by the weight of your maneuver. The Unarmed fighter can use almost any maneuver and have a defense bar equal to his Unarmed Combat skill. While the Melee fighter will have to try and switch to shield right before being struck (Battle Axe fighter's have notes at the bottom for them). This can cause you to not use your maneuvers as often as you may like but is a sacrifice he must pay. With Shield the Melee fighter has only is only 36 points less, 16%, than the Unarmed fighter at 5 million LP (315 vs 223). The numbers keep getting worse the more LP each player has but 5 million can give a good idea of how much.

The amount of damage (physical or to the defense bar) an attack does is base on another formula: A * sqrt(wA / wB) / 2, where A is the percent of the attack bar use; wA is the weight of the attack; and wB is the weight of the maneuver used to block. This means that if the Unarmed fighter attacks the Melee Fighter the amount of damage he will deal to his defense bar will be about 53% with a full attack bar regardless of how much LP (see bottom for math).

Attack is a lot more complicated than defense as melee combat a wide array of attacks. Though sense Sting, Chop and Punch will all have the same weight to them you will probably use punch for the majority of your damage and Valorous Strike on occasion and as a finisher. Your punch will do about 42% of their bar each attack with a full bar. Though Valorous Strike will take out 73.5% of their defense bar and deal physical damage based on your weapon.

Edit: A section for Battle Axe wielders. When wielding a battle axe you hit an odd balance. If you use the 50:50 build you will be fighting with a 41% smaller bar as you will be unable to use shield as a maneuver. This means that an opponent's punch will deal 70% of your defense bar which is almost impossible to recover from before the next punch is coming. Especially sense you will be using punch to break their defense and dealing the 42% as you shield wielding fighter would. This become mildly problematic. This is why I propose the idea of making a Valorous Strike deplete the same defense as a punch. Thusly your combat will be punching and as normal but if your opponent gets close to death you can deal huge amounts of damage to then with a Valorous Strike. This split would be a bout 64:36. Your delta would be .866 vs their 1.11 and your defense bar will be 25% less than a full Unarmed fighter. Your punch (and Valorous Strike) will deal 44.7% of their defense while they deal 55.9% at about the same 25% difference. I see this more viable in a group build where you would need to dispatch someone quickly as your attacks would deal huge amounts of damage with the battle axe when you do use it.

I hope this sheds some light on the merits of Melee Combat to people who doubt it. I'm tired of hearing people saying that its a stupid build that has no merit. But I think with these number its clear that it is viable. Though I still think you should hit 100 Unarmed before going into Melee Combat at all.

The MATH:
When looking at function we can often simplify them to see what the average end behavior is. This can be done to both the Unarmed equation and Melee Combat equation. As end behavior is concerned u(x) = sqrt(2x) & m(x) = sqrt(x). The amount of delta that the unarmed character has is equal to the fourth root of 2; or 2 square rooted twice. The melee's delta is the fourth root of 1/2. Due to the fact that many equations in the the game are roots which by their nature will cause the numbers to reach an equilibrium is what fuels melee being so viable both the deltas are pulled towards 1. Calculating the damage is a little more complicated. The equation is sqrt(u(x) / (m(x) * 1.25)) / 2. Simplified is: sqrt(sqrt(2x)/(sqrt(x)*1.25)) = sqrt(sqrt(2x)/(sqrt(1.5625x)) = sqrt(sqrt(1.28)). The melee's damage is the same except it's .78125 not 1.28 both once again being pulled to 1.


If any of my math is wrong please tell me and I'll correct it.

Edit: Oh and a wiki link for the in game equation I got: http://ringofbrodgar.com/wiki/Combat:_A ... _Maneuvers

[Foarl]

Edit: I misunderstood the weighting of Knock Teeth, and just completely bungled the numbers for strangle. I still stand by the fact that the math is wrong for max def bar takedown though. For punch I see a maximum of 44.72% def bar kill for 1:1 combat skills. Don't know where the 50%+ comes from.

Some of your numbers seem a little off to me? But I digress, the point is that these numbers do not favor the melee fighter nearly enough to make the loss of maneuvers variable uses.

