Strategy 009: Generalized Quarry Theory
—Written by Zirk
Note: All quarry testing was done with standard Hako match settings. The settings can be viewed at the start of almost every video. I would like to mention that if you ever do your own quarry testing, try to record it and record the entire match from start to finish, as I have done. It’s possible that we may want to look into other factors like the number of kills a player has, which team got the first kill of the match, etc. So, by including this in your videos, we can use old videos to add to the data pool.
There is a lot of speculation here, so if you have unanswered questions/comments, note them down as you read, and if they remain unanswered by the end, post them in the comments for discussion.
I. The only requirements for x-hyper are as follows:
(1) Being in possession of a Petra Shovel
(2) Having the standard number of deaths (1 for Hako, 3 for OM)
(3) Your 2-hour is not up.
The above videos show SAM/WAR, MNK/WAR, and WAR/SAM achieving very high Revitalizer rates (previously known as x-hyper) by only using their 2-hours. All other abilities remain ready for use. In the first video, Zirkk and Thrunceii each quarry 6 revitalizers in about 11 minutes. In the second video, Zirkk quarries 7 Revitalizers in about 9.5 minutes, and Thrunceii quarries 5 Revitalizers in about 11 minutes. In the third video, Zehw quarries 8 Revitalizers in about 13 minutes, whereas Zirkk is also trying to quarry a Revitalizer by burning all abilities except his 2-hour. While Zirkk didn’t achieve it in this video, both Zirkk and Thrunceii do in video 4.
V previously had a theory that the chance of quarrying a Revitalizer, once you had achieved hyper status, was directly proportional to the sum of the total number of remaining cooldown seconds of each job ability divided by the sum of the number of total cooldown seconds of each job ability. This theory is basically impossible to explain with mere words so here is an example.
MNK/WAR at level 60 has the following abilities with their respective recast times:
Hundred Fists – 120:00
Berserk – 5:00
Defender – 3:00
Provoke – 0:30
Focus – 5:00
Dodge – 5:00
Chakra – 5:00
Boost – 0:15
Counterstance – 5:00
Chi Blast – 3:00
Total – 151:45
I’ll round that to 152 cause fuck you it’s my blog post.
Now suppose that MNK had all its abilities up, then used Hundred Fists, Berserk, Defender, Focus, Dodge, and Counterstance all simultaneously. That equals 143 minutes of added up cooldowns.
143/152 = 94%, so V’s theory would say you are at 94% Revitalizer quarry power (100% doesn’t mean you automatically get a revitalizer on your next quarry, as these percentages are an arbitrary relative scale). 80% has approximately double the chance of getting a Revitalizer on their next quarry than 40%, or something along those lines. The take-home message is that the more abilities you have on cooldown, the better your chances of getting a Revitalizer.
Now, it’s quite obvious that the 2-hour dominates the calculation. If the same MNK used only Hundred Fists, he would still be at 120/152 = 79%, so videos 1 and 2 don’t disprove V’s theory yet.
Furthermore, V’s theory suggests it should still be possible to quarry Revitalizers at a much lower rate when the 2-hour is still up while other job abilities are expended. Videos 3 and 4 support this, so V’s theory could still be valid.
II. There is no such thing as x-hyper, x-hyper and hyper are the same thing.
To quote V from Strategy 007: X-Hyper:
“The difference between the ‘regular hyper’ and the ‘extreme hyper’ is that in order to achieve the latter, job abilities must immediately be expended after the use of a Revitalizer.”
I had long been skeptical of x-hyper. It seemed way too out there for SE to deliberately code it in beyond hyper, especially since its possible that hyper would never had been discovered in the first place. Then I thought, “Maybe it’s not too far out there. Maybe all of hyper is broken into tiers, based on the percentage from V’s theory.” For example, if you are >95%, you are basically in x-hyper status (note: to be >95%, you basically have to use the Revitalizer and immediately blow all your job abilities, precisely as prescribed by our current understanding of x-hyper as quoted above). If you waited a little too long, you would fall to 90%, then 80%, and so on. Thus, you would be out of x-hyper and would have a significantly less likelihood of quarrying another Revitalizer on demand. You would have to wait to get another Revitalizer through normal hyper, and at which point, you want to use it and blow all job abilities in order to try to chain Revitalizers together, maintain x-hyper, and become Super Saiyan powerful.
