WoW: MoP Drop Rate Statistics Calculators

Normal Loot

Drop Rate
Number of Kills		Probability of drop =
Probability		Kills Needed =

Average	Next Drop Prob	Median
???	???	≤???

LFR Drops

Drops per boss
Pieces eligible
Pieces Needed

Average	Next Drop Prob	Median
???	???	≤???

Explanation of the Normal Loot section

First, you'll have to enter in the drop rate. From that, the table below will populate. It will tell you the average number of kills needed for the piece to drop, the probability that it will drop on the next kill (which should be equivalent to the entered probability) and the median number of kills required to see the item drop. If, for example the median number of kills is 4, then there is a 50% or better chance it will have dropped on or before the fourth kill.

Second, if you enter in the number of kills that you've performed, then it will tell you the probability that the item should have dropped at least once in those kills. If you enter in something in the "Probability" field, it will tell you the number of kills needed to have that probability of the item dropping at least once.

For example, if you have a drop rate of .5 and 5 kills, there is a 0.968 (actually 0.9875, but the results are rounded) probability that the item will drop at least once in those five kills. If the drop rate is still 0.5 and you enter a probability of .90, it tell you that 4 kills are necessary to have a 90% or better chance of the item having dropped at least once.

Explanation of the LFR Drops section

This is based on the LFR loot system that will be introduced in Mists of Pandaria. An explanation can be found here. You just enter in how many piece of loot the boss will drop among the raid, how many pieces of loot in its table you are eligible for, and how many of those pieces you actually want. When you have that entered the table will populate with the same type of information that is in the above table.

I based this on the assumption that a boss will drop a particular number of pieces. If it is the case that you have a fixed X% chance to win loot, then I will alter it. It is also based on a 25 player group. Furthermore, the top section is about a piece dropping and not necessarily that you'll win it. The bottom section involves you winning a piece that you want.

If you have any questions about this or about loot drops, please don't hesitate to ask below. If you have comments, recommendations or requests, then please ask.

Mists of Pandaria's New Loot Systems Analyzed.

Because Community is back on the air and we're talking about random things. I present a relatively random song. Seeing this fan video, one of Community's earliest, let Dan Harmon know that the show had "made it" to a certain degree.

I've talked before about how no voting system is perfect. It seems perhaps that no loot system is perfect either. Blizzard has announce that a new loot system will be used in Mists of Pandaria for LFR and the two world bosses where instead of rolling for specific pieces, the game will randomly pick people to get loot. If the game picks your player, it will pick an item appropriate for your class/spec. They haven't decided if every player has an X% chance to get loot or each the game will randomly choose X people to get loot.

Later in the thread, Zarhym went on to note that the X% chance to drop version of the system is flawed because the number of items a boss will drop will then become random, which could lead to abnormally high numbers of drops or even zero drops on a boss.

The game will roll for you, and it won't say what you rolled. You also don't have the option to pass. If you win loot it will be randomly picked from the items appropriate for your class. So you may get something you already have or something that isn't an upgrade. Furthermore, you won't be able to trade loot obtained by this system.

The advantage of this system is that it removes other people from affecting your chance at loot. Nobody can take your loot from you, it's all up to Lady Luck. With the current LFR loot system, some people roll on everything that they are eligible to roll for and then hold the item hostage to trade for something that they need. This is a dick move.

On the other hand, people can't pass on loot via this system, so loot can go to someone who doesn't need any when there are plenty of other people who might need it. People who might even need that specific piece. This does bring concern about loot waste and making it harder to gear. While that is a concern, keep in mind that only gear that is appropriate to people in the raid will drop. So gone will be the days when spell plate drops and you have no Holy paladin.

Another concern is that this will prevent you from obtaining off-spec pieces. I have a personal address to that concern. If you want off-spec gear, then run as your off-spec. My understanding of LFR is that it's quite easy. This loot system won't be used for normal or heroic raids. In a 25-man LFR raid, there will likely be a person for every type of gear that can drop, with the possible exception of spell plate. So if you're taking an off-spec piece, you're likely taking away from someone's main spec. If you're running a premade LFR or an LFR with a large number of friends, then you're likely to be organized enough that you can afford to run on your off-spec.

This new loot system will affect boss loot tables. In order for this system to work, it will require that all bosses in LFR will have to have at least one item that appeals to every specialization. Between armor, jewelry and weapons this shouldn't be hard. However, it is comforting to have that assurance.

Furthermore, there is talk of a system where out-of-raid actions can give you a charm that will allow you an extra roll for loot on any raid boss, regardless of difficulty. This roll also doesn't impact other players, but gives you an extra chance. Furthermore, if it fails to give you boss loot, it will give you something like gold or consumables. When the boss dies, a prompt will ask something along the lines of, "Would you like to use your charm?"

This system too, seems to bear the consequence that all bosses, even in the world of normal and heroic where loot is typically not shared across bosses, must have something that can appeal to everybody. The alternative is that the charm loot would have to come from some sort of shared loot table, which would make it not unique to the boss, which would somewhat defeat the point.

