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Chrono Boost Math

Forum Index > StarCraft 2 Strategy
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Volka
Profile Joined December 2010
Argentina410 Posts
Last Edited: 2011-03-06 16:42:46
February 23 2011 00:24 GMT
#1
I'm surprised there's not a thread about this, at least none that I could find.
I've made a table with all the units/upgrades build/research times modified by chronoboosting (CB).

Here it is:
Excel table.

I've compared the results with what we see on the game. It seems consistent. I'm quite confident on its veracity.
However, I've thought the math by myself, and since I'm not particulary good at it, I'd like you guys to check it out and see if it holds.
Also, take into account that english is not my native language so I may not express my self clearly enough, unfortunately.

If you don't mind about the math, just jump to the Conclusions&Important Timings.

Introduction
+ Show Spoiler +
As you know, every CB puts the building into an "accelerated state" in which it'll build/upgrade 50% faster for 20 seconds (those 20 seconds are "game seconds", and can be counted by the sc2 time counter).

In normal circumstances, a building builds/researches at a speed of 1 (30 seconds to complete a 30 "production units" unit/research).
The acceleration factor (50%) tells us that, during a CB's duration, the speed at which it builds/reseaches is 1.5 (20 seconds to complete a 30 "production units" unit/research).

That of "production units" is confusing. This is what I mean:
If you leave your mouse cursor over a construction bar, you'll see as your chrono that the speed at which the numbers go up increases. So the building is doing more "production units" by game second.


Why the math?
+ Show Spoiler +

I didn't mean to make this a "math postulate". I'm just expaining how I get the numbers in case:
a) You're curious and you really care.
b) Something MIGHT be wrong because nobody is perfect. In that case, more talented people can review it and I'll fix it.

In you don't care about the math, just skip all that and go to the juicy parts: conclusions and numbers.


Chrono Boost Reduction
+ Show Spoiler +

You can deduce, or do enough experiments, to get this formula.

Cr= Cd*Cf-Cd= Cd(Cf-1)

Where:
Cr= Chrono Reduction. Save of time in seconds caused by one CB.
Cd= Chrono duration (20 secs).
Cf= Chrono factor (1.5).

Computing the numbers you get:

CR= 10 seconds.

So: one Chrono Boost == you save up 10 seconds.


General Build Time formula
+ Show Spoiler +

If you apply more than one CB, then of course you get linear results:
Two chronos= 20 seconds.
Three chronos = 30 seconds.
And so on.

So the general formula to get a Bt modified by CB is:

Bt'=Bt-N*Cr

where N is the number of chronos applied.


Minimum Build Time
+ Show Spoiler +
If you apply continuous CB (one after another) is like you have accelerated time by 1.5. So the fastest BT' you can get is BT/1.5.
Which is 50% faster. This is the limit.


Number of continuous CB needed
+ Show Spoiler +

To get the maximum number of CB, you just solve the equation for N using BTmin.

BTmin=Bt/1.5=Bt-N*Cr


CB and Nexus energy
+ Show Spoiler +

We'd like get a formula that can tell us how many continuous CB (one Chrono every 20 secs) can we get from a Nexus.
This can also be used to, for example, know much energy is needed to CB Warpgate research.
That formula is (contribution of Jaeger, thanks):
Nc*Ec=Nn[Ei+ Rg* Dc*( Nc-1)]

where:
Nc= Amount of continuous CB we can get.
Nn= Amount of Nexi.
Ei= Initial Energy of Nexi.

And we solve for Nc or Ei, whichever we want to get.
We can get interesting results from this. More on conclusions.


CB and shields!
+ Show Spoiler +

I accidently found out this thing. Don't know if it's wide known but I haven't heard of this anywhere.

The fact: CB accelerates the speed at which shields recharge by 50% too!

I've tested this on a Nexus, testing how much it takes to replenish its shields without and with continuous CB on the Nexus.
Normally, when the building is no longer being attacked, shields recharge a constant rate of 2 SHP per second.
With CCB, I've found that they recharge faster, at a rate of 3SHP/sec.

You can see the results inside the Excel chart.



Conclusions & Important Timings
+ Show Spoiler +

*First conclusion: One Chrono Boost == you save up 10 game seconds.

*Second conclusion: CB is linear. The more you chrono, the more you save up and always with the same proportion.

*Third conclusion: You can get something up to 50% faster using CB. No more. This is the limit.
Note that 50% faster DOESN'T mean that it takes half of the time. It takes 66% of the original time to build (or 33% less time).

