Mathy Math time.
Intro:
How can you predict when a research goal will be completed?
The simplest, yet tedious method is simply adding up each turns research total. But what if you're in a hurry to see whether you can reach construction four by the end of the first year (you can, on standard), and what exactly that magic scale buys you.
Blather/background:
I'll leave the mathematical theory behind it for later, and throw you a quick formula you can use for an
estimation based on the idea that each turn, you recruit a mage in your capital and dedicate him to research. Obviously, there are ways to speed and slow this down, but this'll give you a clear idea what you can achieve. The formula I give here becomes obsolete after you set up secondary research centers, or diversify your commander recruits, but this is a good yardstick for the first year. Heck, one time I found two libraries (Sages) within a few provinces in my capital. Needless to say, research climbed dramatically.
ESTIMATE HERE:
sqrt(aggregate research total for level x 2 / Research points of mage)
EXAMPLE HERE:
To give an example, I'm playing MA Agartha on a standard game with three magic scales, for +2 to research. My Golem Crafters cost 200 gold, and with bonus, 8 rp each.
To research construction four (items), or enchantment 4(Enliven Sentinels), I need (40+60+100+160) or 360 Research Points. I double that, to 720, and divide by 8, my research points per Golem Crafter, in this game). That results in 90. I enter that in my calculator and press sqrt. The square root of ninety is ~9.4. I round that up to ten. I can forge my first greater magic item 10 turns after my first mage starts recruiting.
If I'd gone with no magic scales, and Earth Readers, I would need sqrt(720/3) or 16 turns.
I forget the name of the exact mathematical formula- correct me if I get anything wrong. Feel free to correct me with proper terminology too, or point out a hideous error. But the basic mathematical theory is that you can predict the sum of a series of numbers (linear growth) by multiplying the average of all the numbers times the number of terms in the series. In the einstein story, he was asked to provide the sum of all numbers from one to a hundred. The teacher expected everyone to add them all up, but he answered immediately.
How did he do it? He took the average of the first and last term, and multiplied it by the number of terms in the sequence. I'm explaining this so you can figure out when your research will complete with say, a great sage.
It'd be wonderful if someone turned up a math webpage that described this all accurately, and clearly but you'll have to settle for me ATM.
On a smaller scale of 1 to 10
(1+10)/2*10= 55
1+2+3=6
4+5+6=15
7+8+9+10=34
6+13+34 = 55
If we're using our Pretender as a researcher, our first term is the amount of RP he contributes, and we start on turn one. If we're using just mages as researchers, we start on turn two. And our first term is the amount of RP they contribute. We'll go with the latter.
n is the number of terms in the sequence, or the number of turns since our first mage starts researching till the time the goal is reached.
t1 = first term, 8 RP of Golem Crafter
tn = last term, 8xn
ARG = Aggregate research goal, or 360 in this example
the basic formula.
(t1+tn)/2 * n = ARG
pumping in what we know...
(8+8n)/2 * n = 360
Trying to isolate n, the unknown variable, we multiply both sides by two.
(8+8n)*n = 720
We now multiply that out
8n+8n^2 = 720
We now divide both sides by 8.
n+n^2 = 90
We can pump various turns into the variable n for a precise answer, but since this game is filled with plenty of variables, an estimate is all we really want. So, we just pump the right half into a calculator and press square root. We then round up to the nearest ones place.
Now, there's all sorts of things you can do if you really want to be an aggressive researcher, that throw this out the window, but some of them, like another library and/or fortress just require two series.
All in all, the point of this is simply to provide a measuring stick to weigh your progress against that critical first year, and decide how aggressively you need to recruit mages, what it will cost you, and what you do with them. And what's practically achievable. I don't actually use this formula during a game, but in play by email you have all the time to micro you want.
I've been yapping all this time, but its easier than being concise. Hope you've found this of some use. Let me know if you appreciate it, or it put you to sleep.
Research Cost
Linear Mode
