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A Protoss follow-up to my Terran economy discussion thread on the value of Orbital Command Timing...
Here I discuss the value of chrono boosting probe production pre-saturation by answering some common (and usually unanswered) questions:
(updated using more accurate mining data at the recommendation of ABCSFirebird)
Operating Assumptions
+ Show Spoiler +- All numbers assume 1-base play up to full saturation. - Chrono boost is used starting on the 11th worker, and continues at cost until full saturation (30 probes) - Gas is taken and mined optimally before the 17th mining worker. - Travel time and scouting worker are not factored in (at least not yet). - 4 mineral patches are considered "near" and 4 are considered "far" as categorized by this thread.
How many minerals do you actually gain by chrono boosting probe production to full 1-base saturation?
TL;DR - 413.7
Using maximum chrono on your nexus, It's possible to reach full saturation in 5:38 with constant probe production. This uses 7 chrono boosts. (You will eclipse 25 energy shortly after reaching full saturation with optimal probe production.)
Because you reach saturation earlier (5:38 vs. 6:48), we must also consider the time from 5:38 to 6:48, referred to hereafter as "bonus mining time."
@6:48, non-chrono'd saturation probes have gathered ~4749.8 resources.
@5:38, chrono'd satuartion probes have gathered ~3946.4 resources.
@6:48, chrono'd saturation probes have gathered an extra ~1218 resources (~5164.4 total)
The difference here is ~414.6 resources at 6:48 game time.
What is the approximate value of each of the 7 chrono boosts? (updated using more accurate mining data)
1st - 157.7 minerals
2nd - 81.9 minerals
3rd - 63.7 minerals
4th - 52.8 minerals
5th - 34.2 minerals
6th - 18.3 minerals
7th - 5.1 minerals
* Each value after the 1st dependent on using the previous chrono boost(s).
Assuming constant worker production, how much does it cost me to chrono my Cybernetics Core for Warpgate Research in the standard 1-gate core opener?
In a 1-gate Core opener into 4-gate rush, you would only use the initial chrono boost on your Nexus. So, the true cost of rushing warpgate research is:
1st chrono Nexus
2nd-6th chrono Warpgate
7th, 8th not Nexus (units? forge?)
-Total economic penalty: 261.1 minerals
--But I want to use chrono on my Nexus now to make up for the lost production time. How much will I gain if I use my 7th and 8th Chrono boosts on my Nexus to help me reach full saturation faster?
1st chrono Nexus
2nd-6th chrono Warpgate Research
7th, 8th chrono Nexus
-Total economic penalty: 242.6 minerals
As you can see here, chrono boosting your Nexus to make up for the earlier sacrifice on probe production only nets you 18.5 minerals... for TWO chrono boosts.
How about if I chrono boost my 9th/10th Probes before the 9 pylon finishes, rather than after?
Most people probably assume it is better to hold the chrono boost until the 11th worker begins production, and you're absolutely right.
In fact, it costs you 84.9 minerals in lost income by saturation time. Even though your 9th and 10th workers come out sooner, you supply block yourself for roughly 8 seconds, and your 11th and 12th workers actually come out much later. Your saturation timing ends up being slowed by roughly 10 seconds, fully mitigating the (very) short-term gain in production.
Do you have any data on 2-base play? What about an expansion timing? How are these affected?
Currently this data only supports 1-base play, but I hope to have support for multiple bases soon.
This is all pretty interesting, but show me your work.
chrono.xls (updated 12/16 12:00pm est)
Thanks for any and all feedback, and please post away. How might this information affect your future usage of chrono boost?
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I think in matchups other than PvP a lot of people are expanding before 30 probes, in which case chrono on probes becomes a ton more valuable (since you can transfer them immediately).
This is good to know though, thanks.
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This is quite interesting, for this shows how much more economically behind you are if you do a 4gate push, but have your opponent hold it off. Although different factors such as being able to pressure earlier and expanding while doing this pressure will compensate for that.
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great post. nice work. its appreciated knowing the exact figures
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thanks. very interesting. how did you get all this information?
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Thanks for the info. Definitely will not be chrono boosting past the 4th probe anymore if i'm one basing. Now i'm curious about 2basing. Thanks 
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I like how you identified when the mineral comparisons were being done. IE "The difference here is ~414.6 resources at 6:48 game time." Knowing when your advantage is fully realized is very helpful. Thanks!
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Awesome, thank you so much for compiling this information!
