How To Measure Time: The Click System
Terse
Join Date: 2002-11-23 Member: 9748Members
Join Date: 2002-11-23 Member: 9748Members
<div class="IPBDescription">Looking at time from spawn to 2nd hive</div> I've been thinking about how important time is in establishing a base. Winning a game is about managing time, but we don't really have a good way of showing time in terms of resources. I've tried to see if it's possible to break down the problem into units so we can figure out if there's an optimal way of winning a game. There are a lot of blank spaces and guesswork in this, but I figure the precise numbers can always be tweaked if we have a framework.
From <a href='http://nstactics.lanvancouver.com/faq.html' target='_blank'>http://nstactics.lanvancouver.com/faq.html</a>
<FAQ>
Each resource cycle, each Resource Tower a team has produces 1 Base Resource Point. Normally the resource cycle is 6 seconds long. This base production is then multiplied by the team size and scaling factor of 0.23. This is the nominal amount of resources put into the team pool. If the teams are unbalanced, the team with the smaller number of players receives a bonus, based on the fractional difference in the number of players.
</FAQ>
TotalResources = NumTowers * MAX(NumAliens/NumMarines, 1) * NumAliens * 0.23
TotalShares = (3 * NumGorges) + NumSkulks
The equation for an individual player (NumShares = 3 or 1, depending if you're a gorge or not) every six seconds is:
resources = (NumShares * TotalResources) / TotalShares
After much fiddling around, I finally got smart and stuck this all into a spreadsheet. So let's punch out the numbers. A typical game will have 8 players a side:
Number of Towers: 1
Number of Kharaa: 8
Number of Marines: 8
Resources per Cycle: 1.84
Size Resource Bonus: 0
Total Resources: 1.84
Number of Gorges: 1
Number of Skulks: 7
Shares for Gorges: 3
Total Number of Shares: 10
Gorge % of Resources: 30.00%
Resources for Gorge: 0.552
Resources per sec: 0.092
Seconds for resource: 10.86956522
Here's the total time for a resource ranging from 1 to 20 players, with the percentage of resources the gorge gets:
1: 26.08 seconds (100%)
2: 17.39 seconds (75%)
3: 14.49 seconds (60%)
4: 13.04 seconds (50%)
5: 12.17 seconds (42%)
6: 11.59 seconds (37.5%)
7: 11.18 seconds (33.33%)
8: 10.86 seconds (30%)
9: 10.62 seconds (27.27%)
10: 10.43 seconds (25%)
11: 10.27 seconds (23%)
12: 10.14 seconds (21%)
13: 10.03 seconds (20%)
14: 9.93 seconds (18.75%)
15: 9.85 seconds (17.65%)
16: 9.78 seconds (16.67%)
17: 9.71 seconds (15.79%)
18: 9.66 seconds (15%)
19: 9.61 seconds (14.29%)
20: 9.56 seconds (13.64%)
52: 9.03 seconds (5.56%)
The click time ranges from 12 seconds to 9.5, with the 10 second mark at 13 players a side. It levels out rapidly after hitting 10 seconds, and the difference between 8 and 13 players is less than a second.
Let's compromise and say 10 seconds is a click. This is a useful measure because it allows us some equivalence between resources and time. It's not realistic once you factor in the bonus and overflow, but it's useful in the early game.
The reason we're doing this is to find out how long it takes for a gorge to get from spawn to second hive. Say we're playing with 13 Kharaa, 1 gorge. The earliest a Gorge can change is after 3 resource points. A skulk will get a resource point every 26 seconds with no gorges around.
3 x 26 = 78 seconds.
10 seconds gestation time.
221 seconds second tower drop.
+ 30 seconds build time @ 1 rpc = 3 resources.
= 339 seconds @ one tower.
110 seconds third tower drop.
-30 seconds from build time
+ 30 seconds build time @ 2 rpc = 6 resources
= 110 seconds @ two towers.
