Stables vs. TG's

[bowman]

So the forum has been pretty slow lately, I thought I'd get everyone's opinions on some numbers I've been crunching in regards to Stables vs. TG's.

**Warning! Calculus ahead!**

I started with just trying some different ratios and determined there is (sometimes) an optimum balance between the two.

Starting with a few definitions:
raw = the raw OPA from elites/specs/soldiers
per = the percent of land available for stables/TG's
be = building efficiency
tg = percentage of land to devote to Training Grounds
st = (per-tg) = percentage of land to devote to Stables

So,

OPA = (raw + (60*st))*(1+(1.5*be*tg*(1-tg)))

substituting (per-tg) for 'st', we get

OPA = (raw + (60*(per-tg)))*(1+(1.5*be*tg*(1-tg)))

Now, to find the optimum, I differentiate with respect to 'tg'

dOPA/dtg =((raw + (60*(per - tg)))*(1.5*be*(1 - tg) - (1.5*be*tg))) -
(60*(1 + 1.5*be*(1 - tg)*tg))

. . . and set the derivative equal to 0

0 = ((raw + (60*(per - tg)))*(1.5*be*(1 - tg) - (1.5*be*tg))) -
(60*(1 + 1.5*be*(1 - tg)*tg))

Here's where it gets complicated. The optimum 'tg/st' ratio is a function of 3 variables (raw, per, and be). As an example, I'll use typical values for 'raw' and 'be', and give the optimum 'tg' and 'st' values as functions of 'per'.

So, letting be = 1, and raw = 60, we get

tg = 0.00185185*(360 + (180*per) - (180*Sqrt[3 + per + per^2]))

(the other solution is nonsensical)

Looking at this equation, it is clear that if 'per' is less than 11% it doesn't make sense to use any stables at all. However, as 'per' increases, the optimum percentage of stables increases (at per = 25%, tg =14% and st = 11%).

Of course, as 'be' or 'raw' increases, the solution will yield more TG"s, as they benefit from higher BE and higher raw OPA.

Likewise, the Artisan personality will yield more stables in the solution.

I'd love some input from the community, i.e. ideas, things I've overlooked, etc.

[UtopiaOfGreed]

There is no calculus in this post.

Rejected.

[bowman]

Last time I checked, derivatives were taught in calculus class.

I could be wrong . . .

[bowman]

But thank you for that incredibly useful input.

[SillyPanda]

I will admit that these equations are elegant.

HOWEVER.

You forgot draft rate. Formulaic understandings of [insert any given subject matter] strategies often ignore the "Human Variable". Which is to say that each person is different and likewise must adjust for each one. Which is what these equations don't do. If you and me both hit 120 opa that's fine and dandy. However, if you hit 120 opa with 75% draft (stupid, I know, its just an example, so let it slide) and I hit 120 opa with 50% draft (again, its an example) our ratio of ST's vs TG's will vary substantially. Yet, according to these equations they wouldn't.

Before anyone skims through the post.

raw = the raw OPA from elites/specs/soldiers

Does in fact, not, take into account physical numbers. 80 opa from 10K elites and 80 opa from 13.3K elites are 2 different numbers. Going by 1 leaves the other short, and going by the other leaves its opposite wanting more.

Again, these equations are elegant. However, at current, non-applicable.

[bowman]

As far as I can tell, the only way draft rate should affect the ratio, is through its effect on BE. And BE is taken into account in the equations.

I believe you may have misunderstood my definition of 'raw'. I was taking this variable to be the combined raw offense per acre from elites, specs, and soldiers (all units except horses.) The mix of units that constitute this value is irrelevant as long as it is greater than the number of horses, which it will be in most cases.

[SillyPanda]

...

okay.... Hypothetical Situation:

- I play an Orc. You play a Human.

- We're both at 80 raw opa.

- I hit 80 raw opa using 10K elites. You hit 80 raw opa using 13.3K elites.

- At that point... if we use opa instead of draft rate or physical count of specs/elites/sols. I'd only get 10K worth of ST and you'd still need 13.3K.

Ergo, If I go off your numbers I, then as an Orc would have 3.3K more horses than what I could ever use sitting around eating food and crapping on my stable hands.

Likewise, If you use my numbers you'd be 3.3K horses shy of your optimum value. And have elites all like,"Hey, wtf mate... where'd you get a horse to ride on, I want one to!?"

In the end, if I've only got 10K elites/specs/sols/leprechauns/whatever... I want 10K horses. If I've got 50K, then I want 50K horses... and on and on.

Granted, if your changing the naming convention of raw to qwequegs for all it matters, is fine, and perhaps a good idea. However, at the point that raw/qwequegs/jordans/wickets/SillyPanda's Mom on Valium/Grozzit Forum Trolls/whatever still amounts to raw opa.... OPA (Offense Per Acre)... this issue will continue to arise.

kthnxbye

- SillyPanda

[bowman]

I understand what you're talking about and I have considered it. You can't have more horses than units. However, you'll find that the optimum solution for most cases yields LESS than one horse per unit.

[SillyPanda]

....

Access the hypothetical situation from my previous post.

(my hypothetical orc)

(80K + 10K) x 30%(from TG's) = worse than (80K + 5K) x 30%

how?

[bowman]

You're assuming that the solution will yield one horse for each elite, and I'm saying it generally doesn't. The reason is that there reaches a point where TG's generate more OPA than stables. My equations are attempting to determine where that point is, given base OPA, available land, and BE.

[SillyPanda]

While, your way of dodging the question was almost as elegant as your equations. The question still remains:

How is:

(80K + 10K) x 30% = 117K

worse than:

(80K + 5K) x 30% = 110.5K

?

[bowman]

Obviously it isn't, but the two situations will be using a different amount of land, which is the factor you aren't considering.

[KuhaN]

Interesting.

Most people run ~17% TGs midround, and assuming 60 raw opa like you said with 100% BE (BE should be more like 85 btw, it'll never stay at 100 midround).

You're saying it'd be better to run 13% TGs and 4% stables rather than ~17% TGs, anybody wanna argue against this?

[SillyPanda]

Obviously it isn't, but the two situations will be using a different amount of land, which is the factor you aren't considering.

- I hit 80 raw opa using 10K elites. You hit 80 raw opa using 13.3K elites.

Orc elite: 8/*

Human elite: 6/*

...

80K + 10K

80K + 13.3K

the variant difference in those is 10K 1:1 on orc elites (80K/8 = 10) and 1:1 on human elites (80K/6 = 13.3). 80K of thee aforementioned OPA offense per acre, 80 opa, which should've been a given that both provs were at 80 opa of.... 1K acres. Ergo... 80K

Which is how the orc would wind up with 3.3K horse sitting around (using human values) and the human would b short 3.3K horses (using Orc values).

All of which, was previously covered.


Um, yeah.


kthnxbye.

[bowman]

Going with your example, 80K offense, with say 1600 acres, 100% BE, and 20% of your land to work with, the solution would yield an optimum of 9.7% TG's and 10.3% stables.

So that gives, 80,000 + (165*60) = 89,900
and, .097* .903 * 1.5 * 1 = 13.14%
so, 89,900 * 1.1314 = 101,712

or, 63.57 OPA