In order to be able to use this guide you need a scientific calculater that is capable of calculating logrithims. The math really isnt that complicated just follow my steps.
Here is a spread sheet that is great in terms of planning out a city http://miramar4.com/training.php this spread sheet doesnt tell you what attack level you need per unit time, so the following is still realitivly useful.
IVE BEEN TOLD THAT SOME PEOPLE'S BROWSERS ARE IDENTIFYING VIRUS' ON THIS SITE, USE AT OWN RISK
*Note* I did not make the spread sheet it was refered to me
So there are lots of guides on this forum site listing what hero attack is needed in order to be able to make instant troops. These levels are listed below, the first column is the hero attack needed without Excalibur, and the second column is the hero attack needed with Excalibur applied:
warrior 432 / 346
worker 571 / 457
scout 709 / 568
pike 790 / 632
sword 871 / 697
arch 959 / 768
cavs 1030 / 824
porter 1168 / 935
cats 1249 /1000
ballista 1388 / 1111
rams 1468 / 1175
pult 1526 / 1221
These attack levels are common knowledge throughout evony, but what isn’t known is what hero attack is needed to obtain a certain training time. For example Player X wants to know what hero attack is needed in order to be able to make 1 second scouts. Player X wants this information so that he can predict when he should start to remodel his cities and increase his population.
What we need to be able to calculate what hero level is needed for each troop time is the basic equation for troop building.
This equation is: time=(base buildtime)(.9^σ)(.995^hero lvl) I will call this eqn#1
Where: σ=the level of military science or metal casting, whichever one is relevant
So in order to calculate training times we need to know the following information: Base buildtimes, Military science/Metal casting tech levels, and the hero level.
So its logical that in order to find what hero attack is needed to obtain a certain time we need: Base buildtimes, Military science/Metal casting tech levels, and the time desired.
We can manipulate eqn#1 using logrithims and get this as the basic equation:
ln[(time+1/base bt)/.9^σ]/ln (.995)=hero lvl I will call this eqn#2
Again where: σ=the level of military science or metal casting, whichever one is relevant
*note* the time+1 is necessary so that when eqn#2 spits out the hero level needed you will get the level that pertains to the beginning of that time range rather than the end of the time range
So now we have the equation, you know what time you want the equation to spit out, you know what your Military Science / Metal casting tech level is, what you don’t know is the list of basic buildtimes. I found them and posted them below:
The list of basic buildtimes for each unit are:
warrior - 25
worker - 50
scout - 100
pike - 150
sword - 225
arch - 350
cav - 500
cat - 1500
balli - 3000
ram - 4500
pult - 6000
The ones in blue are the ones that need military science techs
The ones in orange are the ones that need metal casting techs
So now we have all the variables so I will provide an example, using Player X, who wants to know what hero attack is needed so that he can make 1 second scouts, he knows that he has level 10 military science, and using the buildtime chart he knows that scouts have a basic buildtime of 100, so he puts these numbers into eqn#2
ln[(time+1/base bt)/.9^σ]/ln (.995)=hero lvl with Player X becomes
and the hero attack that comes out is 570. So he knows that with a 570 attack hero his scouts will go from taking 2 secs to make to taking 1 second to make. Any attack less then 570 he will have a scout building time of more then 1 second.
Part 2 With Excalibur taken into account
Lets say that Player X has an Excalibur that he wants to apply to the hero, but he wants to wait until applying it will give him 1 second scouts.
We know that Excalibur raises hero attack by 25%, so we can introduce that to eqn#2 by multiplying the hero attack level by 1.25.
so it looks like this: ln[(time+1/base bt)/.9^σ]/ln (.995)=(hero lvl)(1.25)
then we divide both sides by 1.25 to get hero attack level by itself and we get
(ln[(time+1/base bt)/.9^σ]/ln (.995))/1.25=hero lvl this is eqn#3
Using Player X again, with his desired time of 1 sec scouts, his military science being level 10, and knowing from the chart that scouts basetime is 100, we put the numbers into eqn#3 like:
Hero attack level is 456
And now Player X knows that when his hero gets to 456 he should apply Excalibur in order to get 1 sec scouts. If he applies it anytime before 456 attack he will have a scout building time greater than 1 sec.
Credit to Diamondragan for his work found here: http://bbs.evony.com/showthread.php?t=88137