*Fourth conclusion: Buildings shields recharge 50% faster when CB! Test it yourself


Assuming continuous CB:

Colossus
*BT'= 50 (you save 25 seconds).
*CB needed= 3.

Inmortal
*BT'= 37 (you save 18 seconds).
*CB needed= 2.

Void Ray
*BT'= 40 (you save 20 seconds).
*CB needed= 2.

Warp Gate research
*BT'= 93 (you save 47 seconds).
*CB needed= 5.

+1 Ground Weapons Research
*BT'=107 (you save 53 seconds).
*CB needed= 5.

CB and Nexus
-Empty Nexi (Ei=0).
You can get 1 CB every 45 seconds.
If you have more than you Nexus, then time is split. Example: 2 Nexi, then 1 CB every 22.5 secs, which is almost enough to get continuous CB.

-Full Nexi (Ei=100).
You can continuously CB 6 times (waiting a little you'll have 7). For instance, that's more than enough to fully CB Warpgate research (only need 5 CB).

More data on the Excel spreadsheet.



That's it guys. Please let me know what do you think. Open for suggestions.
http://www.starsite.com.ar
GenesisX
Profile Blog Joined February 2010
Canada4267 Posts
February 23 2011 00:26 GMT
#2
Good, simple post. I think the main misconception people have is that they think that Cboost helps production by 100%, when its actually 50%. I know I did, lol.
133 221 333 123 111
DrBoo
Profile Joined April 2010
Canada1177 Posts
February 23 2011 00:32 GMT
#3
Thanks for this post helpful insight with math and etc is always appreciated.
"DrBoo is an elaborate troll" -Pufftrees
CodECleaR
Profile Joined November 2010
United States395 Posts
February 23 2011 00:34 GMT
#4
Ty, math was never my strong subject xD
How do you beat a terran who's hardcore turtling off 3 base? Flip him on his back and walk away."
Sek-Kuar
Profile Joined November 2010
Czech Republic593 Posts
Last Edited: 2011-02-23 00:47:48
February 23 2011 00:42 GMT
#5
I wouldnt call it simple unless you have some sort of math Ph.D. - imo its really complicated way to "explain" quite simple thing.


But whatever, some ppl might like, but you are missing one thing:
Nexus regenerate 25 ene in roughly 45 sec (45*0,5625= ~25), so using energy from single nexus you can boost something by 50% for 20 seconds every 45 sec, so one nexus is capable of boosting something by 22% in total using constant chrono boost (50%*20/45) if no energy was saved.


This means that when you have only one Nexus and with no energy saved, if you start CB something you can reduce build/research time to ~82% of original.
Scientists finally discovered what's wrong with the female brain: On the left side, there is nothing right, and on the right side, there's nothing left. [http://eu.battle.net/sc2/en/profile/213948/1/DJVibrejtr/]
Jaeger
Profile Joined December 2009
United States1150 Posts
February 23 2011 00:42 GMT
#6
Should add that since chrono boost requires 25 energy and lasts 20 seconds and a Nexus regenerates energy at 0.5625 energy per second having 2 nexus almost allow you to chrono one building constantly.
https://www.dotabuff.com/players/8137911
avilo
Profile Blog Joined November 2007
United States4100 Posts
February 23 2011 00:46 GMT
#7
good stuff, and holy shiot...saving 25 sec on collosus is pretty insane...-_-
Sup
Rantech
Profile Joined April 2010
Chile527 Posts
February 23 2011 00:50 GMT
#8
Very useful information here, nice work, i was trying to find something like this. Thx.
Beefwipe
Profile Joined October 2010
United Kingdom56 Posts
February 23 2011 01:27 GMT
#9
My common misconception was that chrono boosted things by 20% for 50 seconds :')

Obviously I know it doesn't but sometimes I think this for some reason!
Indrium
Profile Joined November 2010
United States2236 Posts
February 23 2011 01:31 GMT
#10
Excellent info to anyone who isn't as nerdy as me and actually crunched this out!

