How to Calculate Training Cost-Effectiveness

[Pinky]

One of the things I've been vocal about in this round is the cost of Training at the Barracks. It's not going to change, at least until the next round begins and the Conquest is reset. So, I might as well share with you the methodology of how to figure out when and why to buy it. This is going to take a while because I have to explain it in detail, but once you read it all then you'll see that it's just a series of very simply math problems.

The first step is to recognize the exponential factor. Exponents have an arcing effect which changes over X, not a constant progression, so it's not wise to buy Training simply because you have the money for it: if you buy it when your item stockpile is too small then the cost-effectiveness of Training will be less than if you had simply bought items which puts you at a lower level than a peer who has bought items, but if you buy it too late you put yourself at risk against a peer player who bought Training. You need to know the right moment to Train.

Since Training only affects item's Point value, we need to figure out how many items to stockpile before the next level of Training becomes desirable. In order to do that, we have to know what item to buy. So, let's begin by taking a slight but wholly necessary detour and figure out what items we should be buying.

tier1 item: 20 Points costs 25 G (0.8 Points Per Gold)
tier2 item: 30 Points costs 50 G (0.6)
tier3 item: 50 Points costs 100G (0.5)
tier4 item: 95 Points costs 200G (0.475)

There are several more items, but we can already see a clear trend: as the cost of the item goes up, the effectiveness of spent gold goes down. Considering that you can train a virtually unlimited number of Troops to use the items and the fact that it's so much easier to train Troops than buy items, there is no reason for players seeking #1 status to ever upgrade to or directly purchase any item above tier1. With that mystery solved, we have also discovered that 0.8 PPG is the magic number to determine Training viability - if the next level of Training will not gain you at least 0.8 PPG then it is not worth the money and you need to buy more items, but if the effect of Training is greater than or equal to 0.8 PPG it is time to buy.

Now, we can get to the calculations.

To find the cost-effectiveness of Training, first find the number of items we can purchase for the amount of gold that the Training costs.

Tier1 Training costs 1,000G which is worth 40 tier1 items.
(1000/25=40)
($/25=I) [use these equations by inserting relevant values]

Then, calculate how many Points the cost-equivalent amount of items is worth.

tier1 items give 20 Points each. 40 tier1 items produce 800 Points.
(40 x 20 = 800)
(I x 20 = P)

Take the amount of bonus that the Training will deliver. This one is simple. Every level of Training in this round of Conquest adds 20% more to your item value. This makes the process of calculation much, much easier since the exponent never changes. If it did change, then we'd be up Shit Creek without a roll of toilet paper, but it doesn't... for now.

So, we have two very important figures: the first is "P", or the Point value of items that were of equal cost to the other number, which is 20%. 20% of your Offense or Defense must be greater than or equal to P in order for Training to be worth the investment.
(20% >/= 800)
(20% >/= P)

Since 20% is a nice, round number this step is easy. Multiply P by five to find what 100% of your item stockpile's Point value will have to be in order to make Training a good purchase.
(800 x 5 = 4,000)
(P x 5 = S)

According to the math in this particular instance, your item stockpile's Point value has to be 4,000. This is the last step: how many items does it take to get to the center of a Tootsie Pop to equal S? To find this, we simply divide the requisite stockpile's Point value by the per-item Point value.
(4,000/20=200)
(S/20=X)

200 items. In order to make tier1 Training worth your while you must first have at least 200 items of the appropriate kind, either weapons or armors. Once your weapon or armor item stockpile reaches that number, the amount of gold you need to spend on tier1 Training becomes useful. Afterward, once you go back to buying items the exponential factor of the Training continues to increase in your favor. 20% of 200 items gives 800 Points; 20% of 250 items gives 1,000 Points; 20% of 500 items is 2,000 Points, and so on. Don't get dragged off point by the promise of power-to-come: buying Training will always lead to greater gains later down the road regardless of when you get it, but it's more efficient to spend money on items first until you get to the point when Training is projected to be worth more than a cost-equivalent amount of items. Thus comes the phrase cost-effective.

Now, just to see how this works in rapid fashion, let's calculate the point at which the final tier of Offense Training - Mystic Upgrade - becomes cost-effective.

1) ($/25=I)
50,000G/25=2,000 Items

2) (I x 20 = P)
2,000 items x 20 = 40,000 Points

3) (20% >/= P)
20% >/= 40,000

4) (P x 5 = S)
40,000 x 5 = 200,000

5) (S/20=X)
200,000/20=10,000

Unless I've missed something, you will need 10,000 items to make the last level of Offense Training worth your gold. The last level of Defense Training is even more expensive - good luck with that. Also, you can replace steps 2-5 by multiplying "I" by five (I x 5 = X), but it's important to show you every step so you would know how to do this by hand without making any blind leaps... and I was bored. Haha, it's too late now, you'll never get those five minutes back! Nevar!!!