I was all ready to go into this post to tear down and examine the problems with these new loot systems. However, as I started writing it and reread some things to make sure I didn't misstate anything, I realized that not only did I like it (which I already did), but I think it's brilliant. I feel this is a great system and will be a fantastic upgrade to the preexisting LFR loot system.

I'd like to do an investigation into the loot distribution that happens with this new system and how much loot does get wasted in using this new system versus the old system. I'll have to run some simulations to get it done, but I think it will prove to be very interesting.

Night School: The Math of Drop Rates

Hopefully that chestpiece is in this pile somewhere...

Drop rates are where most people will encounter and be aware of randomness in World of Warcraft. The other places would be in crits and random procs, of course. There can also be quite a bit of misunderstanding about how they work. Everybody knows the basics, of course: when the boss dies, the game rolls some random numbers and finds those numbers in the loot table to see what the boss should drop. Different items have different drop rates, which come from that item occupying a larger or smaller section of the loot table, making it more or less likely to drop. Other things, like tier tokens and legendary weapon fragments are often rolled for on separate tables from the normal loot.

For the duration of this post, I talk about drop rates with the percents, but all the math with be done with the decimal. So, 10% is 0.10, 5% is 0.05, and 100% is 1. Percents (Latin for "per 100") are a great way to talk about these things, but you cannot do the actual math with them, one must convert them to decimals.

How long until this item will drop?
That's the big question, isn't it. When will my shield drop? Why can't I get a shoulder token? Where is that stupid phoenix mount? Let's just assume that you're the only person contending for a particular item, and that when it drops it will go to you. Will you indulge me by allowing me a table? Who am I kidding? I'm putting a table here whether you like it or not.

Minimum Kills for X% of people?
	Drop rate
% of players	50%	10%	1%
50%	2	7	69
10%	4	22	230
1%	7	44	459

An entry from this chart should read as, "With a drop rate of 10%, 50% of players will have to kill the boss 7 or more tries."

So how do you like those numbers? That mount that has a 1% drop rate? There's a ~50% chance it will take you 68 or fewer tries. There's also a 10% chance it will take you 230 or more tries. You might notice that the numbers for 1% of players is roughly double that for the 10% of players. This is because 1% is 10% of 10%. But where does all this come from?

Suppose the probability that an item will drop is p, and the probability that it won't drop would then be 1-p. If you want to know the probability that something will drop after you've killed the boss x times, that's actually difficult to directly calculate, because it could drop multiple times. When calculating probabilities, you'll very often run into situations where the thing you want to know is hard to calculate directly, but the opposite of it (in this case, the probability that the item won't drop in x kills) is very easy to calculate. In that case you calculate the probability that it won't happen and then subtract the result from 1.

In our question, calculating the probability that something won't drop is easy. You simply take the probability that it won't drop from a single kill, 1-p, and raise it to the power of the number of kills, x. You multiply because these are independent events, meaning that the outcome of one event (a kill) does not affect the outcome of the other events. This makes the probability that the item won't drop is*

and the probability that it will drop at least once is

One thing that could be noticed from playing around with that equation is that, for any positive value of x,  unless p=0 or 1, the formula will never equal 0 or 1. In other words, the only times when there is absolute certainty is when the drop isn't random, or you haven't killed the boss yet. Here is a chart that depicts the probability that an item will have dropped based on how many kills have been attempted. Here, the probability of a drop is 10%.

Wolfram Alpha is a great source for doing math.** 

You'll notice that even at the number of kills get's very large, the probability that the item will have dropped never actually hits 1. So no matter how many times you kill, there's no guarantee that the item will drop.

There is an article written by Brian Wood on WoWInsider that contains a wonderful calculator for drop rate percentages such as this. I highly recommend that you check it out here.

Corollary: Average Number of Drops
Of course, the previous section is based on an assumption that you'll only want one of an item, and that it will only drop from one boss/monster. Say you are farming something that has a <100% chance of dropping from whatever you're killing. Let's say it's Relics of Ulduar. It has an 11% percent chance of dropping off of Mildred the Cruel If you want to know the average number that you should expect to get after so many kills, you just multiply the probability of it dropping by the number of kills. If you were to kill Mildred 26 times, then you should expect to have an average of .11*26=2.86 Relics of Ulduar.

The mousover text for those equations contains the LaTeX code used to produce them at the Online LaTeX Equation Editor. Note: "\left(" and "\right)" weren't actually necessary for those, I could have just used "(" and ")" but it's considered a best practice to use the longer ones because they scale in size with their contents. Consider the example below:

**I used Wolfram Alpha to produce the graph up above. It's an amazing thing. Like if Google could do your homework. It can factor polynomials, give population statistics, and even do calculus. I used the free trial of the pro service to get the graph above. The whole thing blows my damn mind.