What's wrong with my calculations?

[hydra_ex]

Since there's obviously something wrong if I found that rapiers/scimitars are better than heavy picks for a FB.

Rapier/scimitar (keen): 1d6 base damage, 15-18/*2, 19-20/*5
Heavy Pick (keen): 1d6 base damage, 19-20/*7

So, because the base damage on both is the same, we can just calculate which weapon a +1 damage modifier favours.

Rapier/scimitar (per 20 hits):
1: 0
2-14: 13
15-18: 4*2 = 8
19-20: 5*2 = 10
Total per 20 hits: 31

Heavy Pick (per 20 hits):
1: 0
2-18: 17
19-20: 7*2 = 14
Total per 20 hits: 31

So a if +1 increment to damage is the same for both, then a +n increment to damage is also the same for both.
(Even against fortification, they're the same; remember not to simply modify the damage they get on crits by the fortification, since they always get at least +1 damage. For example, a heavy pick crit under 50% fortification would not deal 50%(7) = 3.5. It would deal 1 + 50%(6) = 4, since the 1 damage is still applied on a negated crit).

(In fact, a quicker way to do this would to just measure what I'll call "crit addition" - how much more damage a weapon deals over just a flat +1 each hit for ever +1 damage added (i.e. no crits). To calculate it, just do threat*(multiplier-1), because we can assume a weapon which just hits 1 each hit has a multiplier of *1. So a rapier/scimitar would have 12, and so would a heavy pick. This makes it clear that difference fortifications has no affect on the difference in damage)

Furthermore, bursts affect both equally. A heavy pick's burst is 3d10, while a rapier's/scimitar's is only 1d10. However, a rapier crits 6 times, so cumulatively it is 6d10, while a heavy pick gets only two, for 6d10 as well.
(Remember that bursts apply normally, even on fortification)

Up until now, it looks like both weapons are in fact identical. But, there's one catch: seeker gives a minor boost to rapiers/scimitars.

Over 20 hits, +1 seeker damage gives 4*2*1 + 2*5*1 = 18 more damage to a rapier, while only 2*7 = 14 more damage to a heavy pick.

Granted, it's only 0.2 damage per swing more per seeker damage (so that's 1.2 if using a bloodstone), so it's a minor difference. But still, conventional wisdom says I'm wrong, so I had to have made a mistake somewhere.

[k1ngp1n]

Conventional wisdom is wrong, your calculations are correct.

If we look strictly at the damage die, seeker adds damage to base die before multipliers. This favors weapons with wide crit ranges.

On a FB barb, rapiers/scimis have seeker apply to the following damage die:

15: 2
16: 2
17: 2
18: 2
19: 5
20: 5

and picks have

19: 7
20: 7

So while rapiers/scimitars have the same crit power as a heavy pick, seeker is applied on any crit attack, which has 4 more die available to seeker, since it adds to base as well as the crit portion.

[k1ngp1n]

Additionally: the addition of seeker is identical on a khopesh and a scimitar/rapier. Khopesh has more total crit power available to it, so its the superior weapon, but seeker's bonuses are indentical for the two weapons.

[Thrudh]

But picks go to 11, I mean 7!

(And that big number is what really counts, after all)

[PopeJual]

Rapier/scimitar (per 20 hits):
1: 0
2-14: 13
15-18: 4*2 = 8
19-20: 5*2 = 10
Total per 20 hits: 31

Heavy Pick (per 20 hits):
1: 0
2-18: 17
19-20: 7*2 = 14
Total per 20 hits: 31

This looks good to me.

You get 6 extra hits worth of damage across 6 numbers on your d20 for the scimitar and rapier.

You get 6 extra hits worth of damage across 2 numbers on your d20 for the heavy picks.

If you have some magic way to bring more 19's and 20's to your die, then you'll be better off with the Heavy Picks (autocrit = Heavy Pick heaven, obviously)
If you have some way to add to your crit range, then you'll be better off with your Heavy Picks.
If you have some way to add to your crit multiplier, then you'll be better off with the Scimitar/Rapier.

Barbarians can get nice results with Stunning Blow, so that might something for you to consider when picking the weapon.


Edit: The reason why Scimitars/Rapiers come out ahead of Heavy Picks with Seeker damage factored in is that Seeker damage adds to the base damage on a crit as well as to the multiples and adds nothing to non-crit damage. If you get generic +damage on a weapon instead of extra Seeker plusses, Heavy Pick and Scimitar/Rapier will stay the same.

Khopesh is slightly better than all three of them outside of autocrit situations when Heavy Picks will always win out.