But about math, take the defense bar attack for equal UA/Melee between two people:

Punch

Def bar dmg: A * sqrt(wA / wB) / 2
=100 * sqrt(100 / 125) / 2
=100 * sqrt(0.8)/2
=100*0.8944/2
=100*0.4472
=44.72%

[TeckXKnight]

The transparency of your numbers is much appreciated. My post will offer no such thoroughness though. The scenario is such that I'd still doubt the success of the melee fighter though. The 100 UA fighter is recovering faster and breaking through more defense/time with less ip. As, if the melee fighter is utilizing Sting or Valor Strike, not only do they have a substantially longer cooldown time, they've burned a considerable amount of ip that needs to either have been stored up or rebuilt before they can use maneuvers like Flex, which are much more time efficient over Jump. So then the melee fighter is using punch instead and breaking less defense due to their investment in melee. The boon is substantial though the moment you can get their defense low enough to let off a VS or Sting. This is assuming the UA fighter isn't pushing them for quick, weak hits that grant Advantage. It isn't hard to maintain defense while pushing advantage through punches.

Hmm, nevermind, I can see the fight going either way depending on what moves the combatants plan out and prepare for. If it was a 1v1, I could see the melee fighter getting to 8 ip via DoG, and Charge!, then throwing a punch and switching to meditation, sting like a bee, punch, no pain no gain, and Sting. The UA fighter could win just as handily if they dropped an evil eye in at any point in this onslaught, as they'd be able to pick themselves up, recover, and push their Combat Advantage, erm, advantage to victory.

It is an interesting idea you have posited. I'd still be terribly cautious about being the melee fighter though as if you switched to the maneuvers at any point, you're going to be down in defense fairly substantially (the 1.25x melee does help considerably.) I'd never want to be caught dead trying to use Bloodlust like that though.

Perhaps it is just such that it opens a different venue of strategies and combinations, that we do not commonly think of, is all? It's a lot easier to tell a newbie to use Oak Stance and Bloodlust while punching to victory than to explain the complexities of special moves and moves.

[bitza]

Punch

Def bar dmg: A * sqrt(wA / wB) / 2
=100 * sqrt(100 / 125) / 2

Knock Teeth

Def bar dmg: A * sqrt(wA / wB) / 2
=100 * sqrt(200 / 125) / 2

def bar drain from attacks is based on weight, not damage. KHTO is weighted the same as punch, at 1xUA. therefore KHTO and punch will drain the same amount of def bar. try it out. strangle is weighted at 0.8xUA, draining even less than a punch. the damage rating on attacks is, well, the multiplier on damage done beyond the def bar.

also you can valor strike with a stone axe. i'm not sure where people are getting this idea that you can't. i assume you can with a b12 as well, but it's been a while since i've played around with one

[cloakblade]

def bar drain from attacks is based on weight, not damage. KHTO is weighted the same as punch, at 1xUA. therefore KHTO and punch will drain the same amount of def bar. try it out. strangle is weighted at 0.8xUA, draining even less than a punch. the damage rating on attacks is, well, the multiplier on damage done beyond the def bar.

also you can valor strike with a stone axe. i'm not sure where people are getting this idea that you can't. i assume you can with a b12 as well, but it's been a while since i've played around with one

You totally ninja'd the first part from me.

I was trying to Valor Strike last night right after I posted I'll try again today when I have a sparring partner. If its true I'll re-type my section on B-Axe, it was kind of just thrown up there. In the end I think B-Axe wielders are still mildly gimped.

Also:

The transparency of your numbers is much appreciated. My post will offer no such thoroughness though. The scenario is such that I'd still doubt the success of the melee fighter though. The 100 UA fighter is recovering faster and breaking through more defense/time with less ip. As, if the melee fighter is utilizing Sting or Valor Strike, not only do they have a substantially longer cooldown time, they've burned a considerable amount of ip that needs to either have been stored up or rebuilt before they can use maneuvers like Flex, which are much more time efficient over Jump. So then the melee fighter is using punch instead and breaking less defense due to their investment in melee. The boon is substantial though the moment you can get their defense low enough to let off a VS or Sting. This is assuming the UA fighter isn't pushing them for quick, weak hits that grant Advantage. It isn't hard to maintain defense while pushing advantage through punches.

