Vault Hunting 101: A Guide to RNG and LOOT!

110 Runs:
Sledge’s Shotgun - 5 (4.5%)
Pyrophobia - 3 (2.7%)
Shredifier - 2 (1.8%)
WTF - 1 (0.9%)
Hornet - 1 (0.9%)
Norfleet - 1 (0.9%)
Kiss of Death - 1 (0.9%)

OVERALL - 14 (12.7%)

No out of pool Seraphs.

Now that’s a good percentage. 12% is close to the supposedly 10%.

Actually looking at the numbers, if you take BlackHeartV’s assertion that Pyrophobia is in a different pool, then the percentage is EXACTLY 10%.

I’ll probably muddle through another 90 runs this next week/weekend. We’ll see if I get any clearer numbers.

I think I remember idly noticing a slight variation in the NUMBER of drops from Hyperius. If I had documented it, and it coincided with any of the drops (like Pyrophobia) it would greatly suggest another pool.

I will try to document this better for the next 90.

???

The only thing I know that’s been patched in WEP is the ability to spawn reliably outside the CSD once you’ve completed a sufficient portion of the main story, which was added in because it wasn’t working properly. If there was some actual exploit, I haven’t heard of it.

Ditto, this makes me curious.

Though I bet it is just the Animal Rights & Drs Orders combo.

It is a tad game breaking.

Do you think guaranteed legendaries are too good to be true for every LLM? It is. Considering the high spawn rate thanks to Doctor’ Order quest (and the high difficulty mob in Sawtooth Cauldron).

Well, that was what it was like just after UVHM patch dropped. I played all day long and get almost 4 legendaries in each run.

I believe they were not aware (or simply didn’t account) about the “glitch” (or maybe it was intended challenge) where 4 LLMs spawn when Doctor’s Order mission is active. Think about it. Outside this quest, there is no absolutely any other guaranteed spawn of these supposedly rare enemies.

Many ignore about how LLMs were nerfed, because it’s not mentioned in any patch notes. But for me who experienced it, it’s not a laughing joke. The laughing joke is how the devs overlooked this ONE quest (and maybe one area) where these supposedly rare enemies always (or almost always) spawn.

Ah, now I remember. I hadn’t even reached level 50 when UVHM dropped, and I missed all the fun on that. Was that even on all platforms? It was a loooong time ago!

I was on 360. I’m sure it was universal platform.

I believe they were about to make LLMs as glorious as Tubbies in terms of loot. But LLMs can be exploited and Tubbies cannot (and thus, every Tubby always dropped something in their pool, compared to LLMs which sometimes only drop ammo and money even in the highest difficulty).

That makes sense. There probably wasn’t an easy way to distinguish between LLMs in the box room with Doctor’s Orders open and all other LLMs. Well, there would have been, but it probably wasn’t worth the time and effort to alter, test, and certify the code for just that one thing.

I think they were originally trying to introduce the Loot Midgets with that quest, considering the spawn rate is so low, some players might never encounter them before, and also as a challenge when doing that quest, as they are tough (I know someone who opened the 4 boxes in a rapid succession just for the OCD inside, it was me, and I got roasted by them). However they overlooked this when making them into Legendary Loot Midgets.

When I get the chance, Ill do Hyperious farming on ps3 with sal snd post my finfings too. Takes a minute per for cooldown, so not a big deal to get 20 to 30 in before I have to save.

Yeah I should be able to help to.
Are we looking for uvhm, op8, or does the mode matter?

I’ve been doing OP8 on XBox 360.

Ill do OP8 as well. Hopefully by this weekend.

I have 110 runs so far. My wife works late tonight, so I can probably get in a good amount more.

I have been tracking a few things (not that you have to track them also) I have been tracking what prefix and what element all the weapons drop with. Obviously Evolution has neither of these and tattler is always Bladed (although I would swear to a grand jury that long ago I once saw a non-bladed tattler drop).

Did 20 more runs today.
Hornet
KoD
One double Seraph drop.

20 more runs again
KoD
Double Seraph drop

Hey there. I’m a bit new on the forums but I wanted to ask this in regards to your guesstimate of a barrel 2 redundant shock fibber. The only way I can get your 0.074% is 33 x (0.25/7) x (0.25/4) but doesn’t 33% mean 33/100? If I was to make that calculation on my own I would put in 1/3 chance for the barrel and keep the rest. That brings the chance of getting the perfect fibber (not counting grip ofc) much lower.