73 seconds fourth tower drop.
-60 second from build time.
+ 30 seconds build time @ 3 rpc = 9 resources
= 43 seconds @ three towers
200 seconds second hive drop.
-90 seconds from build time.
=110 seconds.
339 + 110 + 43 + 110 = 602 seconds or 10 minutes.
So for the second tower you need to wait 3.6 minutes.
For the third tower, you need to wait 80 seconds.
For the fourth tower, you need to wait 13 seconds (if you're already there).
For the second hive, you need to wait a minute and a half.
Realistically speaking, this means once you've built the third tower, you have 6r and you're getting 3 rpc. If it takes you 60 seconds to get to the hive, you can drop a tower there immediately. I think skulk riding is a good idea, since it would be faster and safer than going alone.
Let's crank up the number of gorges and see what happens.
Number of Gorges: 2
Total Number of Shares: 17
Gorge % of Resources: 17.65%
Seconds for resource: 11.37123746
Number of Gorges: 4
Total Number of Shares: 21
Gorge % of Resources: 14.29%
Seconds for resource: 14.04682274
With four gorges, it takes 5 minutes to build the first tower. Put another way, four gorges on a team of 13 is like having 1 gorge on a 3 player team.
Some people say that you can have two gorges in a team of twenty.
Number of Gorges: 2
Number of Skulks: 18
Shares for Gorges: 6
Total Number of Shares: 24
Gorge % of Resources: 12.50%
Resources for Gorge: 0.575
Resources per sec: 0.095833333
Seconds for resource: 10.43478261
Some people are right. You could do it even faster with a single gorge (9.5 seconds per resource) but he'd really have to be moving.
Things change once you factor in the skulks, because a skulk which has a maximum number of resources won't take any extra resources from the pool, which means a gorge can get up to 100% of the resources. But this can take a while. Let's go back to the 13 player example.
A skulk starts with 10 resources in the banks, so it takes 23 resource points to fill up. With a gorge sucking up most of the resources, a skulk takes 30 seconds for a single resource point at one tower. Things improve around the fourth tower, but even then it's still a resource every 10 seconds.
339 seconds / 30 = 11.3 resources
110 seconds / 15 = 7.3 resources
43 seconds / 10 = 4.3 resources
= 23 resources
Just as the fourth hive is finished, the skulks fill up. The gorge gets 100% of four towers at a rate of two resource points a second and can build a hive in less than 40 seconds... and that's not counting the 9 resources he already has or factoring in skulk deaths.
339 + 110 + 43 + 35 = 527 seconds or 8.78 minutes.
Realistically this is going to be longer if a defense chamber is built, because many skulks will die, respawn and spend 2 resources upgrading carapace. (Which brings up the question whether it's a good idea to build a chamber before second hive, since it will drain resources both from the gorge and from the overflow pool as skulks upgrade.)
In between the time the second hive comes up, the gorge is going to be dropping defense and offence chambers like mad. Even then, it's likely that the gorge will fill up, and the resources will go back into the hive. They'll be used when everyone turns fade and rips the marines arms off.
Something that will make a difference is skulk deaths. A dead skulk uses no resources. To that end, it's actually to the Kharaa advantage to have skulks go kamakaze, since the skulk will be out of play for 3 to 5 clicks. Even with a bad skulk rush, a lone gorge can beat the clock just because all the skulks died gloriously.
This post was originally about whether it's a good idea for a skulk to turn into a gorge if it finds a new resource node. My first answer was that it only makes sense if the skulk is full of resources. It will cost 13 resources to change into a gorge, leaving it with 20 resources, and after that point it will take a click to build the node. After factoring in overflow, it's probably better to wait until the second hive is up before doing this, because by the time a skulk has filled up the gorge is already in position and needs the short term resources more than you do.
I will try and post the excel spreadsheet if the forums will let me.
