+pickpocket vs. +item bonus
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+pickpocket vs. +item bonus
With the rollout of the new limited time Crimbo zone (10% drop from unscaling candy monsters), I gave some thought on how to efficiently farm the drops. Pickpocketing is an easy way to increase drops, but is it efficient to trade +item gear for +pickpocket gear? Would sticky gloves (+20% pp) be better than a cheese eye (+20% item) I gave it some thought, and found out that it was not. Note, this is only true for monsters with single drops.
Here's why:
The way pickpockets (pp) work is that you get a second chance at getting a loot. You don't get two loots. The bonus to pickpocketing is calculated the same way as item bonus modifiers work. It is not additive. You have:
When the combat starts, a roll occurs to see if a pp succeed. If it fails, another roll occurs at the end of combat to see if you win the drop. Therefore, the formula for this series of activities is:
Where the chance formula (above) is used for pp and item.
If we trade in +item gear for +pp gear, we have a bound equation. For simplicity, I'll assume that it's a 1:1 trade, and work out later the ratio needed to make the tradeoff even. As it is a bound equation, lets use Y to represent the total value of our pp_chance and item_chance.
Alternatively, solving for pp_chance:
plugging this back into the expanded formula for Effective_rate:
This is a polynomial of order 2, so we can take a derivative and solve for 0, to find the minima. Y is a constant value, since we've assumed that pp_chance + item_chance is always going to equal the same number. However, item_chance is not, and will vary.
Plug Y back in, solve for zero
Our lowest value will occur when our pickpocketing chance is equal to our item chance! Giving up an equal amount of +item to gain +pp results in the lowest possible value for that level of bonuses.
4 analytic examples (base rate = 30%)
+item = 200, +pp = 0
Effective rate = 93.0%
+item = 150, pp = 50
Effective rate =86.3%
+item = 100, pp=100
Effective rate = 84.0%
+item = 0, pp= 200
Effective rate = 93%
The takeaway message should be that you shouldn't substitute +pp for +item
Here's why:
The way pickpockets (pp) work is that you get a second chance at getting a loot. You don't get two loots. The bonus to pickpocketing is calculated the same way as item bonus modifiers work. It is not additive. You have:
(base_rate) x ( 1 + (bonus/100)) = chance
This means a 10% base drop with a +20% bonus modifier would have a 12.5% chance of dropping, not a 30% chance. And this is true for both +item and +pp bonuses. When the combat starts, a roll occurs to see if a pp succeed. If it fails, another roll occurs at the end of combat to see if you win the drop. Therefore, the formula for this series of activities is:
Effective_rate = (pp_chance) + (1pp_chance)x(item_chance)
= pp_chance + item_chance  (pp_chance x item_chance)
= pp_chance + item_chance  (pp_chance x item_chance)
Where the chance formula (above) is used for pp and item.
If we trade in +item gear for +pp gear, we have a bound equation. For simplicity, I'll assume that it's a 1:1 trade, and work out later the ratio needed to make the tradeoff even. As it is a bound equation, lets use Y to represent the total value of our pp_chance and item_chance.
Y= pp_chance + item_chance
Alternatively, solving for pp_chance:
pp_chance = Y  item_chance
plugging this back into the expanded formula for Effective_rate:
Effective_rate = Y  ((Y  item_chance)x item_chance) = Y + Y x item_chance  item_chance^2
This is a polynomial of order 2, so we can take a derivative and solve for 0, to find the minima. Y is a constant value, since we've assumed that pp_chance + item_chance is always going to equal the same number. However, item_chance is not, and will vary.
0= Y 2 item_chance
Plug Y back in, solve for zero
0= pp_chance + item_chance  2 item_chance
0=pp_chance  item_chance
item_chance = pp_chance
0=pp_chance  item_chance
item_chance = pp_chance
Our lowest value will occur when our pickpocketing chance is equal to our item chance! Giving up an equal amount of +item to gain +pp results in the lowest possible value for that level of bonuses.
4 analytic examples (base rate = 30%)
+item = 200, +pp = 0
Effective rate = 93.0%
+item = 150, pp = 50
Effective rate =86.3%
+item = 100, pp=100
Effective rate = 84.0%
+item = 0, pp= 200
Effective rate = 93%
The takeaway message should be that you shouldn't substitute +pp for +item
Last edited by ketchup monger on Mon Dec 05, 2011 1:23 pm; edited 1 time in total
ketchup monger Forum Newbie
 Number of posts : 43
Registration date : 20110408
Re: +pickpocket vs. +item bonus
Thanks for writing this up. I would ask how a second chance at pickpocketing would change things with the bling of the new wave, but then I realized you would have rave steal at that point anyway, so it would be a silly question(and the answer obvious given the shape of the function). And now I wonder why they gave the DB a second shot at pickpocketing in the first place.
geronimoyang Forum Family

Number of posts : 58
Age : 33
Registration date : 20101126
Re: +pickpocket vs. +item bonus
A double pick pocket is kind of interesting. You'd still get a single loot, but you would have the pp_bonus applied to each attempt.
Effective_rate = (pp_chance) + (1pp_chance)(2nd_pp_chance)+ (1pp_chance)(12nd_pp_chance)(item_chance)
Effective_rate = (pp_chance) + (1pp_chance)(pp_chance) + (1pp_chance)^2(item_chance)
Effective_rate = (pp_chance)+(pp_chance)(pp_chance)^2 + (1  2 pp_chance + pp_chance^2)(item_chance)
Effective_rate = (pp_chance)+(pp_chance)(pp_chance)^2 + (item_chance)  2(pp_chance)(item_chance)+(pp_chance)^2
Some terms cancel out
Effective_rate = 2 pp_chance + item_chance  2(pp_chance)(item_chance)
comparing this equation to the single pp rate formula:
= 1 pp_chance + item_chance  1(pp_chance)(item_chance)
It's no longer possible to say the value of pp_chance + item_chance is a constant number (and makes the math a little tricky).
plotting the function in google docs:
And may as well compare the function from post 1
Effective_rate = (pp_chance) + (1pp_chance)(2nd_pp_chance)+ (1pp_chance)(12nd_pp_chance)(item_chance)
Effective_rate = (pp_chance) + (1pp_chance)(pp_chance) + (1pp_chance)^2(item_chance)
Effective_rate = (pp_chance)+(pp_chance)(pp_chance)^2 + (1  2 pp_chance + pp_chance^2)(item_chance)
Effective_rate = (pp_chance)+(pp_chance)(pp_chance)^2 + (item_chance)  2(pp_chance)(item_chance)+(pp_chance)^2
Some terms cancel out
Effective_rate = 2 pp_chance + item_chance  2(pp_chance)(item_chance)
comparing this equation to the single pp rate formula:
= 1 pp_chance + item_chance  1(pp_chance)(item_chance)
It's no longer possible to say the value of pp_chance + item_chance is a constant number (and makes the math a little tricky).
plotting the function in google docs:
And may as well compare the function from post 1
ketchup monger Forum Newbie
 Number of posts : 43
Registration date : 20110408
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