Determing Hero Troop Training Times at every level

[Lucas101]

*DISCLAIMER*

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

ln[(2/100)/.9^10]/ln(.995)=hero lvl

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:

(ln[(2/100)/.9^10]/ln(.995))/1.25=hero lvl

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

[Lucas101]

So I've searched forums for the equation expalining buildtime of wall defenses, but haven't been able to find it. However, it is obvious that wall d, like the construction and troop building equations, is dependent on the basetime being affected be the relevant hero level, in this case politics, and the appropriate tech level, in this case construction. So the equation that will be used is

(Base time x 0.995^Politics) x 0.9^Construction level=time

The basetimes were unknown, or at least unpublished but using the list on instant wall d levels with lvl 10 construction, it is possible to determine them by changing the equation to look like this.

Base time = [(1/0.9^10)/ 0.995^Politics of instant unit]

Unit hero lvl for instant builds (without W.O.N / With W.O.N)
Traps 607 / 486
Abatis 745 / 596
Towers 826 / 661
Logs 965 / 772
Trebs 1066 / 853

After some basic substitution the numbers below are derived as the base build times (in seconds) of each separate wall defense.

Unit basetime
Traps 60
Abaits 120
Towers 180
Logs 360
Trebs 600

So again using logarithms it becomes apparent that the equation for determining hero politics level for x time is:

ln[(time+1/base bt)/.9^σ]/ln (.995)=hero lvl
where σ is the level of construction

So for an example, Player A wants to know what hero politics level he needs to make build time for traps 2 secs, he has lvl 9 construction.

So time=2+1,
basetime=60, σ=9, put the numbers into the equation like below

ln[(2+1/60)/.9^9]/ln (.995)=hero lvl
408=hero level

With wealth of nations applied As shown above with the Excalibur condition the same must be done with the wall d equation, so the wall d equation for a hero with Wealth of Nations applied is:

(ln[(time+1/base bt)/.9^σ]/ln (.995))/1.25=hero lvl

So using the above example for 2 sec traps and level 9 construction, and a pol hero with wealth of nations applied we get:

(ln[(2+1/60)/.9^9]/ln (.995))/1.25=hero lvl

327 is the politics hero level needed for 2 second traps with lvl 9 construction and wealth of nations applied.

Many will think this guide to be useless, but it is valuable to be able to know when you should be changing barracks to cottages, and these models allow the player to be able to accurately predict a time frame when s/he should start to remodel their cities. Furthermore these models can also predict when a hero is high enough that it no longer needs the academy bonus to produce instant troops. This means that you can have 10k more pop per production que in a scout or other STRICTLY unit building city, that when not needed you can store amongst the alliance members.

Also when used with this tool http://evonypedia.com/Hero_Experience_Calculator this guide is very effective in terms of figuring out how much experiance to stockpile on a hero before holywatering it to get a certain buildtime of wall d units.

Props to Aegless.OG for his guide which can be found here http://bbs.evony.com/showthread.php?t=114222

To avoid future headaches props to Prodigy the 5 for his instant with buffs levels found here http://bbs.evony.com/showthread.php?t=152292
This is also an excellent guide that covers all the basics so I would strongly recomend reading it.

[Lucas101]

K so after finally getting a huge pol hero I was very dissapointed that the incorrect time was shown for lvlingup/lvling down buildings,so being thebored geek that I am I decided to finally finish another portion of this guide that being the buildtimes of town units affected by the politics of the mayor.

So first we start with the equation of the politics level of the mayor affecting the buildtime of townunits. This equation is:
time=(Basetimex0.995^PoliticsLevel)x0.9^Constructi on level which will be refered to as equation 1

using, suprise, properties of logirithms this equation can once again be changed to show what hero politics level is needed to acheive z time

time=Basetimex0.995^PoliticsLevelx0.9^Construction level

time/basetime=.995^PLx.9^CL

(time/basetime)/.9^CL=.995^PL

ln((time+1/basetime)/.9^CL)/ln.995=PL this will be refered to as equation 2

Again the time+1 is incorperated into equation 2 so that you get the begining of the time incriment rather then the end of it.

Thanks to Satan all the buildtimes are known and listed here: http://bbs.evony.com/showthread.php?t=83430 and its post number 4. I'm not gonna repost every townunit because it is alot of informtion and this guide is cluttered as it is. Just remember that for the formula to work properly you must convert all times into seconds.

I will however repost resource feilds of iron and lumber, they are as follows:

Ironmine/SawillLevel
time (in seconds)
190/45
2180/90
3360/180
4720/360
51440/720
62880/1440
75760/2880
811520/5760
923040/11520
1046080/23040

I'm sure that 99% of readers can see the way that the numbers increase on a basic expodential scale as the level increase by one. This rule applies for all town units.

So for a quick example lets say that player Pskonejott wants to know at what level does he need his pol to be at so that he can attain instant lvl 10 sawmills with full techs.

ln((0+1/23040)/.9^10)/ln.995=PL

In this case the number 1794 pops out which is suprisingy low. Can anyone get a hold of Bob with his 2k pol and verify?

The problem with the way that the heroes politics level influences the buildtime of townunits is that after a certai level it makes sense to cease the leveling of the big politics hero, and instead begin to level a diffrent one. This is because of the relationship of the pol hero to townunits being expresed as a logarthmic function, and thus decreases in town unit build time mean a greater amount of politics must be gained in order to ge to the next time incriment. This combined with a higher amount of experiance needed to get to the next experiance level means that at a certain point it becomes very inefficent to level up a pol hero, and instead a player should focus on devolping a second politics hero. What this level actually is, is not known, but can be calculated, that will be my next post, but wont be done for a while.

Sorry for typing in this section espically, my laptop is lagging or something, i have to retype each word three times it seemes

Credit to Satan for his thread, linked above.

[Facade Infinite]

http://bbs.evony.com/showthread.php?t=73243&page=2

That tables off abit... .

However the sort a range gives an idea.

[Lucas101]

http://bbs.evony.com/showthread.php?t=73243&page=2

That tables off abit... .

However the sort a range gives an idea.

yeah lower units are a bit off, but table is great nonetheless, makes my eqn look bad , kinda wish i had found this chart couple months back, would still have some hair left lol + rep

[Lucas101]

Definite Rep.
Now, do u have any idea what the Poly points numbers are for, instant:

Lv.9 Barracks

Lv.9 Academy

Lv.10 Walls

etc?

Finished ..........

[Lucas101]

*Reserved for buildtime of townunits*

[NaughtyKittens]

+rep. Very good information. Thank you. I bet that took a while to create :O

[Alil]

Thanks, very good information. Glad to see you are working so hard to make my life easier.

[Fragsrus]

Lucas101, do you think you could put those formulas into a usuable spreadsheet? Add drop down boxes for the various units, then have a blank field for attribute level and the resulting build time, such that entering the attribute level would produce the build time or entering the desired build time would result in the needed attribute? I think I know someone else that can do it, but figured since this your work I would bring the idea up to you first.