I was simply wondering if you would care to explain the math behind it to a slowpoke like me? :wink:

Oh and what do you mean by bringing guesstimate up to 25%?

I cheated a little: the math uses probabilities (so 33/100 or 0.33) but I wanted to express the final result as a percentage rather than a pure decimal. 0.074% would be p = 0.00074, or less than 1 in a thousand.

It’s an estimate of how many farming runs you’d need to do to give you a 25% chance of the desired combination of barrel, element, and accessory. I’ll re-word that bit.

Vault Hunting 101: A Guide to RNG and LOOT! (Part 2)

Welcome back to our ramble through the whimsical - and occasionally capricious - world of the Borderlands loot system. As was the case for part 1 this guide is not wholly original, but will attempt to cover the key points in a clear and mostly non-mathematical manner for the math-averse. It draws heavily from previous articles, primarily:

In this section, we’ll take a look at the loot system mostly as it relates to farmable bosses within the game. If you don’t know much about the game’s loot system, random number generators, and loot tables, you might want to take a look through part 1 first. Here’s an outline of what’s ahead:

Outline:


Enemy Types and Definitions

Just as there are different rarities of loot in the game, so there are different categories of enemies. More advanced enemies occur less frequently within a given play-through (eg. NVHM or TVHM) but will have more health, deal more damage, and drop better quality loot. Paul Hellquist lists these categories as:

  • Chumps
  • Badasses
  • Super Badasses
  • Ultimate Badasses
  • Chubbies (Tubbies in UVHM part 2)
  • Raid Bosses

Within the game, certain side missions involve named enemies (“Named Bosses”, or mini-bosses). Some examples from the main game include Boll, Henry, and Hunter Hellquist. There are a few others that spawn repeatedly in specific locations even though they don’t have an associated side quest, such as Savage Lee and King Mong. These have a chance to drop a small number of items, including a specific designated drop: an item, such as a weapon, that is of rare unique (ie. red text), very rare, or legendary rarity.

There are also “Plot Bosses”, being those encountered at specific parts in the story, which can be either badass, super badass or raid category enemies. Some of these must be defeated in order to advance the story (eg. Knuckledragger and Captain Flynt), some may only spawn during the story mission (eg. W4R-D3N aka “Warden”), and some don’t Need to be defeated but make like difficult if you don’t deal with them (eg. Mortar and Saturn). Paul Hellquist states that the only named raid bosses in the vanilla game are BNK-3R (aka Bunker), the Warrior, and Terramorphous.

These bosses are progressively more challenging, and drop more loot, as their enemy category increases. Side mission bosses are usually in the Badass category, while story bosses are usually in either the Super Badass or Raid categories. In addition to their larger loot pools, respawning bosses also have their own designated drops, and it is these that are the target of end-game farming.

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Respawning Bosses and their Loot Drops

As covered in part 1, when any enemy is killed the game uses that enemy’s assigned item list and associated loot pools in order to determine what will drop. If the assigned item list contains eight entries, for example, you will get chances of up to eight items. Some of the lists include:

  • Guns and gear
  • Vehicle skins
  • Money (1 or 2 bundles)
  • Eridium (single bar)
  • Eridium (cluster of four bars)
  • Health
  • Ammo

The item pool associated with each list breaks some of these down further, and establishes the statistical weighting that defines the probability of getting, say, a gun or a grenade mod. A further iteration defines the item rarity as one of: common, uncommon, rare, very rare or legendary. Additional iterations determine the specifics of the item.

Boss item lists can also include pools that are restricted to a certain category or rarity of item. That is to say, a specific boss may have a chance to drop a rare or very rare item from the guns and gear pool in addition to a chance to drop an item from the guns and gear pool of any rarity.

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Example 1: Henry

It’s a little easier to see how this works with an actual example so let’s farm Henry, a stalker that has an increased chance to drop the legendary shield, the Cradle as well as a very rare head for each character. For ease of acquiring data, we’ll farm Henry using a level 72 character in TVHM. The following data show the results for successive single-player runs, ignoring ammo, cash, and health drops (since auto-pickup of these items makes counting them tricky):

image

In these runs, Henry dropped between one and four items (other than ammo, cash, and health) each run. This included a total of four of Henry’s designated drop (the Cradle), one of the unique heads, and a collection of white, green, and blue rarity items including guns, grenade mods, class mods, and relics.