However the following two videos have me very convinced that V’s theory is not correct, and there is no x-hyper.
In video 5, Zirkk is on the losing team, but disregard this, as I’m pretty sure that it has no effect on quarry results in this case.
In these videos, Zirkk’s 2-hour is already down from a previous OM. Furthermore, he uses no job abilities at all while quarrying and throws all Revitalizers away without using them (violating both conditions for x-hyper). In videos 5 and 6, his 2-hour has 30-40 minutes and 10-20 minutes respectively until it comes back up during the quarry sequences. This corresponds to as low as 7% by V’s theory, yet Zirkk still demonstrates x-hyper results, quarrying 9 Revitalizers in 11 minutes in video 5 and 12 Revitalizers in 11 minutes in video 6. Thrunceii is quarrying Revitalizers, using them, and then using 2-hour on the side for both a comparison and additional proof of only 2-hour needing to be down.
Zirkk actually demonstrates the most successful x-hyper I’ve ever seen in these videos. It may be possible that tossing the Revitalizers had something to do with it, i.e., maybe the act of using a Revitalizer inhibits your chances for getting the next one (see Section III: The Poison Potion Effect).
From this point on, I think we should not use the terminology of x-hyper to alleviate any possible confusion.
Conclusion: If you died once in Hako and your 2-hour is on cooldown (regardless of time remaining) you are already at your maximum chance for getting Revitalizers. All you can do to get more Revitalizers is get more quarries in at the rook. It’s stupefyingly simple, which is actually even more frustrating for me because I still haven’t mastered it yet.
III. The Poison Potion Effect
Everyone knows how the chance of quarrying a Poison Potion is very high when you don’t have one/aren’t poisoned. That chance, however, goes way down once you have one sitting in your inventory or have used one earlier. During all my testing, I notice something similar happening with Body Boosts. I specifically investigate this in videos 4, 5, and 6. In video 5, Zirkk is dropping all Body Boosts as they are quarried and is able to quarry 10 Body Boosts. In video 6, Zirkk keeps the first Body Boost that he quarries in his inventory, and that is the only one he quarries all game. In video 4, Zirkk uses the first Body Boost that he obtains, and again, that is the only Body Boost he quarries all game.
It is important to note that a contributing reason why Zirkk got 12 Revitalizers in video 6 and only 9 Revitalizers in video 5 is because Zirkk held onto his Body Boost in video 6 (other reason being small variations in luck). If Zirkk held onto his first Body Boost in video 5, his next 9 Body Boost quarries would likely not have been Body Boosts, giving him 9 more chances for a Revitalizer.
Conclusion: Don’t toss all of your Poison Potions and Body Boosts as you quarry them as this will decrease your chances of quarrying a Revitalizer.
…Wait, that wasn’t really helpful, since we never do that anyways. But what if the Poison Potion effect applied to items other than Poison Potions and Body Boosts, items we normally do toss soon after we quarry them, such as Petra Eaters and bar-ointments?
The Poison Potion effect hypothesis (which I’ll be calling ‘Poison Pot Theory’ from this point on) is this: all temporary ‘quarryable’ items in Ballista have 4 different quarry rates.
1. The standard quarry rate: when none of 2, 3a, or 3b apply.
2. The quarry rate when the item is in your inventory.
3a. The quarry rate within X amount of time after using the item.
3b. The quarry rate when under the effect that the item gives.
The rates for 2, 3a, and 3b are assumed to all be lower than the rate for 1.
Some items, such as Revitalizers, don’t have an effect duration, so 3b doesn’t apply to those items.
