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Choices: An analysis of LimitationFollow

#1 Oct 11 2009 at 7:21 PM Rating: Excellent
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Choices: An Analysis of Limitation


Introduction:
In this document, I will mathematically analyze the potential for variance in Final Fantasy XIV based on the game mechanics we have seen thus far, be it in demonstration, interview, or article. I will then offer my personally interpretations on the information, as well as do my best to give a qualitative description of my impressions on the system’s potential, both for the player and for the developer.

First and foremost, this document is specifically about the potential for job variation that is caused by the limitation of the number of abilities available to a player at any given time. I also hope to sway some skeptics toward being more optimistic about the potential positives that such a system will provide. Furthermore, I will be making the following assumptions (for various reasons) for the remainder of the examination:
  • The term “ability/abilities” is a generalization for any move or spell that is used by the player direction, i.e. mounted on the “hotbar”.
  • Every class has the same number of abilities at max “level” (This is to simplify the analysis, I am well aware that it will not be true in the final game, but it allows me to make simple generalizations that are relatively accurate for the current amount of information out).
  • Players will be able to use n abilities at any given time (This is based on the demo seen at Gamescon, in which players could only have ten abilities, and a later interview in which they said they had not yet decided how many slots would be available, implicit in that is that the number of slots is limited at any given time).
  • Moves will be equally useful (This is a gross exaggeration in practice, but please bare with me, I will address the inconsistencies caused by large variations in ability potency later).


Background:
Any situation in which a sub-group of “something” is chosen from a larger group of “somethings” can be simplified by using a binomial coefficient, or “choose” function (this is what I will be calling it from here on out). A choose function will return the number of variations can be created based on a group of size k when selecting a sub-group of length n.

Analysis:
I ran three tests for this analysis, the first two were scenarios in which a variable size sub-group is selected from a static size group (k=20 and k=15 respectively). The third analysis was a generalization in which I looked at the maximum variations possible for a group sized one to forty – the maximum variance is at n = k / 2. I won’t bore you with the numbers, but you can check the charts and values here, here, and here. What I discovered was that the choose functions produced extremely sharp bell curves (low, then high, then low again) centered on the k / 2 line, which is about what I expected to see. What I did not expect to see, was the extreme slops that were involved. The entire function works on an exponential slop.

The third test, on the other hand, was done in order to determine at what rate exactly the variance increased as you added more abilities (operating on the common assumption of using the maximum values for each k value). What I found was that the increase was a standard exponential slope (if this sort of thing interests you, the trend line was y=0.3563e0.6629x).

The bottom line here is, with a class with twenty abilities, which, based on what we have seen about this game so far, I do not believe is an unreasonable number, there are anywhere between 1 and 184,756 combinations of abilities. At Gamescon, we saw ten slots, giving 184,756 possible combinations.

Speculations:
But this has all been numbers, and raw data, as I’m sure most of you are thinking right now, the real world does not work quite that nicely (although I would like you to keep the sheer size of the variations in the for front of you minds for the moment). There are any number of things that can and will skew these results.

First and most notably, depreciations – As I’m sure you all know, no ability lives forever. Something invariably comes along that will depreciate any given ability’s value. That being said, it has already been mentioned in an interview with Square Enix employees that most weapon classes will have several different potential builds included. The example of a non-specific tank class was given, in which you could equip abilities for damage, or defense/hate management. This implies a wide spectrum of abilities, most of which will not overlap in any destructive ways. Provoke, gained at level five, never loses its usefulness after all. Unfortunately, the ball is in Square Enix’s court right now as to how much this aspect of the choose function is useful.

Interestingly, there are other uses for the limitation of abilities. Most interesting of these is the potential for multi-class “lazy balancing”. With a limited number of slots, you have to choose what is more important to you as a character. I has been stated that abilities will primarily be received from weapons, but also be available from other sources. Let us examine, for a moment, a mixture where we have a goodly set of white magic available as well as a healthy amount of tanking options. Normally, you would all this class a paladin. You would also probably be correct. With a limited number of slots, however, the dynamic changes. If you want to be good at healing yourself and others, you will have to sacrifice slots that could have been used for hate management, or blocking moves. The inverse is also true.

I called this “lazy balancing” because it will, to a small extent curb the potential to have spikes in ability. It produces something surprisingly close to a smooth curve from damage, to mitigation, to healing, to buffing, to debuffing. Please keep in mind that this has nothing to do with how those abilities are available to the player, I am merely assuming that they are.