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United Arab Emirates18 Posts
Thank you very much for your effort. I've always felt something was off when I CB the nexus for more than 3 times and/or when trying to make up for lost production time as mentioned.
Hopefully I would be able to use my CBs more efficiently now. I guess focusing on unit production/upgrades if I'm one basing is much more logical according to this.
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Great work man. Amazing contribution to Team Liquid.
Ive always just used the first 2 Chronos for Probes, and now I realize that is the best due too your math.
It would be interesting to see the numbers for 2 bases. I would assume that the first Chrono boosts too get up to saturation would be the Highest net Mineral gain. Very interesting.
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Awesome work! I loved your terran post and recommended it to a friend, but I play toss so this benefits me :-)
For your CB 9,10, does that include a 9 pylon or 8. I'm only silver-gold at the moment and have done 8 pylon a few games against toss to prevent cheese and noticed I am still coming out ahead checking the BO chart after the game. At higher levels though I am curious how bad this will actually be.
Generally, the tenth probe finishes just after the pylon and 11 starts a second or two later.
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Awesome. I always thought it made sense logically that the earlier on you use your chrono on probes the better, but it was nice to see some concrete numbers attached to it.
Thanks!
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Obvious platitudes about in-game variables aside this is good info.
I have a bad habit of only trying to chrono boost my nexus in PvPs, this shows how damaging that line of thought could be
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I looked into the excel file and i am pretty sure that you got the income difference for each worker wrong. 0.7 for 17-20 is definately wrong - according to my measurements (on SoW) they should be about 0.4 and 21-24 0.1 (non on gas). Even if you consider that three probes are on one gas - the 20th shouldnt be the same as the 16th. But maybe i interpreted your table wrong.
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You sir are both a gentleman and a scholar. This is an excellent example of what forum posts should be. Posts like this are the reason why I (usually) resiste the temptation to post whatever random shit is bouncing around in my head.
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Wow. That's almost 2 mules worth!
Don't forget that chrono boost allows faster tech, and faster saturation of expos.
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Nice work, thanks for making this post
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I've been trying out Chronoing Probes until full saturation for a while, and this thread confirms what I was feeling. You definitely can tell those extra few hundred minerals when it comes this early in the game.
Thanks for putting my thoughts into data :D
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wow, chrono'ing probes at the beginning of a game can exceed the income from a mule. amazing work.
so now all we have to do is figure out how to chrono effectively for each opening build. i always figured that the first two chronos going to the 11th and 13 or 14th probes paid off immensely.
so should you still spend the 2nd - 6th chronos on the warp gate research for a proper four gate rush, or spend the 2nd (and maybe 3rd) on the nexus for that extra 150 minerals?
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Very good ily got posting this ♥
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Thanks everyone for the support and feedback. It's very satisfying to see some people are finding it helpful.
On December 26 2010 05:30 wideye wrote:
thanks. very interesting. how did you get all this information?
I modeled most of it using build times and nexus energy regeneration, as well as parsing some data from old theorycrafting threads on mining minerals as sourced on the eponymous liquipedia page.
There may well be some errors in this data, as with any spreadsheet models, so if you see anything questionable please don't hesitate to ask!
On December 26 2010 09:51 FireBlast! wrote:
Obvious platitudes about in-game variables aside this is good info.
I have a bad habit of only trying to chrono boost my nexus in PvPs, this shows how damaging that line of thought could be
Yeah, if there is a way to make it more applicable to specific builds, I'd be happy to try and work on it. I tried to eliminate as many variables as possible when doing this to create some pure data to use as a foundation to build upon.
My goal here was just to crunch some numbers and see if I can't put to the test some of the uncontested conventional wisdom.
Naturally, if you expand, the latter chronoboosts would end up netting a bit more income, but as I stated in the OP, I simply haven't had the time to incorporate 2-base functionality into any of the little tools I've been working on. And since we can't ever get to 2-base play without considering 1-base play, I figure this is a good starting point.
On December 26 2010 09:55 ABCSFirebird wrote:
I looked into the excel file and i am pretty sure that you got the income difference for each worker wrong. 0.7 for 17-20 is definately wrong - according to my measurements (on SoW) they should be about 0.4 and 21-24 0.1 (non on gas). Even if you consider that three probes are on one gas - the 20th shouldnt be the same as the 16th. But maybe i interpreted your table wrong.