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Example 2: Bunker

As mentioned above, BNK-3R counts as a raid boss. Paul Hellquist’s article includes a screen shot of the raid boss item list, so we have a very good idea of what to expect. Of particular interest is that some of the pools in the raid boss item list actually have the chance to drop more than one item. Some of these special raid boss pools are fixed at two items rather than the usual one; others will drop 1 more item than there are players in the game. So, although the following list shows only nine guns and gear item pools, you can get more drops than that:

image

Here’s some stats from a set of TVHM solo runs, during which the notoriously stingy Bunker refused to drop either a legendary of any kind or one of his unique character heads:

image
Note: some of the counts may be out slightly because of confusion between white gear and excess ammo drops.

As you can see, there were on average 26 items (~22 guns and gear and 4 eridium) dropped per run. The greatest variation in numbers was in the common and uncommon categories, while on average I got two each of rare and very rare guns, shields, grenades, etc.

So how did I do relative to the best I could have expected? Looking at the first two pools in the item list above you can see that we are guaranteed 1 drop each from the rare and very rare categories, along with an additional chance for a second of each rarity based on the number of players. Paul’s article lists these probabilities:

  GearDrops_PerPlayer:
    Players    Probability
        1           5%
        2          10%
        3          15%
        4          20%

We also get a guaranteed drop from the GunsAndGear_02_UncommonsRaid pool, which Paul states guarantees two uncommon items. There are two more chances of 5% each for uncommon items, a 5% chance of an item from the general guns and gear pool (which includes all rarities as described in part 1), and two guaranteed drops from the same pool via the GunsAndGearDropNumPlayersPlusOne pool.

Adding all that up, and assuming that we rolled successfully on the GearDrops_PerPlayer items every time, we get a maximum of 11 items, including at least 2 very rare, 2 rare, and 4 uncommon items. If you’ve been paying attention, you’ll realise that this doesn’t add up since I got way more uncommon and common items than this would imply.

There are two possible answers: either the item list and pools were heavily modified since Paul’s article was written, or Bunker gives you more than one crack at the Raid Boss item list. The latter actually makes sense, since Paul’s article goes on to tell us that Terramorphous gives you four cracks at the same list (and therefore much more loot!) I’ll return to this question later.

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Bosses and Designated Drops

A feature of Borderlands is the idea of runnable bosses - ones that you can re-fight at any time. With one notable exception, all the bosses in Borderlands 2 are runnable. (Many players call them “farmable”, but runnable is Paul Hellquist’s term and he designed the loot system so…) In this section we’ll talk about what this means, and how it plays out within the context of the games RNG system. First though, a little Borderlands history (you can skip this if you’ve not stopped playing since 2012 :dukecheese:)

To make running bosses more rewarding, Paul Hellquist took all the game’s legendary items and distributed them among the various bosses. To prevent this from becoming stale too quickly, however, he set a legendary drop rate so that there was only a certain chance of a boss dropping their designated drop each time they were defeated. Borderlands 2 launched in September 2012 and players immediately started reporting the legendary items they’d occasionally get from each boss. Subsequently, a large co-operative effort was launched in the spring of 2013 both to identify all these items and determine their drop rate. These findings were confirmed in Paul Hellquist’s second article as being 1 in 30, or a probability of 3.3%. Borderlands: The Pre-Sequel followed in October 2014, and was widely perceived as having “better” drop rates overall (even though there was a distinct lack of runnabe bosses at first.)

Finally, in April 2015, Gearbox Brand Manager @JeffyBug made the surprise announcement that they were going to experiment with different drop rates in both games on all platforms. A final decision was made to increase the drop rate by a factor of 3, and this was made permanent in a massive patch that fixed many other issues in October 2015.

OK, enough with the history - on to the serious stuff.

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Honey, Where’s My Super Loot?! - Key Questions

So each boss has at least one designated drop, which as discussed previously has a 1 in 10 chance of dropping whenever you defeat them. This is in addition to the loot pool associated with that boss (Badass, Super Badass, or Raid), along with anything else the character designer might have decided to add. Some questions we might want to ask are:

  • Can a boss have more than one designated drop?
  • If so, how does that affect the drop rate and my chances of special loot?
  • How does that work with the item list and loot pools?
  • Can you legitimately get double legendary drops?
  • How can we tell if a particular boss drop is bugged?
  • If I got a boss’ designated drop, is it worth running again?
  • What is your quest, and what is your favourite loot rarity colour?