From <a href='http://nstactics.lanvancouver.com/faq.html' target='_blank'>http://nstactics.lanvancouver.com/faq.html</a>
<FAQ>
Each resource cycle, each Resource Tower a team has produces 1 Base Resource Point. Normally the resource cycle is 6 seconds long. This base production is then multiplied by the team size and scaling factor of 0.23. This is the nominal amount of resources put into the team pool. If the teams are unbalanced, the team with the smaller number of players receives a bonus, based on the fractional difference in the number of players.
</FAQ>
TotalResources = NumTowers * MAX(NumAliens/NumMarines, 1) * NumAliens * 0.23
TotalShares = (3 * NumGorges) + NumSkulks
The equation for an individual player (NumShares = 3 or 1, depending if you're a gorge or not) every six seconds is:
resources = (NumShares * TotalResources) / TotalShares
After much fiddling around, I finally got smart and stuck this all into a spreadsheet. So let's punch out the numbers. A typical game will have 8 players a side:
Number of Towers: 1
Number of Kharaa: 8
Number of Marines: 8
Resources per Cycle: 1.84
Size Resource Bonus: 0
Total Resources: 1.84
Number of Gorges: 1
Number of Skulks: 7
Shares for Gorges: 3
Total Number of Shares: 10
Gorge % of Resources: 30.00%
Resources for Gorge: 0.552
Resources per sec: 0.092
Seconds for resource: 10.86956522
Here's the total time for a resource ranging from 1 to 20 players, with the percentage of resources the gorge gets:
1: 26.08 seconds (100%)
2: 17.39 seconds (75%)
3: 14.49 seconds (60%)
4: 13.04 seconds (50%)
5: 12.17 seconds (42%)
6: 11.59 seconds (37.5%)
7: 11.18 seconds (33.33%)
8: 10.86 seconds (30%)
9: 10.62 seconds (27.27%)
10: 10.43 seconds (25%)
11: 10.27 seconds (23%)
12: 10.14 seconds (21%)
13: 10.03 seconds (20%)
14: 9.93 seconds (18.75%)
15: 9.85 seconds (17.65%)
16: 9.78 seconds (16.67%)
17: 9.71 seconds (15.79%)
18: 9.66 seconds (15%)
19: 9.61 seconds (14.29%)
20: 9.56 seconds (13.64%)
52: 9.03 seconds (5.56%)
The click time ranges from 12 seconds to 9.5, with the 10 second mark at 13 players a side. It levels out rapidly after hitting 10 seconds, and the difference between 8 and 13 players is less than a second.
Let's compromise and say 10 seconds is a click. This is a useful measure because it allows us some equivalence between resources and time. It's not realistic once you factor in the bonus and overflow, but it's useful in the early game.
The reason we're doing this is to find out how long it takes for a gorge to get from spawn to second hive. Say we're playing with 13 Kharaa, 1 gorge. The earliest a Gorge can change is after 3 resource points. A skulk will get a resource point every 26 seconds with no gorges around.
3 x 26 = 78 seconds.
10 seconds gestation time.
221 seconds second tower drop.
+ 30 seconds build time @ 1 rpc = 3 resources.
= 339 seconds @ one tower.
110 seconds third tower drop.
-30 seconds from build time
+ 30 seconds build time @ 2 rpc = 6 resources
= 110 seconds @ two towers.
73 seconds fourth tower drop.
-60 second from build time.
+ 30 seconds build time @ 3 rpc = 9 resources
= 43 seconds @ three towers
200 seconds second hive drop.
-90 seconds from build time.
=110 seconds.
339 + 110 + 43 + 110 = 602 seconds or 10 minutes.
So for the second tower you need to wait 3.6 minutes.
For the third tower, you need to wait 80 seconds.
For the fourth tower, you need to wait 13 seconds (if you're already there).
For the second hive, you need to wait a minute and a half.
