Tatha – Collaboration, Duration, Bandwidth, Restrictions

Now that the basics of the Rank system are out of the way – on to some of the more special cases:

Restrictions

In addition to Ability Variables, some abilities may also contain one or more Restrictions.  These work like negative variables (thought they often have less ranks, often only 1).  For each Restriction purchase during the usage of an ability, the total Rank Cost goes down by 1.

Duration and Bandwidth

Abilities in Tatha do not have ‘durations’ attached to them.  Instead, there are three types of abilities:  Instant, Channel, and Burst Channel.  Instant abilities subtract their usage cost from ones’ current stats immediately upon usage and have no lingering effects.   Channel abilities temporarily consume stats for as long as they are on.   This means that you record 3 pieces of information per stat:

  1. What the current maximum stat is (typically 100, unless modified by abilities or equipment)
  2. What the current stat value is
  3. The sum of the currently active channeled abilities that use this stat as a cost

Of these three numbers, #2 is often called the Bandwidth.  This represents the current maximum for the third number, the Channel.  Any channeled ability can be deactivated at any time, but the effect is terminated immediately with it.  If at any point the available bandwidth is smaller than the current channel, then the player must deactivate channeled abilities of their choice until the bandwidth is equal to or greater than the channel.

Burst Channel is the last kind of ability, and it is simply a combination of two abilities: an Instant and a Channel.  As such it will be listed with two costs: the instant cost and the channel cost.  The last things that can come into the equation here are Overpowering, Contests, and Conditions – all of which will typically drain bandwidth (like an instant), but may do so on a periodic basis or based on a failed roll or other condition.

Collaboration

One might look at the Rank chart and say: “with only 100 Energy, what’s the point of having Rank 5 on an ability that costs 400 Unit Energy Energy – no one can ever cast that”.  And that would be correct – so you need to get more than one to cast it.  Collaboration can be a tricky however, and may not even prove fruitful (too many cooks can spoil a broth).  When collaborating, the output of the group is determined by the following ’simple’ formula:

Total Output = Sum( Ability Unit Cost * ( 2 ^ ( User’s Rank – 1 ) ) ) – ( Ability Unit Cost * (Number of Collaborators * ( ( Number of Collaborators – 1 ) / 2 ) ) )

Whew.. Now this looks pretty complicated , but it’s not.  Another way to put it is that the amount of energy that this rank would cost if the user had the ability at rank 1 is added to a pool and the pool loses the cost of the ability times the number of unique connections between people involved off the top and that .  This pool is then used to cast the ability as if the caster had the ability at Rank 1.  To simplify calculating the number of unique connections, otherwise known as the Triangular Number (ref1, ref2, ref3), here is the following table for most real-world uses of this:


 1:   0
 2:   1
 3:   3
 4:   6
 5:  10
 6:  15
 7:  21
 8:  28
 9:  36
10:  45
11:  55
12:  66
13:  78
14:  91
15: 105
16: 120
17: 136
18: 153
19: 171
20: 190

Now some examples: (for all these examples, the ability cost is 20Energy).

  • 1 Person Rank 4:  160 (Rank 4)
  • 2 People Rank 4 for both:  160 + 160 = 320 – (20 * 1) = 300 (Rank 4 – almost Rank 5)
  • 3 People Rank 4 for all: 160 + 160 + 160 = 480 – (20 * 3) = 420 (Rank 5)
  • 4 People Rank 4 for all: 160 * 4 = 640 – (20 * 6) = 520 (Rank 5)
  • 5 People Rank 4 for all: 160 * 5 = 800 – (20 * 10) = 600 (Rank 5)
  • 6 People Rank 4 for all: 160 * 6 = 960 – (20 * 15) = 660 (Rank 6)
  • 7 People Rank 4 for all: 160 * 7 = 1120 – (20 * 21) = 700 (Rank 6)
  • 8 People Rank 4 for all: 160 * 8 = 1280 – (20 * 28) = 720 (Rank 6)
  • 9 People Rank 4 for all: 160 * 9 = 1440 – (20 * 36) = 720 (Rank 6)
  • 10 People Rank 4 for all: 160 * 10 = 1600 – (20 * 45) = 700 (Rank 6) !!!

So if you notice this pattern here, while simplified because they are all using the same Rank of the ability, you will notice that after a while, adding more people becomes fruitless, even harmful.  Here are some more random examples:

  • 2 People Rank 2 each: 40 * 2 = 80 – (20 * 1) = 60  (Rank 2)
  • 3 People Rank 2 each: 40 * 3 = 120 – (20 * 3) = 60 (Rank 2)
  • 2 People Rank 1 each: 20 * 2 = 20 – (20 * 1) = 20 (Rank 1)
  • 3 People Rank 5 each: 320 * 3 = 960 – (20 * 3) = 900 (Rank 6)
  • 2 People Ranks 2 and 3: 40 + 80 = 120 – (20 * 1) = 100 (Rank 3)
  • 4 People Ranks 3, 3, 2, 2: 40 + 40 + 80 + 80 = 240 – (20 * 6)  = 120 (Rank 3)
  • 4 People Ranks 3, 3, 2, 3: 40 + 80 + 80 + 80 = 280 – (20 * 6)  = 160 (Rank 4)
  • 5 People Ranks 3, 3, 2, 3, 2: 40 + 40 + 80 + 80 + 80 = 320 – (20 * 10)  = 120 (Rank 3)

Some observations can be made about the following examples:

  • The threshold for ‘useless addition’ comes sooner the lower the ranks being contributed are
  • Conversely, the higher the ranks being added, the more resistant they are to the loss
  • Rank 1s are always a hindrance, never a help (because the addition of 1 rank 1 adds at most Unit to the total, but will add at LEAST Unit worth to the loss)
  • This isn’t to say that Rank 1 users can’t help, they just need to spend more than usual (instead of spending 20E, if they spent 80E, they’d be a rank 3)
  • In the last example, the 4 people had an already stable Rank 4 usage – the addition of the extra Rank 2 user actually destabilized the ability, dropping it a rank

However, there is a way to beat the loss.  Any Soul Link groups are counted as a single person as far as the Triangle Number section is concerned.  This means that two users with a Soul Link have ZERO loss, allowing them to effectively double their output (which will mean if they are using the same rank, they will get 1 more than what they could have individually).

  • 2 Soul-Linked People Ranks 4 and 4: 160 * 2 = 320 (Rank 5)
  • 2 Soul Linked People Ranks 3 and 3 + 3 Non-soul linked Rank 3s: 80 * 5 = 400 – (20 * 6) = 280 (Rank 4)
  • 2 Groups of 2 Soul Linked + 1 Non-linked People all Rank 3: 80 * 5 = 400 – (20 * 3) = 360 (Rank 5)

The difference between the 2nd and 3rd example there is not the addition of any people or any ranks, but just the linking of two unlinked users.

Notes

I will probably develop a simplified system for collaboration (based on tables of the likely outputs from this formula), but this system was developed by my usual means:  I know the curve/effect in my mind that I want, and then I look for the formula that produces it.  A simplification would probably look like a rule of thumb for ’small group’ scenarios:  Everyone must use the same rank.  To raise the rank of the output 1 rank, you need 3 people, or 2 people under a Soul Link.

March 10, 2009