OK, so we might not have the answer to all those questions…

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I Need My Super Loot! - Getting Multiple Drops

Yes, a runnable boss can have more than one designated drop, but this works out differently for different bosses. Some, like Savage Lee only have a single designated legendary drop that comes in addition to whatever is in the Badass item list and its associated loot pools. Others, like Henry the Stalker have both a designated legendary drop and a designated very rare set of unique heads in addition to the Badass item list. BNK-3R has two designated legendary drops and a designated very rare set of unique heads, and so on.

In every case, the chance of a designated item drop is still 1 in 10 in every mode, but not necessarily 1 in 10 for each designated drop assigned to that specific boss. As an example, Terramorphous has multiple designated drops, but these are all equally weighted within the 1 in 10 designated drop pool.

Some bosses, however, do have separate loot pools for assigned items, and so can yield double designated drops. A good example is the four Assassins that appear in Southpaw Steam & Power for the side mission Assassinate the Assassins. (They also make an appearance in Digistruct Peak).

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Example 3: The Four Assassins

Any one of the four assassins have a chance to drop the legendary SMG, the Emperor and one of six unique character skins in addition to the standard Badass items. However, each one also has a chance to drop a specific rare unique weapon:

Running the Assassins can be tricky because loot can drop either back into their spawn areas, over an edge, or down through several areas of the floor, making it impossible to reach. With that caveat in mind, here’s some data obtained by running just the first two assassins solo in TVHM with a level 72 siren:

image

Over a total of 70 trials, I found:

  • 6 Emperors
  • 5 character skins
  • 25 Commerces (!) and
  • 18 Judges

In addition, four of the Emperor drops occured simultaneously with either a Commerce or a Judge, but no run included both an Emperor and a skin. This suggests that item list for each assassin looks something like this:

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My Loot Is In Danger! - A Rare Chance for More Drops

Even if a Raid Boss can only drop one item from its designated drop, there is still a slight possibility of obtaining two legendary items at the same time. This is because the Raid Boss item list includes a chance for an item from the world drop guns and gear pool.

As we saw in part 1 from the first Inisde-the-Box article, this includes a low chance of a legendary (at odds of 1 in 10000 or 0.009% in the original game). So if you do get a double drop, be sure to (1) grab a screen shot and (2) celebrate! Mostly, though, this world drop pool is more likely to add a common, uncommon, or rare item to the lootsplosion.

The effects of this are easily seen by farming Bunker. You’ll note that, when the flying Scrooge is defeated, there are at least three distinct drop zones: two arcs of loot fly out across the main terrace, each angled to either side of the stairs to the waterfall; and an additional pile of loot builds up under the Big Gun on Bunker’s underside. (Designated drops, if they are found, tend to appear right in the middle between the two loot ‘arcs’.)

If you refer back up to the earlier discussion about Bunker you’ll note I suggested we got two cracks at the Raid Boss loot pool. Over multiple runs I did indeed get, on average, 1 rare and 1 very rare item in each arc, but sometimes I’d get two. Likewise, the pool of loot under the gun was usually a mix of common and uncommon items, but occasionally there’d be more uncommon than common items, and even an extra rare item. This is the extra chances at the world drop loot pool in action.

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Why Do You Need To Know?! - Inferring Drop Rates From Farming Data

Although it’s not as common as it used to be, there’s still a post about once a month asking if a boss got nerfed or is glitched, because they’re not dropping what they’re supposed to. It’s certainly true that, when the game launched, some of the boss drops were a tad unreliable: the Warrior would lie on top of loot or drop it in the lave; Bunker had a tendancy to fly off spewing loot over the bottomless chasm, and Boll simply didn’t drop his item at all. The good folks at Gearbox worked on all this and, by the time of the last update all these issues were fixed. (There are some remaining issues; you can read this thread if you’re interested.) All that to say, unless you’re playing on a system which has never been updated, a run of bad luck is almost certainly not a result of a programing bug or “silent nerf”.