Under the operating assumptions at the top, I assume that the player takes gas optimally in whatever build he chooses. Note that this slightly impacts numbers, depending on when he takes the gas.
The first 16 miners of mineral patches average ~42 minerals/minute, and the first 2 gas workers gather 42 gas/minute (which I lumped into resources). (so, 1-16 mining, 17,18 gas 1; 19,20 gas 2).
The 2nd two (21-22) are each gathering gas at ~30gas/minute, and the last 8 workers mine at ~18minerals/minute.
You're absolutely correct that the 24th worker is barely going to impact the mineral patch, but then it's very cumbersome to adapt a general model to specific maps to determine which workers will mine sub-optimally, which geysers require 4 workers, when exactly to take your gas, etc etc etc.
This model assumes ideal situations, and places all patches an average distance apart. When beginning the modeling for the WEDAT tool I built last week, I began with a few threads that went pretty far in depth into mining theorycraft, and it just seemed easier to accept their numbers.
Should you disagree, if you can create a better income rate per workers, I'd love to incorporate it. I'm less concerned about defending my own results than utilizing the most accurate and useful data.
On December 26 2010 11:07 Ayrie wrote:
wow, chrono'ing probes at the beginning of a game can exceed the income from a mule. amazing work.
so now all we have to do is figure out how to chrono effectively for each opening build. i always figured that the first two chronos going to the 11th and 13 or 14th probes paid off immensely.
so should you still spend the 2nd - 6th chronos on the warp gate research for a proper four gate rush, or spend the 2nd (and maybe 3rd) on the nexus for that extra 150 minerals?
I think you may misunderstand the numbers I posted.
For example, the 11 chrono boost (1st one) adds roughly 153.5 minerals to you over the time it takes to reach full saturation. One mule by itself early in the game should add 270 minerals over 90 seconds unless it's dropped on a non-near patch.
In fact, Terran Income to saturation time (6:48) could theoretically mine ~1000 more minerals than a full-chrono'd Protoss on 1-base. But of course that doesn't factor in workers having to go off-patch for building, so it's not even a viable comparison.
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This is awesome thank you so much!
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On December 26 2010 11:30 mlbrandow wrote:
The first 16 miners of mineral patches average ~42 minerals/minute, and the first 2 gas workers gather 42 gas/minute (which I lumped into resources). (so, 1-16 mining, 17,18 gas 1; 19,20 gas 2).
The 2nd two (21-22) are each gathering gas at ~30gas/minute, and the last 8 workers mine at ~18minerals/minute.
Alright - now the numbers makes sense - the early assimilators with only two probes in them are a very unusual concept for me, pretty much never used in practice (atleast here in europe). As for the numbers of the last eight: these are my own results after examining the mining rate. They differ slightly from liquipedia and i only ran numeral measurements for the last four - since there is heavy noise - but as you can see it seems to make sense splitting the last eight in groups of atleast four. I don't say my numbers are absolutely correct - but an approximation which states that always about four mineral patches are close to the main and about four are further away would be a lot better in my opinion - you could even use the numbers from liquipedia (like 42 +-3 / minute depending on distance) for this.
However as i entered my numbers in the table, the results aren't that different - so i probably should just thank you for your nice work at use the table as i like to 
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On December 26 2010 13:00 ABCSFirebird wrote:Show nested quote +On December 26 2010 11:30 mlbrandow wrote:
The first 16 miners of mineral patches average ~42 minerals/minute, and the first 2 gas workers gather 42 gas/minute (which I lumped into resources). (so, 1-16 mining, 17,18 gas 1; 19,20 gas 2).
The 2nd two (21-22) are each gathering gas at ~30gas/minute, and the last 8 workers mine at ~18minerals/minute.
Alright - now the numbers makes sense - the early assimilators with only two probes in them are a very unusual concept for me, pretty much never used in practice (atleast here in europe). As for the numbers of the last eight: these are my own results after examining the mining rate. They differ slightly from liquipedia and i only ran numeral measurements for the last four - since there is heavy noise - but as you can see it seems to make sense splitting the last eight in groups of atleast four. I don't say my numbers are absolutely correct - but an approximation which states that always about four mineral patches are close to the main and about four are further away would be a lot better in my opinion - you could even use the numbers from liquipedia (like 42 +-3 / minute depending on distance) for this. However as i entered my numbers in the table, the results aren't that different - so i probably should just thank you for your nice work at use the table as i like to
Yeah, I use those numbers in 3 or 4 different ways, and I openly admit they are generalizations. Naturally, there is no map that exists where the patches are all uniform distance.
