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Headbutts are always multiplied by 0.2, making them less common.
All unarmed attacks (including headbutts and bionics like power claws) are multiplied by 0.3 IF the pawn is holding any type of weapon.
So generally it's not worth it, as the vast majority of attacks will be made by their weapon, and not the claw.
Le edit: Of course, one thing to keep in mind that the claw cannot be disarmed, so that's one positive thing.
So yeah. Even if you do take a close look at the power claw, it just doesn't hold up well against your standard melee weapons. Again, the only real advantage they bring is the inability to be disarmed. And, I guess, the fact that you can force them to drop their ranged weapon and have them use their claws as decent melee weapons.
You can't carry a sword and a gun at the same time tho, nuff said.
Does that make it worth it to make your pawns 16% slower, have lower DPS, for a significantly higher cost in research time and material cost? No, it does not.
Not to mention your point of not being able to carry a gun and a sword at the same time is moot for the OP's question, that being how power claws compared to melee weapons, not to guns. Ranged weapons were not a factor in the question.
But if you really want to make a "you disagree with this" statement, we should ask Brittanian. Do they feel 16% slower movement speed, lower DPS, higher material cost and significantly longer research time makes power claws worth it or not for a melee pawn? I've made my case, listing all of the power claw's numerous drawbacks compared to traditional melee weapon strengths. You've made your case, listing... well, just that the melee pawn can carry a gun. Pretty sure there's enough cards on the table to make a conclusion.
Since, say, a linked monoblade would be categorized as 'high' damage and thus get 75% of the weight to attack with, then the power claw would be categorized as 'mid' damage and get 25%.
In that same vein, running two power claws and no melee weapon would lead to substantially reduced melee dps since the power claw would then be weighed as 'high', allowing other attacks like headbutts and bites to be slipped in as 'mid'.
Am I misunderstanding something about the melee update and the melee weight calculations?
The damage of each attack part is added up and compared to all other parts, and thus produces a percentage. This is the chance that particular attack part is chosen for the attack. Headbutts have an additional condition that their commonality multiplier (probability to be chosen) is 0.2. Further, if holding any ranged or melee weapon, all unarmed attacks gain an additional 0.3 commonality multiplier.
If I remember correctly (the numbers may have changed slightly, but this is just to illustrate how it works anyway), a human fist has a damage power of 7, while a headbutt has a damage value of 5. Thus we can calculate how likely a pawn is to use the left fist by this formula:
LFist / (LFist + RFist + (HButt x 0.2)
7 / (7 + 7 + (5 x 0.2)
7 / (7 + 7 + 1)
7 / 15 = 0.4667 = 46.67% chance.
Now, let's say you install two power claws on a pawn, despite the obvious downsides outlined above. They would then be able to use left power claw, right power claw, or headbutt. This is still a simple calculation as power claws only have one attack type. Knowing that power claws have 18 damage, the chance of using the left power claw would be:
18 / (18 + 18 + (5 x 0.2) = 48.65%
The chance of using either power claw would then be 48.65 x 2 %, or 97.3%.
Let's compare it to an excellent plasteel longsword, like I did above - a cheaper weapon, accessible earlier, and not difficult to reliably create with a decent crafter. This gets a bit more complicated as we need to modify the base longsword's stats for material and quality, but I'll take you through it.
A longsword has three attacks, all of them dealing sharp damage. A handle poke for 9 damage, a point stab for 23 damage, and a blade cut for 23 damage. Plasteel as a material will increase sharp damage by a factor of 1.10, so the damage values for a plasteel longsword will be 9.9, 25.3, and 25.3. Excellent quality adds an additional 1.2, making the values 11.88, 30.36, and 30.36.
Now that we have the final numbers we can use the same formula above - how likely is the pawn to attack with the longsword over another unarmed attack? For this we need to include all the damage values of the sword, like so:
(11.88 + 30.36 + 30.36) / (11.88 + 30.36 + 30.36 + (7 x 0.3) + (7 x 0.3) + (5 x 0.2 x 0.3))
72.6 / (72.6 + 2.1 + 2.1 + 0.3) = 0.9416 = 94.16%
We can also do the same calculation for a longsword-wielding power claw user. But why stop there? With the DPS numbers we used above, we can even calculate the total pawn DPS.
Bogstandard pawn:
93.34% x 3.5 DPS = 3.27 fist DPS
6.66% x 2.5 DPS = 0.17 headbutt DPS
Total DPS: 3.44
Just two power claws:
97.3% x 11 DPS = 10.7 claw DPS
2.7% x 2.5 DPS = 0.07 headbutt DPS
Total DPS: 11.4
Just the longsword:
94.16% x 14.27 DPS = 13.43 sword DPS
5.44% x 3.5 DPS = 0.19 fist DPS
0.4% x 2.5 DPS = 0.01 headbutt DPS
Total DPS: 13.72
Longsword and two power claws:
86.74% x 14.27 DPS = 12.38 sword DPS
12.9% x 11 DPS = 1.42 claw DPS
0.36% x 2.5 DPS = 0.01 headbutt DPS
Total DPS = 13.81
And there you have it, the full mathematics behind the melee combat. As you can see, while two power claws is a significant upgrade over a completely unarmed pawn, it pales in comparison with the cheaper, easier-to-get longsword. You *could* give your longsword-wielding melee pawn two power claws to try to maximize their damage, but that would only marginally (0.09 DPS) increase their offensive capabilities. Comparatively, if you have a pawn with two power claws already and you give them a longsword, you'd increase their DPS by 2.41.
Besides the speed loss... and honestly if you're making a biocybernetic super soldier you're going to replace his legs too.