Rushing time with crowns formula?

[Aitor-NationsLeague]

Hello all, so this is something I have been wondering for a time, I think you will have all realised, that rushing short times is expensive than rushing longer times, I mean, rushing 1 hour twice is more expensive than rushing 2 hours once.

So as I'm a free player and don't have too much money for buying crowns, I'm thinking how to get the most of the ones I get for free... I'm French, so no real need of rushing army, only use is rushing Armory, because it's the real bottle neck, better than rushing buildings.

But so far, I don't know when do crowns get the most value?

These are some examples I can grab from my current buildings and research:

19 hours 240 crowns ~ 12.5 crowns an hour
1 d 7 h (31 hours) costing 343 crowns = 11 crowns per hour of rushing
3 d 6 h (78 hours) 622 crowns = 8 crowns an hour
4 d 1 h (97 hours) 735 crowns ~ 7.5 crowns

So it seems like it approaches 7 crowns after 4 days, and not too much change after? So rushing 3 days or 4 or 5, is already good enough and won't make that much difference after?

Putting that data in this online web page http://arachnoid.com/polysolve/, it really seems to follow a polynomial regression, but I don't know if that will hold for longer times?

So function for calculating how much crowns are we gonna need for a given time:

f(t)=6t+135

I think. :S Unless someone has any link or website where they have figured out better? But anyways I don't think that in Armory there are gonna be too much ocassions for rushing that many days, but was just curious and wanted to check with you if someone has though about this. :S

PD: And yes LOL, I'm bored a lot

 

[Brand Marrow]

I think u should b a researcher like me Aitor, apply your quantitative analysis to some cool biological data

 

[vincentdang4]

This was very helpful. Thank you Aitor.

 

[Aitor-NationsLeague]

I think u should b a researcher like me Aitor, apply your quantitative analysis to some cool biological data

Started studying Physics, but I have to leave it , was going to have Biophysics courses the year I left, I was curious about that

But then guys, what do you think? Does it makes sense what I say? Can you check with the experience of your current buildings?

The only issue is that, as I say, there aren't that many 5+ researches in the armory... Generals are 2 days or 3, so I'm still thinking the better way to expend the crowns and rush the overall game... :S Guess when I start research of the Heavy Tank MK2, what is 8 days, I will have that data in crowns to check against that formula... :S

 

[Ravenlord]

19 hours 240 crowns ~ 12.5 crowns an hour
1 d 7 h (31 hours) costing 343 crowns = 11 crowns per hour of rushing
3 d 6 h (78 hours) 622 crowns = 8 crowns an hour
4 d 1 h (97 hours) 735 crowns ~ 7.5 crowns

If this is true then it makes sense. Naturally, Nexon would like us to use crowns to speed up buildings but at least they're giving us a bonus of less crowns per hour the sooner we do it. Thanks Aitor.

 

[GailWho]

Great post!

Here's more data for you ...

8d 23h (215h) 1356 crowns = 6.30 an hour
19h 9m 241 crowns =12.68 an hour

PS I have bachelors in Economics I love math and graphs!

 

[Ravenlord]

''maths and graphs'' ??! Go you party animal .....

 

[Atinyfish1386]

This post has way to much math. It's great info. Thanks!!!

 

[Jo-jo]

The next thing to consider when spending crowns is where you are in a chain of upgrades. For instance, if you rush the last item in the armory in Enlightment Age, you only get that single upgrade sooner. (The armory will sit idle for many days until you upgrade TC) However, if you rush the first upgrade in Industrial Age in the armory, you'll have the chance to get all those upgrades sooner. (As long as you can keep the armory active.)

 

[Jo-jo]

mins	crowns
749	167
3415	502
1795	339
2035	360
117	36
154	43
362	85
1148	243
1435	300
1418	297
749	167
462	105
5	0
1	0
2940	455
6	1
93	31
197	52
188	50
78	28

Here's some more numbers from when I did this a while back

 

[Xerxes]

For buildings, is it relevant how many workers it takes to upgrade? So would a farm (2 workers) with 1 day left, a tower (3 workers) with 1 day left, and a garrison (4 workers) with 1 day left all require the same number of crowns to complete?