At first, for all other items, I thought 3a and 3b could actually be the same thing, where X is simply the duration of the item’s effect. However, from memory and eye balling, when you use an Elshimo Pachira Fruit, you still see the reduced Poison Potion quarry rate. Nevertheless, 3a and 3b both apply to some items (i.e. not Revitalizers), and for those items, I am going to assume that the rates for 3a and 3b are equal. To clarify, an item actually has a 3a and 3b rate, but Revitalizers cannot have a 3b rate. As such, 3b does not apply to Revitalizers.
It is possible that the rates for 2 and 3 are both equal, leaving only (1) the standard quarry rate, and (2) the reduced quarry rate, both of which exist for every item in the game. Now the theory got a lot simpler and coherent, kind of like what happened with hyper. I will call this the ‘Simplified Poison Pot Theory’.
For the rest of this blog, I will mainly refer to a standard quarry rate and a reduced quarry rate, but keep in mind that this is a simplification and may not be true. I feel it is a fair simplification because even if 2, 3a, and 3b are not equal, the level of data collection required to achieve statistically significant results differentiating these different quarry rates will probably never be obtained. We also don’t care about the exact values of 2, 3a, and 3b; we just want to know if they are lower than 1 and if we can adjust our item usage/’droppage’ accordingly to our benefit.
A. Decreased quarry rates of Poison Potions when one is already in your inventory or while poisoned.
B. Near-zero quarry rates of Body Boosts when one is already in your inventory or while under the effect of a body boost.
C. After some quick eye ball tests, Petra Eaters and bar-ointments do not experience the same near-zero quarry rates as Poison Potions and Body Boosts when you leave them in your inventory. However, all items need not be reduced to a near zero rate. Keeping a Petra Eater in your inventory may reduce the chance of getting another one by, say, 10%, so it’s still worth keeping it in your inventory, provided you have room. Unfortunately, this is too small to notice with eye ball tests. Lots of data will need to be collected here to see if understanding Simplified Poison Pot Theory can actually be used to benefit us in games.
D. Videos 4 and 5 have the highest Revitalizer quarry rates I’ve ever seen in any hyper test video. The suggested reason is that Revitalizers maintained their standard quarry rate in these videos while in all other hyper test videos, they were being quarried at their reduced quarry rate.
When I was doing test videos 1 and 2, I was constantly hoping to achieve the same rate of Revitalizers as V did in his x-hyper video. Much to my dismay, after performing some rough calculations, it looked like V was still getting more Revitalizers than me (he averaged about 1 revitalizer per minute while I was always getting less than that). Since V only had one video, maybe he just got a bit lucky in it, but in the back of my mind, I was always worried that expending other job abilities might slightly improve Revitalizer quarry rates. If that was true, it would nullify my discovery of only your 2-hour needing to be down to achieve hyper because optimal playing would still call for expending all other job abilities.
However, like probably most of you, I didn’t actually watch V’s video; I just looked at his results. Upon watching his video, I found that V never tossed a single item; all items were used, except longer items like Elixirs, which remained in his inventory (side note: after using his first Body Boost, V also never got another one). Simplified Quarry Theory can explain why V got more Revitalizers than me. By using all his items or leaving them in inventory, all ‘quarryable’ items were then being quarried at their reduced rate.
Imagine a spectrum of hyper Revitalizer rates. At the low end of the spectrum, you drop all items except Revitalizers, causing those items to stay at their standard higher rate and putting Revitalizers at their reduced rate. Not only is the Revitalizer at its reduced rate, but since the other items remain at their higher probability, they have to steal some of this probability from the Revitalizers, since the sum of all probabilities must add to 1. It’s already been proven that dropping your Poison Potions and Body Boosts has a significant impact on being able to quarry ‘non-Poison Potion’ and ‘non-Body Boost’ items, as I outlined earlier. Other items may have a smaller impact, as well. At the upper end of the spectrum, you use all ‘non-Revitalizers’ and toss any Revitalizers you get, so now, all ‘non-Revitalizers’ are at their reduced rate while Revitalizers stay at their standard rate.
In my videos 1 and 2, I was only using Poison Potions while all other items were basically tossed at random when my inventory started getting full. This would put me somewhere in the middle of the spectrum. V would have been much closer to the upper end of the spectrum, since he wasn’t tossing any items.
