Attacker Protection Build Banks/Armories

[Clampy]

This reminds me of my old simulator. While the above equations are obviously not the whole picture, they are definitely a great start and useful tools. I encourage you to work more on developing more equations for more situations that account for different assumptions.

[didy]

The most efficient way isnt necessary to have most troops oop.
Last ages I always trained knowingly late, nearly only elites, waited for further training until oop. I wanted to have less(!) troops oop. Further I razed buildings 1h before oop and let peasants run away.
This way I had a good enough offense and more imnportant were still in nw-range of the build-up inactives with 1,5 mio cash. So I could make 4 easy plunders for several millions, trained all drafted soldiers already with full leets and help team mates.

With the low numbers of provs per island this will not wotk anymore this age, I guess.

[Eigenvector]

I didn't even read the whole thing seems to much of a load of crap. One can measure the benefits of banks by taking the difference of natural income from total income. Taking the difference will give you a more meaningful answer then "/". One can measure the benefit of armories by taking the different detween the normal cost of the unit and the new cost of the unit. For example, defspec. costs 300gc the new defpec cost is only 266gc. Take 266 from 300 and you get 34gc saved on defspec training.

This is just another case of someone trying to sound smart rather than be smart.

Vines, we are measuring the same thing on different variables. You are measuring net cash while I am measuring ratios. Your measurement of banks is on the additional income you receive and your measurements of armories is on the amount of money it saves you per troop, which measures the two effects on their own terms without trying to reconcile the two. I did almost the same thing except divided both by the intrinsic values, the original values, in order to have a way of comparing their effects. If apples and oranges do different things, you need to put them both on the same scale in order to compare them. Separate analyses are meaningful and will give you a good picture, but lacks a maximization function, which you can also argue is unnecessary. You have pointed out an alternate way of analyzing the situation and I'll give you some credit. However, you haven't actually found a hole in my calculation or produced a counterexample to disprove it, so "the whole thing seems to much of a load of crap" isn't supported very well.

The argument my model is not useful holds a little more water. The model, as all models do, has assumptions, and as others have pointed out, these assumptions don't hold true for all players. If you'd like to remove the assumptions and generalize it completely, you'd just have to keep adding more parameters and make the function ever so much more complicated.

didy mentions "The most efficient way isnt necessary to have most troops oop." Each player has different priorities and your priority may not be to train the most troops; if that's your case, my model doesn't work in your case, so you can trash it. What's efficient depends on your strategy. I'm only taking a particular case, which I assume can be useful for many players.

Bored's argument is that this whole thing is unnecessary, probably because it doesn't provide you much benefit to do the calculation. Very well. Most people manage without any calculations at all and it's definitely possible to have a good build strategy without doing any math. I'm looking for an exact optimal number, which you cannot get without calculations. It's possibly a lot of work for very little use, but it's worth it for me. And I don't even have the optimal build because I didn't take all the factors into consideration, only the most relevant. So it's possible my calculation is even worse than intuition or practice, in which case Asakura would be correct. But I think that my model is reasonably well representative and is likely to provide a good estimation.

Why optimize during protection? Because protection is the only time when models are deterministic, with no randomness; once ur OOP, there are random factors, that you cannot determine for sure, and the model becomes stochastic and very chaotic. OOP, your number of troops is affected by getting attacked, and there's a random chance you get attacked, which is a function of how strong your province is, and we can go on with this...However, during protection you get the benefit of knowing that everything is totally predictable, and so it's the only time where an optimization calculation is even feasible. You can do calculations for OOP, but you can't be 100% confident of the results, you can only specify and confidence interval and even then for less than 100% confidence. And then you have to use statistics to do it. It's at that point when I say it's not worth doing the calculation.

Saveid, you are correct in that armories reduce draft costs which provides an extra benefit I didn't already mention. If you include that, you'll get a better model than mine, in which case you'll probably end up with even more armories. My model is of course, incomplete, but I think it's a reasonable approximation, taking only the factors that affect your outcome the most. Also, I'm playing orc this age, which is affected by draft costs considerably less than the others, and I was thinking a little more for myself than for the general case. ;) About your OOP build, I'm making the assumption of a complete conversion OOP, in which case the OOP build is independent of the protection build. In protection, I'd go 30% banks and 30% arms; I'm thinking about 10 hours to OOP, I'm razing the majority of them and building TGs, forts and whatever else I need. And now you can say I didn't factor the raze and rebuild costs into the equation; correct.

[MorbidAngel]

tl;dr

[Saveid]

Vines, we are measuring the sa ... ation; correct.

I see you have gazed into the eyes of entropy, my friend.

[nooblet]

Few players sit on 400a in protection, even if they want to be primarily warring kds. Coming out with more acreage means having more off/def overall, and more room to grow. That alone will throw off your calculations in a big way

I usually go for 30/25 banks/arms or close to it. For players staying small oop though I'd have some training grounds built in protection, as there's not an absolute need to maximize training (unless you want 'leets or a high tpa out of protection). Plus depending on your plans you may not need that many guilds or towers. 10/2% each is ample for non-mages without ToG.