 

[Aitor-NationsLeague]

@Xerxes: It is the same cost no matter the buildings, so yes, it's relevant, when rushing buildings, ALWAYS RUSH ONLY 4-WORKERS ones

@Jo-Jo: Sure, totally, rushing only make sense if you have something to do next, in my opinion, starting IA Armory is yes the perfect place for spending crowns, because time long there, and you can have resources faster, so according to my theory, for example, rushing: Tanks, rushing 6 days, starting Artillery, rushing 6 days, etc, assuming you can gather the food in those two days, feels like the most optimal usage of crowns for me...

About your data and GailWho 8d 23h (215h) 1356 crowns = 6.30 an hour

f(t)=6t+135 -> 6 x 215 + 135 = 1413, the function that website gave me, overstimates a bit the number of crowns necessary, it still keep lowering with increasing times, although 8d 23h, it's a very long time, not for Armory actually (only Treason tactic), it will be relevant only in the case of rushing buildings, but seems the crowns keep lowering... Probably it reaches 6 crowns for an hour worth of rushing at some point near 10d or more, I guess this might become relevant when we have Global Age, if upgrading times are terrible...

Your data all seems to match with my formula, only for lower times, it understimates a bit the price.

So assuming it can be taken as a good aproximation, a small rule could be:

Rushing less than one day is expensive, more than 10 crowns per an hour worth of Rushing.
It starts decreasing, at 3 days we reach 8 crowns per/hour, 4 days it still a bit more than 7 per hour
And it needs almost 9 days to approach 6 crowns per/hour.

So feels safe to say in my opinion that the best way to use, if possible, will be to rush for at least periods of 3 days.

Save the crowns, and rush at least periods similar to those. Depends if the rushing is for armory or buildings, if buildings we can wait longer, but doesn't feel like the gain in value is that relevant within the pass of days, while waiting from 1 day to 3, we get a significant more value.

Rushing a single time a 3d research >> rush 3 times 1d researches.
Rushing a 6 day research > Rushing 2 times 3d researches, but the gain isn't that much relevant.

600 crowns is a good amount to gather, and then that's "safe" to expend rushing...

 

[vincentdang4]

If you need to rush a trap in 1 day (1 worker), it cost the same amount of crowns as rushing the completion of a barrack in 1 day (4 workers). The number of workers does not matter, it is simply the amount of time

 

[Jo-jo]

I graphed the same curve that Aitor-NationsLeague did, but it kept bothering me. I went back with a fresh set of eyes and approximately 2 gin and tonics and came up with the crown per time formula.


The first 24 hours is a curve topping out at 300 crowns. After that, each additional hour is 6 crowns. The cost never changes after the first 24hrs.

 

[BV123]

For buildings, is it relevant how many workers it takes to upgrade? So would a farm (2 workers) with 1 day left, a tower (3 workers) with 1 day left, and a garrison (4 workers) with 1 day left all require the same number of crowns to complete?

Yes... what VD said is true. The no. of workers do not affect the amount of crowns. A 1 worker item as compared to a 4 worker item, takes the same amount of crowns from the same amount of time.

 

[Empyra]

I think it's,
300 crowns for the first day (12.5 per hour), and then 6 per hour (144 a day) until the 7th day. From the 7th to the 11th day it seems that it's at 4 per hour (96 a day). Day 12 and 13 seem to be at 5 per hour (120 a day). I don't have enough info on over 13 days to know if it's still at 5 per hour between 13 days left and 14 days left.

1 day-300
-----------------(+144 a day)
2 days-444
3 days-588
4 days-732
5 days-876
6 days-1,020
------------------(+96 a day)
7 days-1,164
8 days-1,260
9 days-1,356
10 days-1,452
11 days-1,548
-------------------(+120 a day)
12 days-1,668
13 days-1,788

This works with what I have upgrading right now and am very curious if it's the right formula!

 

[Jester]

For 21 days, its 2714 crowns.

 

[Eddie F1]

What takes 21 days?

 

[Jester]

Forests of course