Unit Valuation

Tophats and I were having a conversation about balancing units, and since the game has many variables, I tried to hold as many constant, or neglect them due to minor influence. So here is the formula:

(((HP/7)* Attack * (pi * mov^2)) / (1+(Cost/1000))^Turns) + (((HP/7)* Defense * (pi * mov^2)) / (1+(Cost/1000))^Turns)

Essentially the attack power divided by the exponential cost + the defense power divided by exponential cost.

If the unit cannot take a city, I divided the attack power and defense power by 3 to compensate for the major difference other units have over it.

In addition I made a graph and entered the number for the majority of the strategy, you can try doing the same to test the
validity of the result.

http://pdfcast.org/pdf/unit-balancing

The finding tells which unit should be used based on turn of the game. If you set turns as a variable, you will receive a nice exponential curve. As you may expect the strong expensive units are more favorable in the beginning and the cheap units are more favorable in the long games.

Let me know what you guys think

This will be very useful.
Finally more than just mere face valuations to see which units to use.

The interesting thing to note is if you give PD infantry a range of 16 (Mov +1 & Carry Inside the transport)

Early value would reach about a whopping 10k total, 4k middle, and 2k late game.

Nothing stand in the way of this mammoth in value. Hence a numeric reason why PD is a very strong strategy. Therefore, if you can increase the range of PD infantry in the game via air tran or water tran, the value of this strategy is very impressive.

Yes, of course, common sense, PD strong but meant to be slow. Inf upgrades takes away nerf, use transports to effectively traverse terrain, you can afford air transports very well with all the money you save, for certain situations. This completely overcomes its weak points and makes it very, very OP.

A lot of this I already do, blitz militia and inf very strong late game. The -1 defense doesn't become so bad when you can speed them in numbers to your front line very quickly. I usually strike one or two turns after reinforcements when the enemy still hasn't got all their units in place for the predictable before reinforcements rush. AA with blitz very effective against SM. This is it's big strength and counter to SM when faced against each other. Usually it would only be useful in cities that you know an SM player will hit, with blitz you can move them to your frontlines along with every other unit.