Realistically speaking, this means once you've built the third tower, you have 6r and you're getting 3 rpc. If it takes you 60 seconds to get to the hive, you can drop a tower there immediately. I think skulk riding is a good idea, since it would be faster and safer than going alone.
Let's crank up the number of gorges and see what happens.
Number of Gorges: 2
Total Number of Shares: 17
Gorge % of Resources: 17.65%
Seconds for resource: 11.37123746
Number of Gorges: 4
Total Number of Shares: 21
Gorge % of Resources: 14.29%
Seconds for resource: 14.04682274
With four gorges, it takes 5 minutes to build the first tower. Put another way, four gorges on a team of 13 is like having 1 gorge on a 3 player team.
Some people say that you can have two gorges in a team of twenty.
Number of Gorges: 2
Number of Skulks: 18
Shares for Gorges: 6
Total Number of Shares: 24
Gorge % of Resources: 12.50%
Resources for Gorge: 0.575
Resources per sec: 0.095833333
Seconds for resource: 10.43478261
Some people are right. You could do it even faster with a single gorge (9.5 seconds per resource) but he'd really have to be moving.
Things change once you factor in the skulks, because a skulk which has a maximum number of resources won't take any extra resources from the pool, which means a gorge can get up to 100% of the resources. But this can take a while. Let's go back to the 13 player example.
A skulk starts with 10 resources in the banks, so it takes 23 resource points to fill up. With a gorge sucking up most of the resources, a skulk takes 30 seconds for a single resource point at one tower. Things improve around the fourth tower, but even then it's still a resource every 10 seconds.
339 seconds / 30 = 11.3 resources
110 seconds / 15 = 7.3 resources
43 seconds / 10 = 4.3 resources
= 23 resources
Just as the fourth hive is finished, the skulks fill up. The gorge gets 100% of four towers at a rate of two resource points a second and can build a hive in less than 40 seconds... and that's not counting the 9 resources he already has or factoring in skulk deaths.
339 + 110 + 43 + 35 = 527 seconds or 8.78 minutes.
Realistically this is going to be longer if a defense chamber is built, because many skulks will die, respawn and spend 2 resources upgrading carapace. (Which brings up the question whether it's a good idea to build a chamber before second hive, since it will drain resources both from the gorge and from the overflow pool as skulks upgrade.)
In between the time the second hive comes up, the gorge is going to be dropping defense and offence chambers like mad. Even then, it's likely that the gorge will fill up, and the resources will go back into the hive. They'll be used when everyone turns fade and rips the marines arms off.
Something that will make a difference is skulk deaths. A dead skulk uses no resources. To that end, it's actually to the Kharaa advantage to have skulks go kamakaze, since the skulk will be out of play for 3 to 5 clicks. Even with a bad skulk rush, a lone gorge can beat the clock just because all the skulks died gloriously.
This post was originally about whether it's a good idea for a skulk to turn into a gorge if it finds a new resource node. My first answer was that it only makes sense if the skulk is full of resources. It will cost 13 resources to change into a gorge, leaving it with 20 resources, and after that point it will take a click to build the node. After factoring in overflow, it's probably better to wait until the second hive is up before doing this, because by the time a skulk has filled up the gorge is already in position and needs the short term resources more than you do.
I will try and post the excel spreadsheet if the forums will let me.
Comments
I don't think the same thing would happen with marines, as the commander has enough of a reserve to build another tower if the first one is destroyed.
It also means that if the marines find and kill the gorge in the first five minutes, the person playing gorge is screwed, since he'll need 13 resources for switching on top of a tower; it'd be better for him to switch places with one of the skulks (who still have the 10 point bonus). But if there are two gorges, the aliens should hope and pray one of them will get screwed.