This is basically the supreme goal of Poison Pot Theory: being able to establish that a spectrum exists for hyper Revitalizer rates and being able to apply this knowledge to get more Revitalizers in Hako games.
The competing theory states that item quarry rates are independent of previous item usage or already having an item in inventory. Poison Potions and Body Boosts are just special cases added in by the design team for the following specific reasons:
1. Early on in the design of Ballista, it became clear that Sleep was going to be overpowered and easily abused, so they gave Poison Potions a very high chance to be quarried. Then, in order to prevent almost all of quarries being Poison Potions, they reduced the chance of quarrying another Poison Potion once you have obtained your first one.
2. Body Boosts are also pretty strong, and it would be kind of lame if you could always have one active. You would always stockpile a spare in reserve and essentially be boosted 100% of the time.
Observations A, B, and C support both theories. Observation D is when I first realized that using an item may have an effect on your ability to quarry another one and is the main observation that is not consistent with both theories. For this reason, getting more data for observation D is my first priority which could confirm that the higher rates observed in videos 5 and 6 were not a fluke. If observation D checks out, then we can move onto more controlled tests with observation E. Since we already know that Using Poison Potion and Body Boosts is beneficial to getting Revitalizers, this should always be done in further tests. We will, then, compare Revitalizer rates when all other items are tossed and when all other items are used. If using the other items consistently allows one to quarry more Revitalizers than tossing other items, the Poison Pot Theory is pretty much confirmed. Then, we can test to see if Simplified Poison Pot Theory is true.
IV. Item Theory
Item theory combines Poison Pot Theory with Hyper Theory and some other minor tweaks. Item theory states that all temporary ‘quarryable’ items in Ballista have 6 different quarry rates:
1. The standard quarry rate: when none of 2, 3a, 3b, 4, or 5 apply.
2. The quarry rate when the item is in your inventory.
3a. The quarry rate within X amount of time after using the item.
3b. The quarry rate when under a status effect related to the item.
4. The hyper quarry rate.
5. The GYAW-hyper quarry rate. (Gettin’ Your Ass Whooped)
Please, note the subtle wording change in 3b. This now can explain increased Echo Drop rates when silenced and can make a prediction that maybe the chance of quarrying ‘au lait’ items is increased while poisoned. Also, to make the theory simpler, Revitalizers can be put into 3b and leave hyper to be defined just by your number of deaths.
I’ve defined GYAW-hyper as being able to quarry Giant’s Drinks. I started doing some testing on the conditions for this (this is the reason why Zirkk was on the losing team for video 5 but then got sidetracked by mad Revitalizer rates). V has also done some testing in which GYAW-hyper was achieved in ‘Strategy 006‘. I think in his tests, he was doing game durations of 1 hour or 1 game day, so hyper would be 3 deaths. From V’s data, he first got a Giant’s Drink when he had 2 deaths and was losing 0-1. That doesn’t seem like that much ass whoopin’ at all and, in fact, can occur before regular hyper.
This poses a problem for Item Theory as it stands now, since it seems like there may be a continuum of hyper states. Since I grouped the differing rate of Revitalizers into 3b, hyper just refers to a state beyond a threshold of deaths. After 1 death, Body Boosts become available, after 2 deaths (while losing), Giant’s Drinks, and after 3 deaths, Revitalizers go way up. Somewhere in there, rates of other powerful items like Megalixers and Hi-Elixirs probably also go up. After 10 deaths, these rates may go up even further. Also, losing by a more significant amount of petras may also increase rates. From past experience, we know that when being way way behind, or way way ahead, things can get even more drastic. For example, it can be extremely tough to get petras, when way ahead.
