# Graduating Class of 1220 / The Anas Equation

This topic is a little like the Drake equation, a lot of "best guess" and "imo" and estimation and reasonable assumptions and so forth. So, accepting that...

Approximately how many apprentices are gauntletted each year?

Approximately how many Spring Covenants show up in the Order each year, or each 7 years?

And about how many Spring(-ish) Covenants would be in existance at any one time?

The reason I ask is multifold- A Spring Covenants most approachable ally is another Spring Covenant- equal power (next to nil), equal need (high), etc. NPC Spring Covenants are great plot devices on many, many levels. And Spring Covenants generate new magi in an area, for PC interaction.

The Anas Equation:

Average # of new Spring Covenants/year =

{C x M x A x 1/G x S} / P

C = # of Covenants in Order
M = Average # of Magi/Covenant
A = % of Magi with Apprentice(s)
G = average # of years for an apprenctice to "graduate"/be Gauntletted
S = % of new magi to seek Spring covenants, (vs being absorbed into existing ones)
P = average population of a new Spring Covenant

C - pretty straightforward
M - a little less so, but likewise
A - Tough one!
G - at first "15" sounds right, but with deaths/rejections/failures, maybe closer to 17???
S - probably(?) a high percentage(?)
P - critical mass for a new Spring Covenant.

I can fake it, but I'm wondering if my assumptions are in the ballpark with others'.

Your equation fails to take into account the number of magi joining spring covenants who are not freshly gauntleted.

And what about lucky Winter covenants that cycle back to Spring?

Regarding the % of magi with apprentices, you might be better off with those two factors:

• the average number of apprentices a magus trains over his lifetime
• the average lifetime of a magus.

That should increase the effective G.

You should also take into account joining spring covenants (which may actually be very ancient winter covenants who are pulling themselves together, for example), which can really complicate matters. But let's blissfully ignore that.

The issues are EXTREMELY subjective, saga-dependant, and so on. At any rate...

For new spring covenants per year I would use the equation
(M x A x RG x S x 1/G)/P

Where
M - number of magi in the order (set at 1200 by ArM5 p. 9)
A - fraction of magi with apprentices at any given time (I guesstimate 0.3)
RG - fraction of apprentices that reach gauntlet (I guesstimate 0.9)
S - fraction of new magi to seek to establish new spring covenant (I guesstimate 0.6)
G - average number of years of apprenticship and other delays before joining a covenant (I guesstiamte 17)
P - average population of new spring covenant (I guesstimate 6)

So I get:
(1200 x 0.3 x 0.9 x 0.6 x 1/17)/6 = 1.9 new spring covenants per year
which is 1.9/13 = 0.14 new spring covenants per year in a tribunal; or 1 new spring covenant per 7 years in a tribunal.

To establish the current number of Spring covenants in the tribunal, we solve
dS/dt = scpy - S/sclt = 0
where S is the number of spring covenants, "scpy" is the above derived spring covenant per year in tribunal increase rate, and "sclt" is the average spring covenant lifetime, which I'd peg as 5 years (as most die within a few years of foundation). The equilibrium number of spring covenants in the tribunal is thus
S = scpy x sclt = 0.14 x 5 = 0.7
There are 0.7 spring covenants at each tribunal, although 1 new spring covenant is founded at it every tribunal session.

As if.