<!--QuoteEnd--></td></tr></table><span class='postcolor'><!--QuoteEEnd-->
Yeah, whenever I play Marines, I always try to run out into the map at the start and pop the gorge while he's sitting around waiting to build a resource tower
<!--QuoteBegin--></span><table border='0' align='center' width='95%' cellpadding='3' cellspacing='1'><tr><td><b>QUOTE</b> </td></tr><tr><td id='QUOTE'><!--QuoteEBegin-->The gorge will have 3.45 * 2 = 7 resources now. It's time for him to go to the 2rd hive. It'll take him 5 clicks to get there, and he picks up 5 * 3 = 15 resources. He has 22 resources at the 2nd hive node, and drops immediately. He then spends 3.45 clicks use building it, gaining 10 resources. He has four resource nodes up, and gains 70 resources in (70 / 4) = 17.5 clicks.
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Almost, but not quite. The 1.84 res would be divided by 11; each non-gorge player counts once, while each gorge counts as three 'assault' players. So, redone:
The hive splits 1.84 into 11 shares, which is .17. It gives 3 shares to the gorge, which is .50r every six seconds, or .08r per second. This means that roughly every 12.04 seconds, the gorge gets a resource point. Say that this period of time is a click.
This probably means that the rest of your post will have to be edited. But it was very good! <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html/emoticons/biggrin.gif' border='0' valign='absmiddle' alt='biggrin.gif'><!--endemo-->
Almost, but not quite. The 1.84 res would be divided by 11; each non-gorge player counts once, while each gorge counts as three 'assault' players. So, redone:
The hive splits 1.84 into 11 shares, which is .17. It gives 3 shares to the gorge, which is .50r every six seconds, or .08r per second. This means that roughly every 12.04 seconds, the gorge gets a resource point. Say that this period of time is a click.<!--QuoteEnd--></td></tr></table><span class='postcolor'><!--QuoteEEnd-->
It would be great if someone could time the use-build time and click time. I'm currently without a HL CD, so I can't try this out for myself.
Maybe some 1337 coder could make a similar thing for NS? <!--emo&:)--><img src='http://www.unknownworlds.com/forums/html/emoticons/smile.gif' border='0' valign='absmiddle' alt='smile.gif'><!--endemo-->
Also, I thought it only took 2 rp to get Carapace?
I agree that having dead skulks will change the values, but by how much? I don't know how to factor it in, and there's enough guesswork involved already.
Changing the click time doesn't really make much difference to the overall equation, since the time to second hive is bound by resources. it just means you spend more time waiting at the 2nd and 3rd towers. In my experience, by the time I get to the third tower I'm picking up resources at a pretty good rate.
(1*8*.23)/8*3 = .69
(1*400*.23)/400*3 = .69
Also I'm pretty sure that more gorges means more resources for the gorges as a whole scaled per gorge.
numTowers= number of towers.
numAliens = total number of aliens.
numGorges = number of gorges in the alien team.
UNIT = 1 'unit' (gorges get 3, skulks get 1 per click)
(numTowers * 0.23 * numAliens) / (numAliens + (numGorges*2)) = UNIT
<!--QuoteEnd--></td></tr></table><span class='postcolor'><!--QuoteEEnd-->
Oh crap.
You're right. The (BigTeam/SmallTeam) stuff is a bonus that should only apply to the smaller team. It doesn't apply to even teams.
I will go fix this up.
According to the way you put in the scaling factor (Resources/Tower/Click = 0.23 * NumPlayersAlien), a single Skulk will get 0.23 resources per click, taking 109 clicks (Well over 10 minutes!!!) to get enough resources for a single resource tower. Based on ingame experience with small numbers of players, this is absolutely NOT true. Your figures also show that more players = more resources per Gorge for the same number of resource towers, but this is also not true... playing as a Gorge I can tell you that smaller games mean more resources for a single Gorge. (which is why it's advantageous to have 2 gorges if you have 7 or more players on a team)
Based on ingame experience, I'd guess that scaling factor indicates how much bonus resources you get for each additional player. So, while a single player on a single resource tower will get 1 resource per click, two players will share a pool of 1.23 resources, three players will share 1.46 resources, etc. The equation then becomes:
ResourcesPerTeamPerClick = (0.77 + (0.23*NumPlayers))*NumTowers
NumShares = NumPlayers + (2*NumGorges)
ResourcesPerPlayerPerClick = Shares*(0.77 + 0.23*NumPlayers)*NumTowers/NumShares, where Shares = 3 for Gorge and 1 for anyone else.