I really didn't think about posting it. You are a superior human, Volka.
Manifesto7
Profile Blog Joined November 2002
Osaka27150 Posts
February 23 2011 01:33 GMT
#11
Moved to strategy, and also put into the spotlight.
ModeratorGodfather
Jumbled
Profile Joined September 2010
1543 Posts
February 23 2011 01:38 GMT
#12
Good idea to put it all in a single simple post. These are all basic facts that everyone should know about chronoboost, but sadly a lot of people don't.
Jombozeus
Profile Blog Joined August 2010
China1014 Posts
February 23 2011 01:38 GMT
#13
On February 23 2011 09:42 Sek-Kuar wrote:
I wouldnt call it simple unless you have some sort of math Ph.D. - imo its really complicated way to "explain" quite simple thing.


But whatever, some ppl might like, but you are missing one thing:
Nexus regenerate 25 ene in roughly 45 sec (45*0,5625= ~25), so using energy from single nexus you can boost something by 50% for 20 seconds every 45 sec, so one nexus is capable of boosting something by 22% in total using constant chrono boost (50%*20/45) if no energy was saved.


This means that when you have only one Nexus and with no energy saved, if you start CB something you can reduce build/research time to ~82% of original.


I appreciate the OP but... You really dont need a math Ph.D. for this :S
Eeeegor
Profile Joined April 2005
Australia809 Posts
February 23 2011 01:40 GMT
#14
Great post - nice and simple.
Day9 Made Me Do It
Manifesto7
Profile Blog Joined November 2002
Osaka27150 Posts
February 23 2011 01:40 GMT
#15
This is a good chance for someone to ease into liquipedia too.
ModeratorGodfather
Apolo
Profile Joined May 2010
Portugal1259 Posts
February 23 2011 01:49 GMT
#16
On February 23 2011 09:26 GenesisX wrote:
Good, simple post. I think the main misconception people have is that they think that Cboost helps production by 100%, when its actually 50%. I know I did, lol.


Yup. And also that P can't get anything 50% faster, just 33%. That is, constantly using saved chronoboost, they can only have 13 units instead of 10, or in other words, have those 10 units 33% of the time to produce them earlier. At this light now, doesn't seem that good at all when comparing to what mules can do
`Zapdos
Profile Blog Joined November 2010
United States935 Posts
February 23 2011 01:49 GMT
#17
On February 23 2011 10:40 Manifesto7 wrote:
This is a good chance for someone to ease into liquipedia too.


I think mani needs help.. He's got spotlight fever!
www.twitch.tv/thezapdos come watch me :]
Zips
Profile Joined August 2010
United States146 Posts
February 23 2011 01:51 GMT
#18
Hrm, you should add this to liquipedia
Munk-E
Profile Blog Joined July 2010
United States672 Posts
Last Edited: 2011-02-23 02:18:59
February 23 2011 01:58 GMT
#19
no offense, but you kind posted the same formula like 5 times.
i mean you said chrono boost divides speed by 1.5
and then you pointed out 1-(1/1.5)=.33333
and then you posted like 5 variations of this formula and applied it to a few units.
not really impressive.

you just used variables and then said what they are for, and ended up just stating what is already known.

((20*(1.5-1))=10, You need to divide the build time by 20 to find out how many times you should use something that takes 20 seconds.)

But hey, you made it look impressive enough to get spotlighted, so congrats!
You recognise me because of my signature!
Torpedo.Vegas
Profile Blog Joined January 2011
United States1890 Posts
February 23 2011 01:59 GMT
#20
On February 23 2011 09:42 Sek-Kuar wrote:
I wouldnt call it simple unless you have some sort of math Ph.D. - imo its really complicated way to "explain" quite simple thing.


But whatever, some ppl might like, but you are missing one thing:
Nexus regenerate 25 ene in roughly 45 sec (45*0,5625= ~25), so using energy from single nexus you can boost something by 50% for 20 seconds every 45 sec, so one nexus is capable of boosting something by 22% in total using constant chrono boost (50%*20/45) if no energy was saved.


This means that when you have only one Nexus and with no energy saved, if you start CB something you can reduce build/research time to ~82% of original.


I definitely think the OP (which is already good) could be enhanced by factoring in "N" number nexuses and their respective energy regeneration rates. It would take this otherwise abstract information and place it into a more practical scenario.

Taken even one step further, one could conceivably apply this to specific early build orders and by factoring together the OP, Build Times, Mining Times, and Energy Regen rates, create some sort of Chronoboost optimization program or guide. As of now a lot of high level players figure this out via trial and error as well as intuition. But having a formal mathematical template to experiment on with the only subjective limit being APM could be a very beneficial tool for Protoss Players of all skill levels.

This is a good start.
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