Found the thread, here's a copy:
I'm surprised no-ones done this yet. I recently decided to calculate how ineffective Chronoboost is vs the mule. For the purpose of these calculations a Mule is worth 6 workers which takes into account its ability to ignore a mineral fields saturation combined with its minerals per second income worth of around 4.5 workers.
Heres the calculations so you can see for yourself.
Chronoboost duration = 20 seconds
Chronoboost function = speed up by 50% = divide by 1.5
To find out how much of a benefit Chronoboost should grant something, multiply its duration by its effect. Thus
20*0.5 = 10. A Single Chronoboost over time will equate to 10 seconds of gametime saved. Lets check this is right by working out probe buildtimes.
Probe buildtime = 17 seconds
Chono probe = 11.33333 seconds
To consume a whole chronoboost you need 2 probes, which provided you do a second chrono the moment the first 1 finishes (not possible really, energy is spent faster than gotten) then it would take 22.66666 seconds. However since the last 2.6666 seconds are not chronoboosted we slow it down by 50% (or *1.5) which makes our answer the following.
20+(2.6666*1.5) = 23.999999 or to make things easier, lets just say 24.
A single chronoboost on 2 probes will take 24 seconds, 10 less than other races which holds true to the previous calculations. Since probes take 17 seconds to build that means for every 2 chronoboost used on probes, you have 1 extra out compared to Terran with 3 seconds off the next one.
Since the existence of mules is worth 6 Probes our goal for this set of calculations is to get 6 probes ahead, or to shave off 17*6 seconds, or 102 seconds. This requires 11 Chronoboosts. overall.
Now heres the fun bit.
(25 / 0.5625) * 11 = 488.888889
To get 1 chronoboost worth of energy requires 44.4444444 seconds of gametime, 11 of them requires 489 seconds of gametime or 8 minutes 9 seconds
So there you have it. It takes 8 minutes of pure chornoboosting on the probes to get an economic gain equal to a mule being summoned.
8 Minutes 9 seconds to acquire the chronoboost required to be on par with a mule, 8 minutes 29 seconds to actually have the probes equal to it. If I do the calculations above with scv=5 instead of 6, it is still a whopping 7 minutes.
And yes, once you have an OC provided you *gasp* have macro you can chain mules since their duration is equal to the energy gain rate of an Orbital Command. Mules last 90 seconds and it takes 89 seconds to get 50 energy.
Before anyone bothers trying "but OC costs 150 minerals and we don't start with it!" crap remember this.
--Each probe costs 50 minerals, meaning 5-6 probes extra is 250-300 mineral, 100-150 more than the cost of an OC.
--You can get that OC and plop a mule LONG before the 7 minute mark.
--An extra 5-6 probes requires its own 100 mineral Pylon.