Confused about adding innate attacks to weapons
 

There seems to be a discrepancy in cost when adding an innate attack to a ST-based weapon compared to an unarmed strike.

Per the FAQ, adding fire damage to a sword may be priced as follows:

12 points:
Burning Attack 3d [15] -20% (Melee Attack, reach 1 -25%; Link +20%; Accessibility (wielding a broadsword) -15%)

Even though a sword is a ST-based weapon, the FAQ specifically notes to not add (Melee, ST-Based +100)

Defining the attack as a follow-up to a single weapon is about the same cost:

12 points
Burning Attack 3d [15] -25% (Melee Attack, reach 1 -25%; Follow-up +0%)

However, try to add damage of some sort to an unarmed attack, you have to add the (Melee, ST-based +100%) modifier. Adding 3d crushing damage to unarmed strikes costs:

26 points
Crushing Attack 3d [15] +70% (Melee Attack, Reach C -30%; ST-Based +100%)

Why the point difference? What logic is there for required a +100% modifier for unarmed attacks but not ST-based weapons?

Also, how would you add burning damage to an unarmed strike?

EDIT: Meant to write "3d" instead of "2d" for the crushing attack.

Re: Confused about adding innate attacks to weapons
 

That FAQ entry pre-dates Imbuments which might be what you actually want in this case.

Re: Confused about adding innate attacks to weapons
 

It should also be noted that ST-Based (+100%) allows you to use Swing damage unarmed, as well as adding those dice directly to your damage roll, instead of being a follow-up attack.

Re: Confused about adding innate attacks to weapons
 

Each build will function slightly differently. Let me explain
You don't add ST-Based, because the fire damage is not dependent on the ST damage. It's in fact independent and must face DR separately to the ST based attack. It also works with every broadsword the character uses.
First, you don't add Melee Attack when using Follow-up, so the cost is 15, not 12. Second, you only get the follow-up when using a specific sword (that's follow-up at the +0% level), not any sword as in the previous case. Third, it ignores DR is the carrier attack penetrates, so unlike the previous case, it will only face DR once most of the time.
Also, here the damage is done by the character
Unlike in the previous two cases, the extra damage helps penetration, so it will never face DR more than once (Link will always face DR twice, Follow-Up will face DR is the carrier attack can't defeat DR on it's own). Assuming 2d base damage from ST in all cases, against DR 10: Link will rarely do damage for the ST based damage, and half of the time for the burning damage (average of 3d is 10.5); Follow-Up will still rarely deal damage for the ST based part, but sometimes (on a roll of 11 and 12 in 2d) deal full damage ignoring DR for the burning damage (If DR was lower, like 5, it would nearly always ignore the DR for the burning damage part). With ST-Based, you have a single 4d attack that will only face DR once, and will penetrate quite often.
With I would use follow-up to the unarmed attack, or use Imbuements.
Indeed, the rules are quite inelegant without Imbuements, as this is the case that Imbuements were created to handle.

Re: Confused about adding innate attacks to weapons
 

Kuroshima, thank you for the detailed response. A couple comments:

Makes sense. Armor Divisor (2) is +50%, so I guess applying that to both attacks equals about adding +100% to one attack.

B104 says "Melee Attack" is one of the modifiers that changes the cost of "Follow-up". So I guess here if I was using a small class of weapons (eg all broadswords), Follow-up would cost -25% + 10% = -15%, for a total cost of 13 points. Not a huge cost difference.

Regarding follow-up: the bits about DR are still a little confusing. It sounds like if the first attack fails to penetrate DR, then the total DR applies to the follow-up attack, right?

So to use your example: If I roll 9 damage with a flaming sword against a target with DR 10, and roll 12 burning damage with my follow-up, I only do 12 - 10 = 2 burning damage in total. But if I rolled 11 damage with my sword, then I do the full 12 burning damage for a total of (11 - 10) + 12 = 13 damage (1 cutting and 12 burning). Is this correct?

I don't know how the imbuements work, but it sounds like "follow-up" for an unarmed strike may be able to simulate what I'm looking for. Thanks again!

EDIT: Forgot to ask: it looks like in RAW there's no way to boost damage for striking with a weapon (like, say, a staff) other than Striking ST. Would something along the lines of:

Crushing Attack 3d [15] +65% (+100% ST-Based; Melee Attack, Reach 1,2 -20%; -15% Accessibility: wielding a quarterstaff)

for 25 points be an acceptable way of boosting a mundane crushing weapon?

Re: Confused about adding innate attacks to weapons
 

You have the idea of Follow-Up and DR correct. Power-Ups 1: Imbuements is cheap, and definitely worth it for what it seems you're trying to do!

Re: Confused about adding innate attacks to weapons
 

The thing is, the baseline costs are for either natural weaponry (claws, strikers, etc) or for Innate Attacks. There is also "Any natural or weapon attack" for +50% in both GURPS Power-Ups 1: Imbuements and Power-Ups 4: Enhancements. Note that when you take it as a follow-up of a natural weapon attack, it's a +0% modifier, so I would make it a +0% modifier for a single specific weapon.
Exactly. A linked attack will always face DR separately, a follow-up will only face DR separately if the carrier doesn't penetrate.
Imbuements are special skills (similar to spells) that either add enhancements, or change the base type of a non-innate attack. They allow you to add, for example, armor divisor to attacks made with any sword you find, or change the damage from cutting to burning, or so loads of other nifty things, like adding follow-up damage to the attack, changing reach, converting a melee attack to a ranged one,... Each skill requires a given level of a special advantage, called Imbue, that does nothing by itself other than serve as a prerequisite.
The canonical way of doing this is to buy limited Striking ST. The limitation is found in Powers, nd is, IIRC, -60%.