Another potential advantage to the limited ability access is purely development directed. With the slot limit, developers have two very interesting options. For one thing, if they feel that the game is becoming too stagnant, and players are becoming too set in their ways. Merely adding one slot would drastically change the balance of abilities. Builds that were previously unviable due to not having enough space suddenly work, whereas previously powerful sets fail to make use of the new ability slot, due to the new ability not being smoothly integrated into whatever made the previous set powerful. Unfortunately, how useful this technique is depends greatly on how willing the player base is to go out and try new things, instead of just tacking on another kind-of-useful instead of trying to optimize with the new potential.

The other potential use for the limited slots for developers is for challenges and events. Salvage made use of a system in which equipment slots were locked, as well as magic, melee, ect. It was not the most popular of end-game activities, but it did prove the concept. Also, it would not have to be a total lockout. For instance, in a given situation, you may have to make do with -2 from your normal slots, due to some in-game reason (just woke up?).

Conclusion:
Given that Square Enix are thinking about the maximization of variance in class abilities. I would be willing to bet that we will be seeing somewhere close to ten slots available to us, as well as around twenty abilities for each class. This would maximize the potential for the system. On the other hand, given Square Enix’s propensity to add abilities later in the game’s lifetime, we may see fewer abilities to leave room for more later, something close to fifteen. We can also only hope that the player base will keep an open mind to new combinations throughout the game’s lifespan.
#2 Oct 11 2009 at 8:51 PM Rating: Good
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Interesting analysis.

Assuming you have 20 abilities at max level then it may be safe to say you would have about 10 abilities at 1/2 of max level. If you have 10 slots throughout the game, then all the way from 0 to 1/2 max level, there is no variation in the way you fill your ability slots.

Do you think SE should/will make it so the # of ability slots slowly grows in relation to the number of abilities you have, thus maximizing variation? It may be a hassle when switching to a different "build", unless SE makes it so the macro system can be set up to automatically fill in your slots with the abilities you want. For example, you could make a Paladin Macro that would fill in the 10 slots with the abilities you think are the best for Paladin (tweaks can be made after, depending on the situation).

Do you know how often or when ability slots can be swapped out? If they can be swapped out at anytime it makes the system pointless; I'm guessing they can be swapped out during the same time a weapon can be swapped (while not in combat).
#3 Oct 11 2009 at 8:54 PM Rating: Good
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Interesting speculation with the slot limits, and the potential challenges that will inevitably appear with the removal of some of them in events. I would assume, or indeed, hope that at least mages would have more than a pool of 20 abilities/spells to select from.
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#4 Oct 11 2009 at 9:20 PM Rating: Excellent
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Fantastic analysis.
I find your conclusion well supported, well written and highly appealing.


Quote:

I would assume, or indeed, hope that at least mages would have more than a pool of 20 abilities/spells to select from.


I think the higher the potential customization the more the classes could be boiled down into their core functions, so the less spells would be necessary.

Think of how many spells are directly shared by multiple classes (RDM: Silence, WHM: Silence), spells that are shared by multiple classes in function if not in theme (RDM: Refresh, BRD: Ballad), and spells that exist outside the scope of a class for no other reason than to keep them from being helpless in soloplay (WHM: banish line, banishga line, holy line, dia line.)


#5 Oct 11 2009 at 9:54 PM Rating: Good
I doubt they will choose the number of abilities mathematically.
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#6 Oct 12 2009 at 5:02 AM Rating: Good
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I would do you one better and hope that rather than assigning 20 class-based abilities, which will be easily reduced to optimal setups, even if only situationally optimal, they instead make the entire pool of abilities accessible. So if in your example of 20 abilities, there were 10 classes, now that instead becomes 200 abilities available to each player. Restrictions can be placed on certain conditions, of course, such as weapon equipped, and effectiveness can be altered accordingly.

Further still, as you note the implications of increasing slot availability by 1, an AP system adds further depth to a generic slot system. For example, rather than 10 slots, you are allotted 100 points, each ability weighted according to its power. This makes it easier to adjust for balance-- rather than ensuring that all abilities have similar merit, you can simply adjust the cost of assignment so that less useful abilities are appropriately cheaper. It also enhances the complexity of choosing what abilities you will use.

This is what I've been asking for for the last few years. I just recently started playing Dissidia and was pleasantly surprised to find some of these concepts in action. It gives me greater faith that SE may follow suit in XIV. On the other hand, even if they do, in the time it's been, I've already developed another game system to add onto that one which I'll want to see next time. It's too early to talk about it now, but rest assured it would be completely ******* awesome. I'll look forward to arguing for it for a few years after XIV is well underway.
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#7 Oct 12 2009 at 1:24 PM Rating: Good
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You, yeah you, the guy wit the fancy numbas. Git away from mah game. RAWR!
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#8 Oct 12 2009 at 3:25 PM Rating: Decent
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I really didn't understand the charts, but I think it's a good idea on SE's part to limit what skills we could use at one time. And if there are that many combination's, it'd be cool since you'd never find your twin really :P
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#9 Oct 13 2009 at 9:18 AM Rating: Decent
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Very well written.

