# Chrono Boost Math

 It has been suggested that this article or section be merged with Chronoboost . Reason: This should work fine as a subsection of Chronoboost (Discuss).

Chrono Boost Math page briefly clears up some possibly ambiguous parts of this powerful Protoss ability. Chrono Boost, while it is widely used in mostly all levels of play, is still misunderstood by a surprising number of players.

## Introduction

Chrono Boost(CB) puts buildings into an "accelerated state" in which they'll build/upgrade 50% faster for 20 in-game seconds; the actual length of which depend of game speed, and are measured by the SC2 game clock. On the building's interface, you will not notice any change in the projected research time, but the progress bar will fill up faster. The 50% acceleration factor means that while a building is Chronoboosted, the speed at which it builds/researches is 1.5 times faster than normal. (e.g. 20 seconds to complete 30 seconds of work).

## Chrono Boost Reduction

Chrono Boost lasts 20 seconds, and normally:

• 20 (game seconds) = 20 (game seconds of work)

Chrono Boost, however, increases the work a building does by 50% (or factor of 1.5):

• 20 (game seconds) = 20*1.5 = 30 (game seconds of work)

So each Chrono Boost fully applied (i.e. that does not end before the production ends) saves you 10 seconds of production or research time, which is a 33% reduction in the total research/production time.

Take for example using Chrono Boost on a Colossus, which normally takes 75 seconds. Assuming that Chrono Boost is activated perfectly simultaneously with the Colossus, after 20 seconds, the Colossus progress bar is at the 30 second mark, saving ten seconds. Again, with the second Chrono Boost, after 40 seconds, the Colossus progress bar is at the 60 second mark, saving another ten seconds. Now there are only fifteen seconds left on the progress bar. If Chrono Boost is used a third time, in the first ten seconds of the Chrono Boost, it performs 15 seconds of work, which finishes the Colossus, and the second half of the Chrono Boost is wasted. So the three Chrono Boosts save a total of 10 + 10 + 5 = 25 seconds.

## General Build Time Formula

(Build Time)=(Build Time)- 10*(# of chronos)

## Maximum Number of Useful Chronoboosts

Chrono Boost performs 30 seconds of work for every 20 seconds of time; to find the total production time, assuming continuous Chrono Boosts:

• (Chrono Boost Time)/20 = (Normal Time)/30
• (Chrono Boost Time) = (Normal Time)*2/3

Because Chrono Boosts take 20 (game seconds) to complete and cannot stack, the maximum number of chronos you can apply that will help is:

• (№ of Chrono Boosts) = (Normal Time)*(2/3)/20 = (Normal Time)/30

Any decimal part represents chronobost that will be active after the particular action completes.

For example, an Immortal normally requires 55 seconds of time:

• (Chrono Boost Time) = (55)*2/3 = 36.667 seconds
• (№ of Chrono Boosts) = (55)/30 = 1.833

So only one Chrono Boost can be fully spent on one Immortal; if a second Chrono Boost is spent, 3.333 seconds of the Chrono Boost will happen after the Immortal has finished.

### Energy Regeneration and Chrono Boost

Of course, you can only continuously apply chronoboost if your nexus has the energy for it. A nexus regenerates 0.5625 energy per second, so one nexus regenerates the 25 energy required for Chrono Boost every 45 seconds (approximately). Normally:

• 45 (game seconds)= 45 (game seconds of work)

As we saw earlier, each Chronoboost allows you to get an extra 10 seconds of work done.

• 45 (game seconds)= 55 (game seconds of work)

This is a factor of 55/45=1.2222 faster, or 22%.

One nexus is therefore capable of reducing production time by about 22% over the long term if a Chrono Boost is used as much as possible. (The speed will be slightly different if the research/production time is not a factor of 55). So regardless of the fact that Chrono Boost only takes 20 seconds itself, with a single nexus, only one Chrono Boost can be spent every 45 seconds.

## Important Timings

Assuming continuous Chrono Boost :

Unit Normal Build Time Fastest Build Time Time Saved CBs needed
Colossus 75 50 25 2.5
Immortal 55 37 18 1.8333
Warp Gate research 160 107 53 5.33
+1 Ground Weapons 160 107 53 5.333

## How much energy to save to...

When saving up energy for a number of continuous Chrono Boosts, the full amount of energy isn't required right away, as the nexus will generate energy while Chrono Boosts are used.

The required saved energy is:

Time required: 45(X-N(20/45)(X-N)) Energy required: 45(X-N(20/45)(X-N))*(25/45)

Where X is the number of Chrono Boosts needed, and N is the number of Nexi (starting at 0 energy)

Which can be simplified: 25X-(20*25/45)N(X-N)

Below is the required amount of energy at which you can start your first Chrono Boost for each required number of CB.

# of chronos 1 nexus
1 25
2 38.75 (39)
3 52.5 (53)
4 62.25 (63)
5 80
6 93.75 (94)