What neckpiece to wear for WS on THF.

Today I was browsing the web and found a very interesting Live Journal on what neckpiece to use on THF with Mercy stroke. Yeye, I know, I dont have the Mandau yet, but the point that I found to be was so interesting was that I was in fact correct (weird I know) all those times I've stated I'd use the Kubira Bead Necklace over a Sea gorget.

My summary of the ranking for neckpieces is (based on data below):
SA+MS: #1 Kubira Beads Necklace
SA+MS: #2 Justice Torque
SA+MS: #3 Love Torque
SA+MS: #4 Soil Gorget
TA+MS: #1 Justice Torque
TA+MS: #2 Kubira Beads Necklace
TA+MS: #3 Soil Gorget
TA+MS: #4 Love Torque

I'm just gonna paste the formulas and comparisons here below, but if you want to check the original link it is http://shamayaasura.livejournal.com/4151.html .
So all info below is credited to Shmayaasura.

1-Hit Sa+Mercy Stroke
Soil Gorget
1-hit Sa+Mercy = {(39bD + 12fStr + f[0.83 * f(0.6*125)]WSC)*3.1fTP + 103dex} * 1.914pDif * 1.25piercing
= ((113".25" * 3.1) + 103)*1.914 *1.25
= 1083dmg
To generalize this comparison, to make it more accurate for everyone and not just my own set, I can alternatively not truncate anything. Skipping truncation gives me,
= 1086.4dmg

Justice Torque
Additional 5str will not affect my fStr here. It will change pDif slightly, from a non-crit median of 0.914 to 0.924 with only 2".5" attack.
1-hit Sa+Mercy = {(39bD + 12fStr + f[0.83 * f(0.6*130)]WSC)*3.0fTP + 103dex} * 1.924pDif * 1.25piercing
= ((115".74" * 3.0) + 103)*1.924 *1.25
= 1077dmg
Skipping truncation steps to generalize this, I get,
= 1082.8dmg

So far it looks like Soil Gorget is better here for 1-hit Sa+Mercy. If Str is lower, Justice Torque will become better. Similarly if fStr is lower (ie you're fighting much harder stuff), Justice Torque will also become better. Same if pDif is lower. Given how close they are here for 1-hit, it's very likely that Justice Torque is better for anything HNM level. This, again, is also 1-hit. The more hits you add, the better Justice Torque becomes in comparison.

Now let's take a look at love torque and kubira bead necklace for 1hit SaMS, this time also skipping truncation to favor generalization for each example.

Love Torque
1-hit Sa+Mercy = {(39bD + 12fStr + f[0.83 * f(0.6*125)]WSC)*3.0fTP + 108dex} * 1.937pDif * 1.25piercing
= ((113".25" * 3.0) + 108)*1.937 *1.25
= 1084.1dmg

Kubira Bead Necklace
1-hit Sa+Mercy = {(39bD + 12fStr + f[0.83 * f(0.6*129)]WSC)*3.0fTP + 107dex} * 1.923pDif * 1.25piercing
= ((115".24" * 3.0) + 107)*1.923 *1.25
= 1088.2dmg

2.48-Hit Sa+Mercy Stroke
As mentioned earlier, /nin with traditional merits and WS gear (5/5 triple, brutal earring), the average mercy stroke is 2.48 hits. While there are a number of offhands available, the most common used for DD'ing is still probably blau dolch, which is also what I have.

Soil Gorget
2.48-hit Sa+Mercy =
({(39bD + 12fStr + f[0.83 * f(0.6*125)]WSC)*3.1fTP + 103dex} *1hit *1.914pDif
+{(39bD + 12fStr + f[0.83 * f(0.6*125)]WSC)*1.0fTP} *0.24hit *0.914pDif
+{(33bD + 10fStr + f[0.83 * f(0.6*125)]WSC)*1.0fTP} *1.24hit *0.914pDif)
*1.25piercing
= 1.25*(869.1 + 24.8 + 119.3)
= 1266.5dmg

Justice Torque
2.48-hit Sa+Mercy =
({(39bD + 12fStr + f[0.83 * f(0.6*130)]WSC)*3.0fTP + 103dex} *1hit *1.924pDif
+{(39bD + 12fStr + f[0.83 * f(0.6*130)]WSC)*1.0fTP} *0.24hit *0.924pDif
+{(33bD + 10fStr + f[0.83 * f(0.6*130)]WSC)*1.0fTP} *1.24hit *0.924pDif)
*1.25piercing
= 1.25*(866.2 + 25.7 + 123.4)
= 1269.1dmg

Love Torque
2.48-hit Sa+Mercy =
({(39bD + 12fStr + f[0.83 * f(0.6*125)]WSC)*3.0fTP + 108dex} *1hit *1.937pDif
+{(39bD + 12fStr + f[0.83 * f(0.6*125)]WSC)*1.0fTP} *0.24hit *0.937pDif
+{(33bD + 10fStr + f[0.83 * f(0.6*125)]WSC)*1.0fTP} *1.24hit *0.937pDif)
*1.25piercing
= 1.25*(867.3 + 25.5 + 122.3)
= 1268.9dmg

Kubira Bead Necklace
2.48-hit Sa+Mercy =
({(39bD + 12fStr + f[0.83 * f(0.6*129)]WSC)*3.0fTP + 107dex} *1hit *1.923pDif
+{(39bD + 12fStr + f[0.83 * f(0.6*129)]WSC)*1.0fTP} *0.24hit *0.923pDif
+{(33bD + 10fStr + f[0.83 * f(0.6*129)]WSC)*1.0fTP} *1.24hit *0.923pDif)
*1.25piercing
= 1.25*(870.6 + 25.5 + 122.7)
= 1273.5dmg

SUMMARY:


JUSTICE TORQUE
#2 for Sa+Mercy by this comparison (greater colibri march/madrigal no food), and #1 for Ta+Mercy. Should be the best mercy neck for HNM's.

KUBIRA BEADS NECKLACE
#1 for Sa+mercy by this comparison, and should be #2 for Ta+Mercy.

LOVE TORQUE
Lingers somewhere in between the above two necks and soil gorget for Sa+Mercy. Likely inferior to all for Ta+Mercy. When you're very high on pDif , gorget should be best, but I'm not sure if there's a point where love torque would ever be the best option. #3 by this comparison for Sa+Mercy, and #4 for Ta+Mercy.

SOIL GORGET
#4 by this comparison for Sa+Mercy, and #3 for Ta+Mercy. However, this is probably going to be the best mercy neck at some inflection point of pDif, when pDif is high enough. If not on merit level mobs, this might be the best option for very weak mobs, like too weak to even match. But then again, the first hit of mercy becomes less and less important as pDif rises. Either way, it doesn't matter.