As you can see in the above post, @kedricos asked how much I valued a dbow.
There are a lot of factors that could potentially play into how much an item is worth. These include:
- Rarity of the item
- Usefulness of the item
- Difficulty of the dungeon or boss that drops the item
- Do you have to make a special trip to obtain the item - Not everyone goes in the shatters, but everyone does O1, so crown’s worth increases compared to A.S.S. since you have to make a special trip to get it
- Aesthetic appeal of the item - some people want an item, because they like how it fits their set, ie. mg shield
- Existence of substitutes - acropolis armor is almost identical stat-wise to abyssal armor
- Rarity of substitutes
- Price of substitutes
- Number of people that play the class that uses the item
- How long it takes you to acquire the item
All of these various points tie into the overall supply and demand for the item. Supply and demand are what ultimately decide the price of the item, so each of these factors will ultimately impact the price; however, that list contains a lot of variables that are pretty hard to quantify.
####As such, we will be calculating the MAXIMUM price that anyone should theoretically pay for an item, white bag or otherwise. Logically, we are answering the question “How much should I pay for an item, before it becomes cheaper for me to just farm the item?”
To do this, I will be looking at how long it takes to acquire an item (white bag or otherwise) and then comparing it to the amount of life that I could acquire in that same time by running tombs.
Firstly, I will calculate how much life I can obtain per unit of time by running tombs.
For the sake of this scenario, I will assume that the average group of 3 people in a tomb can do a tomb in 20 minutes. In this scenario, on average, I will get 1 life per tomb.
This means that if I am doing tombs, I can get life at a rate of:
- 1 life per 20 mins =
- 0.05 life per minute =
- 0.000833 life per second
I will use this as a baseline.
For this example, I will be using the dbow. I am going to make the assumption that I can find a UDL dungeon in about 1 minute and 30 seconds. I can complete the dungeon in 30 seconds, from dungeon start to loot dropping. This means that I can complete UDLs at a rate of 1 per 2 minutes.
Furthermore, I will assume that dbow drop rate is 1/80, as per the drop rate tables.
Next, I am going to calculate the number of UDLs that I need to run in order to be 95% sure that I will get a dbow.
The reasoning is as follows: The chance of getting dbow is NEVER guaranteed. Therefore, even if I run a million dungeons, there is still a tiny chance that I won’t get the dbow. I would have to run an infinite amount of dungeons to ensure with 100% certainty that I would get at least one dbow.
As such, I will use 95% confidence. This is because anything less than 5% has been deemed by the statistical community to be so insignificant that it should not have an impact on your calculations, due to the rarity at which the event occurs.
In order to actually calculate something like this, you traditionally turn to the binomial distribution formula, which looks like this:
1 - b(x; n, P) = nCx * P ^ x * (1 - P) ^ n - x
or
1 - b(x; n, P) = { n! / [ x! (n - x)! ] } * P ^ x * (1 - P) ^ n - x
where:
- b(x; n, P) is the probability of the event not happening
- n is the number of trials that you run - aka the number of dungeons
- x is the number of occurrences that you want - aka the number of dbows you want to obtain in those trials. For our purposes, this will always be 1
- P is the probability of the event occurring - aka the drop rate of the dbow
However, since we are doing this where the number of occurrences we are looking for will always be 1, we can use an alternate formula that is much simpler:
1 - b(x; n, P) = (1 - P) ^ n
Plugging in the numbers from our simulation yields:
1 - 0.95 = {1 - (1 / 80) } ^ n
Solving for n gives:
n ≈ 238
####This means that if you were to run a UDL 238 times, you would be 95% confident (which is statistically about the same as 100% confidence) that you would receive 1 dbow.
Now let’s put it all together. 238 UDLs at a rate of 1 per 2 mins would take you 476 minutes (excluding the time it would take to do oryx or vault).
At a rate of 1 tomb per 20 minute, you could do 23.8 tombs.
At a rate of 1 life per tomb, you could obtain 23.8 life from tombs in the time that it takes to get 1 dbow.
Even if we assume that you somehow vaulted and kept all that wis that you got, assuming a conversion rate of 16wis per life, you would have earned an additional 16.125 life worth of wis pots.
Taking the difference yields the value that you got from the dbow alone.
As such, we get:
#The DBow is worth a maximum of 7.625 life.
So what does this actually tell us? Well, basically it says that the time you spend searching for the dbow is equal to 7.625 life if you were to spend it on tombs. In other words, if someone offers you a dbow for anything UNDER 7.625, then you MAY be getting a good deal. I say MAY be getting a good deal, because there are other factors that contribute to the actual price. If you are asked to buy it for OVER 7.625 life, then your time is better spent just farming for the dbow yourself in the UDLs.
This sort of logic can be applied to virtually every item in the game, so long as you keep in mind that it is not a price guide, it is simply the upper limit for which something should be bought for.