For this reason, I feel it is best for Item Theory to do away with arbitrary hyper thresholds, and quarry rates for all items be described as follows:
Base quarry rate + Death Factor + Score Factor + Inventory Factor + Recent Use Factor + Status Factor + Uneven Teams Factor
These 7 terms could be properties of all Ballista temporary items. Here are some rough examples:
Base quarry rate : High
Death Factor : Zero
Score Factor : Zero
Inventory Factor : -High
Recent Use Factor : Zero
Status Factor : -High
Uneven Teams Factor : Zero
Base quarry rate : Low
Death Factor : High
Score Factor : Unsure
Inventory Factor : Unsure
Recent Use Factor : -Low
Status Factor : High
Uneven Teams Factor : Unsure
Base quarry rate : Zero
Death Factor : High
Score Factor : High
Inventory Factor : -High (Assuming its same as body boosts)
Recent Use Factor : Zero
Status Factor : -High
Uneven Teams Factor : Unsure
Having a positive High Death Factor means that the number of deaths greatly influences the total quarry rate of an item. As such, more deaths increases the rate.
If the Competing Theory against Poison Pot Theory turned out to be true, this general framework still holds. It’s just that most items have Inventory, Recent Use, and Status Factors of zero.
V. Generalized Quarry Theory
Generalized Quarry Theory attempts to explain all quarry results. I imagine it would go something like this:
When you hit ‘/quarry’, the random number generator selects one of the following outcomes:
1. You get an item, proceed to Item Theory.
2. You get a petra.
3. You get nothing.
Probabilities are assigned to each of these 3 outcomes, and these probabilities vary with distance from the Rook. They may also vary with respect to the Death, Score, and Uneven Teams Factors. Being way behind in petras and/or having lots of deaths and/or being on the team with fewer participants may greatly reduce the chance of #3 happening, as well as increase the chance of #2 even more when further from the rook. #2 could also depend on your X and Y coordinates. It is often observed once you quarry your first petra: if you stay in the same spot more petras tend to follow.
There are some things not included in Generalized Quarry Theory, such as the effect of Petra Shovels and Ballista Bands. At this point, having a Petra Shovel is assumed. This leaves a question open that I’ve been wondering about: what effect does Ballista Band have, if any? All the JPs whose videos I watch on YouTube (Irvinez, Teska, and Berserkr, I think Berserkr is Saraphy’s galka?) use Ballista Band on their front line jobs. Teska takes Ballista Band off when on PLD. Since the intention of Ballista Band is you may not want petras, could it passively decrease the chance of #2 and increase chance of #1? Petra Shovel is already proven to alter quarry results in ways other than its intended function, so investigating Ballista Band could be worthwhile.
I’m going to do some more testing when my final exams are over. Hopefully, this pans out and we can get some useful results out of this that we didn’t have before. Much discussion will also be needed.
VI. Uneven Teams
During testing, I noticed that the rooks would make a sound and light up shortly after killing Thrunceii. Then, after a few seconds, they would make another sound and light off. This can be seen and heard when I first kill Thrunceii in video 1 if you turn up your speakers (the Rook is at fences). At first, I thought this was indicating the granting of gate breach or something, but it turns out the Rook lights up in this manner whenever one team has more players in the zone than the other team!
The Rook lights up when Thrunceii is returning to camp and thus is temporarily not in the zone. You may have noticed sometimes if you ‘/sea ballista’: sometimes someone is missing from the list probably because he went to camp right as you searched. Although not shown in the above video, when Thrunceii waits out his death time and revives on the spot, no Rook lighting occurs.
This is important because the game makes a note when teams are uneven, and at least one thing (Rooks lighting) is coded to happen. This is why I ninja’d an Uneven Teams Factor into Generalized Quarry Theory, since the Death and Score Factors are intended to give the losing team a chance to make a comeback, so an Uneven Teams Factor makes sense.
Although this doesn’t hold much practicality for most games, this is extremely important for all future quarry tests. If you are doing quarry tests and have someone kill you, that character must stay in the zone with you while you do your quarrying. That character can’t leave or log out.
Now that I think about it, it’s very possible that V did this during his x-hyper video, and that could be the explanation of him getting more Revitalizers than me instead of Poison Pot Theory. You can see why I said it’s important to video your tests; you never know what important details you might leave out if you just presented certain results in text form or what other details someone might notice!