Quote:
Assuming you have 20 abilities at max level then it may be safe to say you would have about 10 abilities at 1/2 of max level. If you have 10 slots throughout the game, then all the way from 0 to 1/2 max level, there is no variation in the way you fill your ability slots.

Most games offer little to no variance prior to a job defining level. This can be where a job path splits into two distinct jobs or a spell/ability is obtained that no other job in the game has access to or can duplicate. Based on the analysis, I don't believe you would see an excess of 10 abilities w/ a max of 20. Assuming that 1/2 Max level is 37, and taking into consideration that in XI SE has offered more abilities at max level through merits instead of through progress from 38-75, it's likely that you will see anywhere between 1/4 - 1/2 of available abilities. The exception is if you don't view scaling abilities as independent ones (e.g. - Dia II, Dia III).


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#10 Oct 13 2009 at 3:10 PM Rating: Decent
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Very well written. It's the kind of writing and analysis i would rather see on countless game forums.

The first thing that came to my mind was Guild Wars, which used a ten slot limitation on all of its abilities. I thought it was a fantastic idea in that game, and one relatively well implemented. If i remember correctly from the Gamescon gameplay video's and interviews, even weapon skills like Red Lotus Blade took up a slot. We all know that WS will require TP to use this time around also, and that's an extra gauge beyond to watch beyond HP and MP. That means another layer of combinations with the presumed return of skill chains. Another thing to consider are if they even decide to keep the traditional Final Fantasy Ability and spells this time around, seeing as they've already thrown out the 'jobs'. There's also question to whether passive abilities or 'job traits' take up slots.

There are the other two disciples in which the ten slot limit wouldn't make sense to implement to. It's confirmed that you need a tool, materials and a crystal to craft and synthesize , so a crafting class shouldn't need to have an ability to get the job done. there hasn't been anything with regard to how a Disciple of the Land should work either. It could be that Each Disciple has different rules on how their respective skill system works. Maybe each would have their own spin on the ten slot limit.
#11 Oct 13 2009 at 4:39 PM Rating: Decent
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Well...

1. Your math is wrong, if I'm understanding your assumptions correctly.
Quote:
The bottom line here is, with a class with twenty abilities, which, based on what we have seen about this game so far, I do not believe is an unreasonable number, there are anywhere between 1 and 184,756 combinations of abilities. At Gamescon, we saw ten slots, giving 184,756 possible combinations.

You are assuming a pool of 20 abilities players may choose to fill a 10 slot bar, right? The possible number of combination here is close to 6.7x10^11, not 184,756. The equation is 20!/10!.

2. Your assumption that there will be a set of abilities players can take into battle at any one time that is significantly smaller than their set of total abilities is somewhat silly. Shure Guild Wars did this, but that's about the only game I know of. WoW, War, Lotro, and many other MMORPGS give you access to all of your abilities all of the time.

3. Your assumption of equal usefulness invalidates your data, because we know this does not occur--to an extreme degree. I know you acknowledge this, but this one factor contributes to a huge error margin in your results that makes them not represent reality at all. For example, if were playing an FFXI whitemage and could only take 3 abilities into combat at a time, would you ever use a bar element? Your highest level Cure or Curaga would be a required ability, while many others would be other looked completely. There would be something like 10 viable combination rather than 6840 (20!/17!).
#12 Oct 13 2009 at 5:07 PM Rating: Excellent
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Quote:

1. Your math is wrong, if I'm understanding your assumptions correctly.
Quote:

The bottom line here is, with a class with twenty abilities, which, based on what we have seen about this game so far, I do not believe is an unreasonable number, there are anywhere between 1 and 184,756 combinations of abilities. At Gamescon, we saw ten slots, giving 184,756 possible combinations.


You are assuming a pool of 20 abilities players may choose to fill a 10 slot bar, right? The possible number of combination here is close to 6.7x10^11, not 184,756. The equation is 20!/10!.

2. Your assumption that there will be a set of abilities players can take into battle at any one time that is significantly smaller than their set of total abilities is somewhat silly. Shure Guild Wars did this, but that's about the only game I know of. WoW, War, Lotro, and many other MMORPGS give you access to all of your abilities all of the time.

