Okay so here goes some slight balancing in my opinion.
I personally think these swords should all be around the same level of effectiveness with each their own speciality.
Longsword (Slightly slower, heavier and hard hitting)
Katana (Faster, hitting for quite little, lighter)
Heavy Bastard sword (Overall balanced weapon)
Prices on these should be around the same aswell in my opinion, around the price that the longsword cost now, so that would mean 6660 or around there.
Personal reason for wishing these changes is, I kind of like the heavy bastard sword, but overall it feels like a gimped version of the longsword and also to keep the katana from being as much of a spam weapon as it is, while I really think the longsword could use something that sets it a bit apart from the heavy bastard sword.
so here goes my suggestions on stats
Katana.
weapon length: 95
weight: 1.8
difficulty: 12
speed rating: 101
weapon length: 95
thrust damage: 17 pierce
swing damage: 36 cut
slots: 2
(Changes, increased difficulty to use it to 12 from 9, lowered the slots required to 1, increased damage by 1)
Reasons for changes, would keep it from being the complete and utter spam weapon it is now by increasing the requirement to use it, however it would still be the fastest true, increased the weight to keep it from glancing off armor as much.
Longsword.
weapon length: 106
weight: 2.0
difficulty: 10
speed rating: 97
weapon length: 106
thrust damage: 24 pierce
swing damage: 38 cut
slots: 2
Secondary Mode
(Changes, increased damage by 2, increased weight by 0.2, lowered speed by 1)
Reasons for changes, the longsword feels like just a more effective version of the heavy bastard sword and I kind of would like to see it have it's own niche among the hybrid swords and considering it is the sword among the hybrid swords that looks the heaviest, it made sense to make it the "hard hitter" of the hybrid swords.
Heavy Bastard Sword.
weapon length: 105
weight: 1.6
difficulty: 10
speed rating: 99
weapon length: 105
thrust damage: 22 pierce
swing damage: 36 cut
slots: 2
Secondary Mode
(Changes, lowered weight by 0.4, increased speed by 1)
Reasons for the changes, well the heavy bastard sword felt useless as it is, it's heavier than the longsword, yet shorter and when heirlooming even does less damage, so only reason to ever pick this as your weapon of choice would be if you were low on cash, but due to the small difference in price, it really isn't worth trading in your longsword for this. So making it the sword in between the katana and the longsword made sense, the blade that has been balanced between speed, power and weight, without excelling in either.
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Open to criticism.
EDIT: Updated some stats to better suit the concerns stated.