How to get a Battered Hilt.

Stop running Pit of Saron.

I'll explain: Blizzard messed around with the drop rate quite a bit, but settled on it. The blue post I would like to draw your attention to is this one:

The increase in drop rate is more significant than the removal of this item's chance to drop from Skeletal Slaves, particularly for those clearing all three wings as intended.

Now, I've emboldened that last bit, because I'm pretty sure people haven't quite grasped how the drop chance on Battered Hilt works.

Firstly, let's dispel a myth: The chance of a Battered Hilt dropping off one mob in a 5-man Icecrown instance is not 1%-2%. Oh, yes, the Armoury claims that it is 1%-2%, but do you want to know why that is? "Extremely low" is the lowest category they have. I'll show you another example to demonstrate this: The Tiny Emerald Whelpling drops from mobs at a rate of 0.2%, recorded by 190,000 trials using Wowhead's looter. What does the Armoury tell us about it? Extremely Low (1% - 2%).

So, why do I say "Don't do Pit of Saron"? Well, this is myth #2: The chance of a Battered Hilt dropping off a mob in Halls of Reflection is not the same as the chance of it dropping off a mob in Pit of Saron. For this, we need to look at the aforementioned blue post: He says that if you clear all three dungeons, you have an increased chance of getting a Hilt drop. In a way, what he is saying is true according to the myth: If you do Forge of Souls and Pit of Saron, you have more of a chance of getting a Battered Hilt than if you just do Forge of Souls. But if you click "Next blue post" on that link, you get this:

No, the drop rate is flat. You have a fixed chance of getting the item every time you run one of the dungeons. What we did in these recent fixes is substantially increase that chance and remove this item's ability to drop from the creatures most frequently and easily being farmed for it.

Read that extremely carefully: The chance for a Hilt to drop is equal for the dungeon; it is not equal for each cross-dungeon mob. I will explain this with statistics:

Let's say that you have a fair, six-sided die, and you're trying to roll a 6. Of course, your chance of success is 1/6. You also have something called the "Expected value", which is the number of trials that you expect, from looking at the probability, you will need to complete in order to get a success. Predictably, this is 1/(1/6) = 6. If you roll the die 3 times, you're going to have a 1-(0.85^3) ( = 38.6%) chance of rolling at least one 6. If you roll the die 6 times, a 1-(0.85^6) = 62.3% chance. And so on.

What do you do, though, if you want to make sure that you have an equal probability of rolling a 6 on two dice, but you're allowed to roll one more times than the other? Well, not too hard: You increase the number of faces on the die that gets rolled more often. That way, the probability of rolling a 6 on one individual roll will go down, which increases the expected value.

So, let's say you have a 6-sided die and a 10-sided die. You want to rig it such that you have the same chance of rolling a 6 on both. The default chances of success of this are 1/6 and 1/10. We'll say, for simplicity, that you want a 1/6 chance of rolling a 6 on the 10-sided die. This means that you only roll the 6-sided die once, but you roll the 10-sided die 1-(o.9^n)=1/6 times.

1 = 1/6 + (0.9^n)
5/6 = 0.9^n
ln(5/6) = nln(0.9)
ln(5/6)/ln(0.9) = n = 1.7304....

Obviously, we can't have 1.7 trials, but you see the point being made here: As with all algebra, changing the variables while keeping only one unknown allows us to rig systems for equal probability in unequal starting circumstances.

This brings us back to Blizzard's semi-cryptic message about the drop rate. This is why I started going on about dice: You have various different numbers of trials in each of the instances -- one mob kill is equal to one trial. So, this example differs because we know the maximum number of trials allowed per instance. We also know the probability we wish to achieve: We want to rig the drop chance of each instance mob so that the overall chance of a Hilt dropping in Halls of Reflection is the same as Forge of Souls and Pit of Saron. The unknown, then, is p: to what level is each mob in each instance rigged in order to produce an equal total chance?

Let's say that the overall total probability we're trying to achieve is 0.02 -- a 2% chance. That seems reasonable for an iLvl251 weapon: 50 trials is about two weeks of running through all three instances.
Forge of Souls has 39 lootable mobs including bosses. This means 1-(q^39)=0.02
0.98 = q^39
39√0.98 = q = 0.99948... p = (1-q) = 0.0005. So, you have a 0.05% chance off any individual mob in FoS to get a Battered Hilt, assuming a 2% total chance.
Pit of Saron has 62 lootable mobs including bosses. This means 1-(p^62)=0.02
62√0.98 = q = 0.99967... p = 0.0003. A 0.03% chance. Roughly 40% lower, per mob, than Forge of Souls.

This means that, to achieve the same drop chance from Pit of Saron as you do in Forge of Souls, you have to do 58% more clearing. If you ignore mobs, then you won't even get to 2%: Your chance will diminish. It'll be appallingly low if you're only clearing half the instance in order to get through it quickly.

There are 36 mobs/lootable objects in HoR, so your chance there is slightly higher than in FoS on a per-mob basis.

Because Pit takes up so much time to clear through, it's better for the sake of efficiency not to do it at all. Forge of Souls and Halls of Reflection are both worth doing: In Forge you have minimal effort to pick up the 6 mobs not directly on your path to the finish, and in Halls every trash pack is mandatory anyway.

So if you want to get a Battered Hilt, and don't want to spend an additional 5-10 minutes clearing insignificant trash in Pit of Saron for the sake of having the same drop chance as the other two instances, just don't go in there at all. It's not worth it in Pit of Saron to ignore half the trash, because you ruin your chances of getting one. That is not to say that if you just run HoR and FoS, you will have a greater chance of getting a hilt than running all three -- but the time:reward ratio will be lower by ignoring PoS.

And please don't join purely for trash only to leave before the first boss of any of these instances. That's just poor form. If you want to do that in a guild group, that's fine; don't subject LFDs to your selfishness.