3. Your assumption of equal usefulness invalidates your data, because we know this does not occur--to an extreme degree. I know you acknowledge this, but this one factor contributes to a huge error margin in your results that makes them not represent reality at all. For example, if were playing an FFXI whitemage and could only take 3 abilities into combat at a time, would you ever use a bar element? Your highest level Cure or Curaga would be a required ability, while many others would be other looked completely. There would be something like 10 viable combination rather than 6840 (20!/17!).


I have been trying to stay out of this discussion and allow other people to weigh in as they please, but since this directly deals with my work, I have a few responses. First of all, the binomial coefficient formula is:

n!
------------
k!(n - k)!

which in this example reduces down to:

20!
---------
10!(10)!

or

20!
--------
10!^2


I am as apt to make stupid mistakes as the next person, but I did check these numbers religiously before posting. They are correct.

Secondly, my assumption that we will be using a small subset of a large pool of abilities is not groundless, in fact, it is based specifically on the fact that there was a finite number of slots available at Gamescon, and then later, an interview confirmed that they had not decided what that finite value would be. Even if they have not decided what it is, there is a finite number of available abilities at one time. As for how many total abilities we will have, that is part of what I was attempting to prove was logical, mathematically. I also believe there is plenty of evidence in FFXI to back up my claim just based on previous experience with SE.

Finally, you are exactly correct, in fact that is my point. If a white mage could only use 3 spells, most people would have chosen "highest cure" "Protect" and "Erase" (probably). But the limitation would spawn subcategories all by itself. In endgame events for instance, you would start looking for specialists. A white mage who was used to being a buffer, as well as one who was experienced as a healer, along with one who was experienced as a status healer. It even has a place in parties, some monsters will require more status ailment cures, while others will offer the opportunity for buffing to work well. Limitation has, in fact, increased the number of options available to your everyday white mage.

Edited, Oct 13th 2009 7:08pm by Hulan
#13 Oct 13 2009 at 5:16 PM Rating: Decent
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I have to take an exam shortly, so I do not yet have time to write a full response, but I wanted to first apologize for taking such a belligerent tone. I now understand the error I made in math earlier.

Edited, Oct 13th 2009 6:30pm by Allegory
#14 Oct 13 2009 at 5:34 PM Rating: Good
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No offense taken, I was just responding to make sure I cleared up any misunderstandings about my theory, as well as refine it if you do find something fundamentally wrong with it. I have to admit, you gave me quite a scare there though, I went and rechecked my numbers just to make sure. I would have had quite the apology to make if that had somehow slipped through.

I chose the binomial coefficient function because it is the best way to determine the number of unique combination that can be obtained when choosing a number k elements from a list n elements long. Of course, it gives no information about how unique each combination is, merely that it is at least one element different from any other combination. I wasn't interested specifically in the application of the combinations. Rather, I was attempting to prove that there is a great deal of power in limiting the player to a set number of abilities, and then providing us with a large group to choose from. Whether you or I are correct in the number of combinations, it is well over 1000, which should be more than enough to keep any ambitious and curious players busy trying out new things. In application, you may be correct, the players by pigeon hole themselves into set groves and roles. But based on this analysis, I propose that this is a shame, and that, based on what we know so far, we will have literally boundless possible builds to try.

As for what you say about most abilities being overwritten or just plain useless. I did to some extent take that into my estimates on total abilities. I did not write it before, but one of the things I considered when deciding test case sizes was the number of unique abilities we might have. Personally, I do not think it is unlikely that SE will provide every weapon with a wide and diverse variety of abilities to choose from. Some weapons, such as Staff, may suffer more from ability depreciation than others, but if we look at black mage in FFXI, there are 6 Elemental spells (which are not all useful in FFXI, but it is easy to see ways that this could not be the case), add to that the 6 AoE Elemental spells, and you have 12 basic "Nuke" spells. Considering FFXIV is supposed to specialize in many x many combat, I believe AoE spells are a reasonable addition to this set. On the other hand, black mages also have access to enfeeblement magic, sleep, bind, slow, poison, bio; as well as absorption spells like aspir and drain. That's two more sets, of size 5 and 2 respectively, and I'm sure I'm forgetting some, I have not played black mage in quite some time.

Other examples exist, but I will move on. SE has implied that we can actually cross over some classes by use of equipment that grants non-class abilities. This would add yet more viable options. Black magic from staff, white magic from gear - you can suddenly equip a spectrum from white to black, and have to choose to what degree you specialize in each.

Edited, Oct 13th 2009 9:07pm by Hulan
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