## Some remarks on drop rates

I'm going to keep this relatively short, because a full discussion of probability could fill several college semesters. However, there is one misconception that some

Let's say you read that Shattered Sun Supplies have a 10% chance to contain a Badge of Justice, and, excited, you go out and do enough dailies get 10 Shattered Sun Supplies. You open them all and find not a single Badge, or you find five badges. Do either of these outcomes mean the 10% drop rate is wrong? No! They do not! All a 10% drop rate means is that for each Supplies, there is a 10% chance that it contains a Badge. Random events have no memory, so no matter how many badges you get in the first nine Supplies, your chance to get a Badge in the tenth Supplies is still 10%. The traditional analogy is that if you flip a coin nine times and get heads each time, the chance of getting heads on the next flip is still 50%.

Now it is true that you will

TL;DR version: A drop rate is a probability, not a guarantee.

*WoW*players have that has been bugging me lately.Let's say you read that Shattered Sun Supplies have a 10% chance to contain a Badge of Justice, and, excited, you go out and do enough dailies get 10 Shattered Sun Supplies. You open them all and find not a single Badge, or you find five badges. Do either of these outcomes mean the 10% drop rate is wrong? No! They do not! All a 10% drop rate means is that for each Supplies, there is a 10% chance that it contains a Badge. Random events have no memory, so no matter how many badges you get in the first nine Supplies, your chance to get a Badge in the tenth Supplies is still 10%. The traditional analogy is that if you flip a coin nine times and get heads each time, the chance of getting heads on the next flip is still 50%.

Now it is true that you will

*probably*get a Badge in ten Supplies if the drop rate is 10%. If you're interested in how likely it is, here's the calculation to do. The chance of*not*getting a Badge in one Supplies is (100% - 10%) = 90%, or 0.9. Raise that to the tenth power, for your ten independent Supplies-opening events, and you get the chance of, ten times out of ten, not getting a Badge: 0.9^10 = 0.349, about 35%. So in fact, out of ten Supplies, you will get a badge (100% - 35%) = 65% of the time, about two thirds.TL;DR version: A drop rate is a probability, not a guarantee.

Filed under: Analysis / Opinion

## Reader Comments (Page 2 of 3)

## Tekkub Apr 29th 2008 6:54PM

I love the people in my guild that cry about a "bad batch" of prospecting... I just burn thru whatever I'm crushing and feel happy in the knowledge that, over the long run, I get raw blue gems.

People spend too much time looking at the small picture when it comes to droprates.

## Nizari Apr 29th 2008 6:55PM

Now can you explain to them that when you sell in bulk you discount the price per item versus when you sell individually?

## schwonga Apr 29th 2008 8:38PM

That is only the case b/c of how RL handles advertising and incentives to the public. Really there is no real economic reason to put bulk items cheaper as the individual items besides beating out that buyer nervousness and getting them to buy your bulk.

All about incentives, and many times you can corner the market (or take advantage of a strangely empty one) and place prices as you see fit.

## Dave Apr 30th 2008 10:38AM

Discount? What's the point of that?

I don't know about you, but I personally jack the price of things in bulk rather than individually. People will pay it!

I can sell 1 Large Prismatic Shard for 25.99. That's not bad, but someone's going to under cut me and it's going to waste my time and I might not even sell that single shard.

However, I can take a stack of 6 large Prismatic Shards, perfect for someone who wants to buy a ready-to-go stack to enchant their fancy new weapon with +dmg or whatever and list that stack of 6 for 169.99. I jacked the price of each shard by 2g or so. I guarantee that stack will sell QUICKER than the individual shards!

My only assumption at this point is that people in WoW are terrible at math and just don't care how much things cost if they can get it with one click rather than 12.

The AH is not Costco. You shouldn't expect to get a discount on anything at all, especially when people aren't given a "price per unit" sort of measurement on their screen without some help.

## jdkenada Apr 29th 2008 6:55PM

Right now my Grade 10 teacher is screaming out "I told you that you would use this someday!!!"

## Simon Jia Apr 29th 2008 7:24PM

this is basic statistics. But statistically speaking, if you open enough bags, the overall drop rate will be close to 10% with a smaller and smaller error margin. Of course the sample size will be in the 100,000 ranges in order to even see it gets close to 10%.