If you can come up with some better numbers, I'd like to use them. Even very slightly more accurate for most cases would still be an upgrade.
My question for you though is then, would it behoove me to split mining workers 1-8 and 9-16 into groups of 4 as well, since we're assuming four patches are near and four are far?
And how diagonals impact this rate specifically?
I believe that my method averages out to the correct amounts at saturation (which is principally what I'm looking at), but if there is a way to make the numbers more accurate for any time X pre-saturation it would certainly make the data more useful.
Thanks for your input.
edit:
Referring again to this thread, I updated some of the mining numbers, which better adjust for mineral patch distances.
The results are very, very similar (as the income differences were very small to begin with), but it does slightly tilt the value of the earliest chrono boost even more.
1st chrono - 157.7 minerals
2nd chrono - 81.9 minerals
3rd - 63.7 minerals
4th - 52.8 minerals
5th - 34.2 minerals
6th - 18.3 minerals
4wg loss: 242.6 minerals
- Delays in worker production are unaffected by mining rate adjustments per worker (assuming the same saturated sum). Therefore, this number is unaffected, although the loss per unit of time does change slightly.
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On December 26 2010 21:13 mlbrandow wrote:
My question for you though is then, would it behoove me to split mining workers 1-8 and 9-16 into groups of 4 as well, since we're assuming four patches are near and four are far?
Only if a player is forcing the first eight probes to mine from the four nearest patches. At high level you see people doing this sometimes, but i don't think it is really worth it since forcing one probe to a mineral patch where already another probe is mining can be some lost mining time if the timing is bad.
Well maybe to illustrate, lets assume a player forces probes and he is lucky with the timing, then there are 8 probes on 4 close mineral patches and each probe is mining with 45/min. The next 8 probes go to the far patches and there they are mining with 39/min. Obviously that results in an average mining rate of 42/min.
If you don't force probes, which most people don't, than you end up with pretty much the same (2 probes on each patch at a total of 16 probes). The first 8 evantually spread equally on 8 patches, so some are mining with 45/min, some are with 39/min, for the next 8 it is the same.
The thing is - nobody can use cb for getting some of the first 8 probes faster and if cb is used for 9-16 there is only an advantage in comparison to cb at >17 probes - so there is nothing to discuss, and therefore i wouldn't split 1-8 or 9-16 in groups of four.
But now there are 4 mineral patches which are saturated with 90/102 - and four with 78/102. So probes 17-20 are likely to go on the 78/102 patches (since the probability that these are already in use isn't as high as for the 90/102 patches). So you gain 24/min for each probe. And for the last four only 12/min.
Obviously these numbers are heavily overlayed by noise caused from probes running around and not staying on a mineral patch - but they are a better approximation, which is somwhat important for the cb examination, because earlier cb is more effective than the later one - and catching up by using cb after "wasting" some for warpgatetech is pretty much impossible.
And how diagonals impact this rate specifically?
What do you mean with diagonals?
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On December 27 2010 01:26 ABCSFirebird wrote:What do you mean with diagonals?
I was looking at a post on MULE efficiency from a while back (can't seem to find it now), and it showed RGY-colored patches for every mining position of every 1v1 map. Green meaning the MULE would return 270 minerals (near), Yellow meaning they would return 240 minerals (far), and Red meaning they would mine 270 minerals but only return 240 (middle). These middle usually were at diagonal positions relative to the CC.
I'll look again to see if I can dig it up. It was an awesome post from several months ago.
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Thanks for the work but 400 Mineral is like one 'free' nexus. I think anyone would take that as a return
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This is just assuming Pylon/Probe production, right? It seems like I never really have the opportunity to CB to saturation. You need the Stalker (or blocking Zealot, or Sentry..), and usually you're blowing 1 or 2 seconds off a CB because of slight mineral shortage here and there.
Maybe it's just me, but compared to Mules and Inject, CB seems a little underwhelming?
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great post, but are you saying we should focus more on cbing our nexus instead of getting warpgate tech? if so...wouldnt that hurt us unit count wise?....sorry for the nooby question
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On December 27 2010 03:19 RLam wrote:
great post, but are you saying we should focus more on cbing our nexus instead of getting warpgate tech? if so...wouldnt that hurt us unit count wise?....sorry for the nooby question
He wasn't saying -- he was giving facts so that people can make more informed decisions.