Hmm, nevermind, I can see the fight going either way depending on what moves the combatants plan out and prepare for. If it was a 1v1, I could see the melee fighter getting to 8 ip via DoG, and Charge!, then throwing a punch and switching to meditation, sting like a bee, punch, no pain no gain, and Sting. The UA fighter could win just as handily if they dropped an evil eye in at any point in this onslaught, as they'd be able to pick themselves up, recover, and push their Combat Advantage, erm, advantage to victory.

It is an interesting idea you have posited. I'd still be terribly cautious about being the melee fighter though as if you switched to the maneuvers at any point, you're going to be down in defense fairly substantially (the 1.25x melee does help considerably.) I'd never want to be caught dead trying to use Bloodlust like that though.

Perhaps it is just such that it opens a different venue of strategies and combinations, that we do not commonly think of, is all? It's a lot easier to tell a newbie to use Oak Stance and Bloodlust while punching to victory than to explain the complexities of special moves and moves.

I do defentantly agree that being caught off gaurd while using a maneuver is a problem and basically cause you to only use maneuvers about half if not less of the time. And yes bloodlust is out of the question. I don't think this build is completely superior to full UA far from it. I don't think anyone should even put a point in MC before 100 UA so that way they even people with 300 UA don't have the full 2.0 delta (though supposedly its only 1.0 until next restart). The purpose of this post is I hate hearing people say that a fighter build is worthless and using a view where the UA fighter has 4x the UA, I know you have done it but you did it to show a point not to try and say on is completely superior. When you look at it on 50:50 split in LP I think its pretty viable especially considering that in a group fight you would like someone to be out of the fight quickly so you can gain advantage over all.

[TeckXKnight]

I was trying to Valor Strike last night right after I posted I'll try again today when I have a sparring partner. If its true I'll re-type my section on B-Axe, it was kind of just thrown up there. In the end I think B-Axe wielders are still mildly gimped.

In my attempts in the past it has gone off without a hinge. It's not something that's difficult to retest though. B12s also rely entirely on a harmonious balance between UA and Melee or they're useless, since they can't use their melee to defend, so they probably rely more on your numbers than anything else. Without a doubt, they are painfully slow once you've swung, so you need to make sure your first hit kills. Not that that's hard to do. Alternatively, a full bar of combat meditation makes the Cleaves quick.

[novaalpha]

Now onward to the math:
The amount of LP it takes to get to any amount of skill can be defined as:
s(x) = 0.5 (x + 0.5)^2 +1.125

?

s(200) = 0.5 * (200 + 0.5) ** 2 + 1.25 = 20101.25
real skill price (200) = 2009900 LP

WTF is this wall of text and what is author trying to prove with his incorrect math?

[cloakblade]

Now onward to the math:
The amount of LP it takes to get to any amount of skill can be defined as:
s(x) = 0.5 (x + 0.5)^2 +1.125

?

s(200) = 0.5 * (200 + 0.5) ** 2 + 1.25 = 20101.25
real skill price (200) = 2009900 LP

WTF is this wall of text and what is author trying to prove with his incorrect math?

My apologize the + is suppose to be a minus this should be negligible to the over all end behavior but may effect some numbers I'll fix when I finish with this post.

The post is suppose to illustrate that a melee combat build could be viable. I often see people go for a 2:1 split of Unarmed to Melee just so they can Valorous Strike for a finisher (and have it actually deal damage if combat gets out of hand) I think this is a flawed build because your points would be better spent on UA to make even higher so you can simply win the battle as one shotting with even a soldiers sword against decent armor is hard.

Edit: Actually I just messed it up there the inverse was correct.

[novaalpha]

All of your math is incorrect.
Full melee/half melee build is not viable in 1v1, but viable if teamed with UA-focused fighters and with proper training.

[cloakblade]

All of your math is incorrect.
Full melee/half melee build is not viable in 1v1, but viable if teamed with UA-focused fighters and with proper training.

Yeah I saw that but they don't just get blown out of the water like a lot of people infer they do. And full melee builds are silly.

And how is all my math wrong. My logic maybe flawed if you want to argue that but my math should be right. I'd like to see how if it is so I won't make the same mistakes.