## JRM Apr 30th 2008 4:03PM

you could, assuming the drop rate is purely random, get an accurate approximation of the drop rate with a sample size of a few hundred (probably less). It is a common misconception that large sample sizes are necessary to obtain accurate results.

## Biff Apr 29th 2008 7:24PM

I can attest to this. I've done the fishing daily quest every day since it became available (spent hours getting my Fishing to 375 just for the cool rewards available from the quest). I've gotten countless fishhooks, about 10 water walk potions, and two Monocles. The only reason I do the fishing daily now is to reassure myself that God hates me.

## Verit Apr 29th 2008 7:24PM

Anytime people complain about drop rates on bosses in WoW - I seriously encourage them to try out another MMO like Lineage 2 or EQ. In L2 there's a % that nothing will drop off a raid boss at all... In EQ you might go about getting to the boss to find out he's already engaged or camped - and even then he/she might not drop what you want.

## xnyhps Apr 29th 2008 8:03PM

Interesting post, but what I wonder is: are droprates 'real' mathematical probabilities? Isn't there for example some sort of fairness-system that makes sure quest items drop before, say, 1,000 kills? I do think this is the case, because otherwise people might get fed up with the game quickly and quit - not in Blizzard's advantage at all.

So, did Blizzard ever confirm anything about this, I wonder?

## Malreth Apr 29th 2008 9:45PM

#25 and #26:

No. To do so, Blizzard would have to keep a record (a state) of the number of Supplies bags opened since your last badge in the character database since if it were kept client-side, you could hack it and give yourself guaranteed drops. Furthermore, they'd have to also keep a state for any given drop on any given mob on any given quest.

Now multiply that by all your quests.

And again by all your alts.

And again by, what... 10 million players?

That's a lot of state to hold at any given time and it's not worth it. If Blizzard really did want to make a certain "collect N drops" quest faster (or slower) to make it seem "more fair", it's much easier to just tweak the drop-rate by a percent or two.

## Malreth Apr 29th 2008 9:46PM

hmm... adding a reply changes the message numbers... oh well. :p

## Dave Apr 30th 2008 11:18AM

Blizzard has said that random is random, except in certain cases where it isn't.

ie: mob drop tables are generated on spawn, not on kill. Therefore if the last person to have killed a mob was NOT on the quest that you're killing them for, they will not respawn with a chance to drop the item you need. Despite what WoWhead shows you as a flat list of drops with percentages, that's not how it works necessarily.

Mobs have multiple loot tables that are independent rolls. For instance, typical random mobs loot tables:

Money Roll

Cloth Roll

Loot roll

Quest item roll.

each of these separate rolls on creation can have different probabilities but in most cases are not tied to each other in any way. Some of them have built-in defaults as to prevent a zero result for whatever reason, some of them don't. (some mobs will come with a piece of something every time... some are frustrating and have a %10 drop rate, etc). They don't even have to be consistent in any way with other mobs, such as the elves that drop rep turnins. You can totally get a loot drop from dead elf AND a scryer signet/arcane tome from the same mob at the same time. You probably won't see it very often because of the probability involved but you know they're on separate loot rolls.

Boss loot however isn't necessarily the same but follows the same logic of unpredictability. A boss may end up with a money roll (usually a near-fixed value), two completely separate loot rolls (ie: token drops are independent from the other drops, and further that on Illidan the warglaives are a totally separate roll and drop, etc) and maybe any other rolls that can happen.

Long story short, random loot is random. But it's not necessarily as simple as a % chance based on overall kills even though it can be represented that way.

## TonyMcS Apr 29th 2008 8:45PM

I think that you need a cap to the number of attempts, otherwise you need a very large number of attempts for the 10% or whatever to appear. If you do it for infinity then you should be sure of 10%, but for this to occur in 40 or 50 tries seems a bit non-random. I think Blizzard is checking to see how many are dropped over a number of attempts and smoothing it out by providing extra drops if you don't get it in a reasonable number of attempts.