But on the very remote chance that there might still be some subtle bug in the code somewhere affecting the one boss you’re trying to farm, what would it take to determine if the drop rate was not what it should be? This is where we get into inferential statistics, and a very good place to read up on it is this post. I’m not going to rehash the whole thing, but I’ll pick up on one particular concept of relevance: confidence intervals. A confidence interval is an estimate of the range either side of an experimental observation that you would expect further observations to lie in (allowing for some degree of error.) They are often represented as the range within which you would expect the actual (technically “population”) value to lie simply because multiple observations should cluster around this value.

So, if you run a particular Raid Boss 10, 20, or 30 times, and get their designated drop 0, 1, or 5 times, can you conclude anything about your observed (“inferred”) drop rate? Let’s return to Henry, simply because I just finished my 100th run on him. Here’s the final tally for 100 runs:

image

You’ll notice that the highest observed drop rates are for rare and uncommon items from the Guns and Gear category, along with single sticks of eridium. These were most likely to occur as a single drop of each rarity, although double drops did occasionally happen. (Ammo and cash dropped pretty much every time, but I didn’t count these.) Both the designated legendary and head dropped infrequently, and never as a double drop, while both common items and eridium stacks dropped at a similar rate.

So how about those designated item drop rates - are they bugged or reasonable? To answer this we need to do some math, and I promised to keep the math to a minimum. If you really need to know how to calculate the confidence interval for such values, you can consult either HeyCarNut’s original post or this Wikipedia article. The following table shows the range either side of the observed number of drops per hundred runs that the true drop rate could lie within, at the 95% confidence level (ie an error rate of 5%). These come (upper rows) from HeyCarNut’s handy table, or have been calculated using the less accurate normal approximation (lower rows), because I’m lazy:

So what can we conclude from this? Not a lot, to be honest. The observed drop rates for the designated legendary and character heads are both consistent with an actual drop rate of 1 in 10, but also consistent with rates that are both lower and higher. In fact, we can’t even be sure from this sample (which is large in gaming terms but small statistically speaking) whether the rate is for either item or for both simulataneously. In fact, the only reason I’ve claimed that it is a 1 in 10 chance of either legendary OR head is by comparison to the available information on Terramorphous. One thing we can do, however, is indulge in a little speculation regarding Henry’s loot pool.

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Reconstructing Loot Pools

We’ve already noted that Paul Hellquist gave us an inside look at the Raid Boss loot definition list, and that Terramorphous gives us four rounds of this in addition to his designated drop list. What Paul didn’t give us is the same information for the other raid bosses; neither did he give us any information about the Badass and Super Badass loot lists, or identify which runnable bosses were in which category. We can, however, make some educated guesses based on the published information and a sufficiently large number of runs on each boss. So let’s have at it!

Example 4: Henry Redux - Super Badass Bosses

Here’s the cumulative totals from multiple farming runs - note that I stopped counting some of the items after a certain number of runs (indicated as the ‘Trials’ row at the bottom of the table):

Drops/Run Cradle Head Purple Blue Green White Eridium Eridium4 Cash
3 0 0 0 0 0 0 0 0 16
2 0 0 0 3 6 0 18 0 12
1 11 13 1 110 109 13 75 11 22
0 189 187 144 37 35 137 57 139 0
Trials 200 200 150 150 150 150 150 150 50

Henry is a Super Badass runnable boss. Looking at the data above, we see that besides one shot at the designated drop pool, we probably have at least 1 chance each for a rare and uncommon item, 2 chances for a single eridium, 1 for an eridium stack, 2 chances for 1 or 2 cash bundles, and at least 1 chance at the world drop loot pool (single player). I get similar results from other Super Badass runnable bosses such as Saturn and King Mong, or regular Super Badass tier enemies such as the pscyho that spawns alongside the first of the assassins in Southpaw Steam & Power.

Example 5: Lee and Boll and Rats, Oh My! - Badass Bosses

Like the assassins, these three (well, seven technically) are all Badass tier runnable bosses. Apart from their designated drop pools, therefore, we’d expect them to show similar results for other items. For 50 runs each of Boll and Lee, and 20 runs of all four Rats (equivalent to 80 runs at one Rat), aside from the designated designated drop the most common items are ammo, 1 or 2 cash bundles, and a common or uncommon item. One time out of the total of 180 trials, I got a very rare item. Oh, and the odd health vial. This suggests that the Badass is slightly better than the Chump one, but not by much (although you could well get better results with 4 players.)


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