There is always a trade-off between investing in economy and unit count -- so yes, there is window where CB'ing warpgate tech will have more units than CB'ing the nexus. Eventually that window will close, and the build that CB's the nexus will have a permanent unit count advantage.
These facts tell you how much you are spending to make that window appear -- and how much you have thrown away if you don't do anything in that window. (e.g. rush, or defend a rush)
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Great read. This also basically can show you the general difference in economy between 4-gating and a standard eco build. Now I'm positive I have a solid strategy vs. 4-gating.
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Personally I think crono boosting units is a bad idea unless you're going for a timing attack or desperately need to defend. Crono boost basically gives you 10 seconds of time. If you crono a zealot or something, just to have it sit at your ramp, it's wasteful IMO.
When I play protoss, I crono boost probes and upgrades primarily, although I have at times crono boosted immortal or observer from a robo before I moved out.
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This doesn't take into consideration the cost of creating production facilities to catch up on production you lose out on by not chronoboosting units or warpgate. Just a small nitpick.
(im not saying it's reasonable to be asking for those figures.. clearly it's borderline impossible. just that the numbers could be a little misleading in the context of a real game)
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On December 27 2010 04:50 Dromar wrote:
Personally I think crono boosting units is a bad idea unless you're going for a timing attack or desperately need to defend. Crono boost basically gives you 10 seconds of time. If you crono a zealot or something, just to have it sit at your ramp, it's wasteful IMO.
Right, it's not something to do on a whim (unless you were going to waste the energy anyways). The most obvious use is to boost out units for a rush (or if you desperately need units to defend).
A more subtle use is to shuffle money around. It lets you build one Gateway, but still produce units as if you had one and a half, letting you free up the money you would have spent on a second Gateway for other purposes, such as an earlier Cybernetics Core, or early Nexus... or even on just continuous Probe production.
Should you think you need the units I speculate it's better to Chrono Boost units than it is to pause Probes to get a second early Gateway and then resume Probes with Chrono Boosts... but I haven't tried testing it.
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On December 27 2010 06:21 Hurkyl wrote:Show nested quote +On December 27 2010 04:50 Dromar wrote:
Personally I think crono boosting units is a bad idea unless you're going for a timing attack or desperately need to defend. Crono boost basically gives you 10 seconds of time. If you crono a zealot or something, just to have it sit at your ramp, it's wasteful IMO. Right, it's not something to do on a whim (unless you were going to waste the energy anyways). The most obvious use is to boost out units for a rush (or if you desperately need units to defend). A more subtle use is to shuffle money around. It lets you build one Gateway, but still produce units as if you had one and a half, letting you free up the money you would have spent on a second Gateway for other purposes, such as an earlier Cybernetics Core, or early Nexus... or even on just continuous Probe production. Should you think you need the units I speculate it's better to Chrono Boost units than it is to pause Probes to get a second early Gateway and then resume Probes with Chrono Boosts... but I haven't tried testing it.
chronoboosting probes also requires u to spend more money faster, delaying your ability to build production facilities or units in the short term.
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Thanks for the reasearch! Figuring out specific ways to use chronoboost for certain strategies is definitely going to be playing a bigger role in the protoss game.
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On December 27 2010 04:55 travis wrote:
This doesn't take into consideration the cost of creating production facilities to catch up on production you lose out on by not chronoboosting units or warpgate. Just a small nitpick.
(im not saying it's reasonable to be asking for those figures.. clearly it's borderline impossible. just that the numbers could be a little misleading in the context of a real game)
I was thinking about this earlier today before I left, and I actually don't think it would be that difficult to map out.
While you technically lose out on the probe mining bonus of a chrono boost if you use that energy to boost unit production from a warpgate, you would also gain a mineral "savings bonus" if you used it on producing a unit, since you could delay (or avoid) construction of an additional facility.
Thanks for the observation though. You're absolutely correct in that the probe mining bonus taken in a vacuum can be misleading (versus the production gain of a unit-producing structure). I'm going to try and factor it into the OP when I can run some numbers.
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well awesome nice initiative and gl!
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It's cool to see how chronoboost effects you economically, i kind of am more of a chronoboost research and gateways guy though. I think 200 minerals later on sometimes does not mean much if i manage to spend the money i have faster and i attack. I think chrono is underrated in its ability to help you spend your money quickly, and sometimes spending your money faster can be better then having more money later on.
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EPT