## Brad Apr 30th 2008 12:07AM

I would hope Blizzard doesn't add drops to atone for low drop rates, no matter how unusually low it may be.

First off, the Law of Large Numbers (http://en.wikipedia.org/wiki/Law_of_large_numbers) guarantees that, over time, random variables (such as the 10% drop rate of the Badge) will maintain a stable percentage at or very, very near the expected probability.

Secondly, you know they wouldn't "remove" any Badges if the drop rate suddenly spikes to an unusually high level, so why should they arbitrarily add Badges if the drop rate goes low for a period of time?

This is, of course, assuming a valid random number generator. Seeing as how we pretty much trust the /roll function, there's no reason to think that Blizzard adjusts things when we don't see the random number displayed in the chat log.

## Taara Apr 30th 2008 4:01AM

Since 2.4 I've been doing those Supply Bag quests. I heard from guildies they have got like 7 badges from 30 bags and so on. I've opened about 80 bags. Every time I hoped to get that extra badge and so far and all I've got is 2 badges.I stopped counting on extra badges from the bags. They are so rare drop for me that I mostly don't even do the quests in shat anymore unless I really have nothing better to do. Doing that huge circle to finish all 4 of them is only clogging my bags with useless lvl 68 greens. I rather hit 8 dailys on QQ island, make 100g in about 30 minutes by doing so and run heroic daily for guaranteed 5 badges or more (depends on the boss count).

My personal badge drop rating from bags is around 2,5%. Not enjoying that.

## Mowgile Apr 30th 2008 4:47AM

@#4: You are nearly correct. If you open 30 Shattered Sun Supplies you have a ~96% chance of getting *at least one* badge.

On the one hand, humans are very good at seeing a pattern where there is none (I didn't get any badges this week at all! The drop rate is messed up! Idol of the Avian Heart has dropped 5 times in a row from Moroes! The drop rate is messed up!). This simply isn't accurate. As the article suggests, a drop rate is a probability, not a certainty. The probability of getting a perfect distribution of loot (say, one each of Herod's Shoulder, Raging Zerker's Helm, Scarlet Leggings, and Ravager) in four runs of Armory is actually quite small - about the same as the probability of getting all four drops the same. Yet when the loot distribution isn't perfect, we notice.

On the other hand, anecdotal evidence with some drops - the ones I've noticed are the Crusader pattern, Various BoP recipes, and any rare 1x quest drop, especially the Creeper Ichor for the Elixir of Suffering quest - suggests that the loot *isn't* normally distributed - i.e. the game isn't rolling a "dice" when a mob dies with a X% chance of it dropping the item. Typically the variance is unusually skewed - you'll either get the Crusader pattern on your first kill, or you'll spend a *long* time grinding for it. That suggests to me that rare drops are spawned randomly based on real time (like mobs, gathering nodes, etc).

It might be that one could predict the drops of, say, the Crusader pattern in the same way that one used to be able to predict the spawns of Kazzak in Blasted Lands.

Of course, you'd need an overwhelming quantity of statistical evidence for that to be anything but conjecture.

## dacamper Apr 30th 2008 6:35AM

I've started to see patterns where there are none on the Attumen loot table, after killing him each week for 3 months the Worgen Claw Necklace finally dropped the one night we entered the instance 30 minutes early. Coincidence? Well of course it was, but through those 3 months I had to try hard not to imagine someone or something hated me.

Perhaps seeing patterns in random occurances is the root of superstition? Has anyone developed any WoW superstitions to ensure "that loot item drops", like always take 40 manna biscuits, always enter the instance at the same time, etc?

## zappo Apr 30th 2008 9:33AM

"On the one hand, humans are very good at seeing a pattern where there is none"

This is exactly what makes 50% of the comments on Thottbot useless.

That being said I've done the daily quests since around 2 days after 2.4 came out. I have never received a badge.

## Brommon Apr 30th 2008 4:02PM

Yes, DaCamper - actually WoW players (and MMO players in general) have come up with a wide array of absurd superstitions. The Deadalus Project actually did a study of these a while back. It's a hilarious read, to see what people will sometimes insist makes their loot drop better:

http://www.nickyee.com/daedalus/archives/001554.php?page=1

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