[Eigenvector]

why wouldnt a DE or human build more banks than someone else?

+30% income and ToG are 2 damn good reasons in my mind....

also, orc saves money on draft costs, so therefore has less need for arms
gnome's army is similarly dirt cheap, so higher bank % are better for them

also, at lower drafts banks, with minimal army, banks far far far outweigh arms, arms rely on 3 things to be profitable, reduction in wages (N/A) draft costs (see the point here) and troop training (doesnt happen until last 18 hours)

i can potentially see the point in building a decent % of arms so they come in just before training time, but no sooner...

EDIT:
your post also assumes draft + training, that only happens for 18 of the 50 hours after buildings come in... for 30 hours, you are only drafting... not training... for that you want a higher ratio of banks over arms

You're make a point in that humans and DEs have additional income inflation factors; I missed those completely. However, the additional income increases your income bonus from banks by the same proportion as your natural income, so I think the bank benefit remains the same.

Adjusting our income function for humans, for example, we just multiply the whole thing by 1+30/100 or 1.3:

I(x)=1.3(1+1.25x(1-x/400)/400)(20250+25x)
The income benefit function is I(x)/I(0), and I(0) becomes 1.3*20250. Because the multiplication factor is a constant and the ratio is multiplied by this constant on top and bottom, it actually cancels itself out and the ratio remains the same.

It's intuitive to think that, assuming buildings are meant to be equal, if you can't use all of the effects of building A but you can use all of the effects B, building B is more useful than building A for you. That would be correct assuming that the two were equal for the same particular goal. However, just for the purpose of training troops armories are actually meant to be better; for miscellaneous income for the rest of the game, during which you don't have as much of a need to train troops, banks are meant to be better. Armories don't actually need all 3 of its effects to be profitable. In my model, I was actually only using 1, the reduced training costs. If you include the other 2 you get a better model and it would actually result in even more armories to banks. However, it's actually not too difficult to picture how armories can be as good or slightly better than banks even just the one effect I used. The bank's income modifier is 1.25 and the armory's reduction modifier is 1.5. So intuition tells us 1 armory should do more than 1 bank. Add in the fact that the bank gives you 25gc and you even out banks and armories. Add in the armory's other 2 effects and armories get a little better again.

You're correct in that training only accounts for a little of the time. That's a pretty big one. Stupid me; I forgot that the time factor of each building is different. OK then, banks are probably better. You win. I made a mistake. The model is still correct as long as the assumptions are true, but apparently, they're not, so it's not very reliable for the majority of protection. But just for that 19 hour training period at the end of protection, my model should be pretty good =D

And Garety, about that income function, mine is hand derived, but I think it's correct although unproven. The outside 1.25x is the increase from the building and the (1-x/400) is the reduction from additional units. My hypothesis was that the effective rate of a building is 1 minus the original rate. Supposing 1% of a building yields 2% of effect. 10% of the building gives you 18%; 20% gives you 32%; 30% gives you 42%; 40% gives you 48%; 50% gives you 50%. Your function yields slightly higher effects than mine does for each of the building rates. I may be wrong about this because I derived the formula myself, but it's hasn't produced a wrong calculation so far on my internal affairs pages throughout the last couple ages. The maximization I solved by graphing with the TI-83; I didn't actually do the derivative ;) but I just stated that that's the way you're supposed to solve it numerically.

[Eigenvector]

nooblet, I recognize that many people choose to grow. I'm not considering those cases and have not calculated for those cases, so the model does not apply for those cases. The model only works under certain assumptions.

Kuhan, if you don't mind my opinion, vines' argument was the least valid one of all and was hardly even an argument. Most of the others had some good points.

[Lead Pipe]

Eigenvector, it's a good start, but the model needs further refinement. It assumes all money is spent on troops, which isn't realistic. You need to factor building costs, BE, thief training, racial characteristics, and perhaps aid or savings. Also, it looks like the model is simply looking for the largest combined bonuses instead of the most efficient build.

[garety]

Yeha eigen, i looked back over my original eqn and my reduction to your eqn, and yeah, i had an error in my reduction. caught it and yeah we both had the same eqn.

[Turtle Man]

does the game have to be this complex? i dont like this game very much when it gives me a headache

[Eigenvector]

haha, no it doesn't my good TurtleMan. If you're not into mathematical analysis, then don't do it. It's not entirely necessary for good gameplay. However, if someone else has already done the work for you, feel free to use it to your own advantage =D

[Bishop]

banks are more flexible than arms, so they always win out.

[Saveid]

Not always, but most of the time.

[Eigenvector]

It's the versatility of banks that carry you through the rest of the age. During, protection, however, your priorities are very specific and you can plan accordingly. Read my response to greenie's argument for my mistake and why banks are still more useful for the majority of protection.