The resources per click for one Gorge on a team of N players then becomes:
1 Gorge, no Skulks : 1 RTC (resource per tower per click)
1 Gorge, 1 Skulk : 0.923 RTC
1 Gorge, 2 Skulks : 0.876 RTC
1 Gorge, 3 Skulks : 0.845 RTC
1 Gorge, 4 Skulks : 0.823 RTC
1 Gorge, 5 Skulks : 0.806 RTC
1 Gorge, 6 Skulks : 0.793 RTC
1 Gorge, 7 Skulks : 0.783 RTC
1 Gorge, 8 Skulks : 0.775 RTC
1 Gorge, 9 Skulks : 0.768 RTC
Note that the resources per click reaches an asymptote at 0.69 (=0.23*3) resources per click for a team with a single Gorge and an infinite number of Skulks.
Now the interesting thing is, having more Gorges on a team does not decrease resources per gorge per tower per click (RGTC) by much. On a team of 8 players:
1 Gorge, 7 Skulks : 0.783 RGTC
2 Gorges, 6 Skulks : 0.653 RGTC
3 Gorges, 5 Skulks : 0.559 RGTC
4 Gorges, 4 Skulks : 0.489 RGTC
5 Gorges, 3 Skulks : 0.435 RGTC
Even with the very non-optimal combination of 5 Gorges and 3 Skulks, each Gorge is still getting 56% of the resources that a single Gorge would get. In fact, 5 Gorges will have the resources to build nearly 3 times as many defensive structures as a single Gorge can. The main reason 5 gorge/3 skulk is bad is rather different:
1) You won't have enough Skulks to eat marines. (BIGGEST problem)
2) On a 1 Gorge team, eventually all your Skulks get 33 resources and the Gorge starts getting TONS of resources. (on a 8 player team, 1 gorge with 7 full Skulks will get 2.61 resources per click, more than 3 times as much as he'd get with 7 empty Skulks) On a 5 Gorge team, assuming the 3 Skulks fill up, the Gorges' resource rate rises from 0.435 to 0.522, only a 20% increase, and still less than the 0.783 RGTC that a single Gorge gets. However, this is a minor problem compared to (1), as Skulks take a long time to fill up.
An interesting thing is what happens when Skulks fill up. On a team with 1 Gorge and 7 Skulks:
No full Skulks : 0.783 RGTC
7 full Skulks : 2.61 RGTC
6 full Skulks : 1.96 RGTC
5 full Skulks : 1.57 RGTC
4 full Skulks : 1.31 RGTC
With 7 full Skulks, your Gorge gets more than 3 times the normal resources. Yet, look what happens when NSPlayer decides to "put his resources to good use" by morphing to Lerk. A single Lerk on your team (using up those 33 resources) will decrease your Gorge's resource rate by 25%, making it take 33% longer to get a 2nd hive. Two Lerks reduce your Gorge's income by 40%, and three Lerks decrease it to <b>half</b>. Going Lerk on a team with one Gorge is <b>the most harmful, resource-wise, thing that you can do</b>. Going Lerk when you are full is <b>much</b> more harmful than simply having too many Gorges; two Gorges and 6 full Skulks will get half the resource rate as a single Gorge with 7 full skulks, but their total resource income is the same, so you can still get the same number of towers and chambers. In contrast, going Lerk steals resources straight from your Gorge, greatly reducing your team's ability to build chambers and towers.
Lesson: <b>Don't go Lerk at the one-hive stage</b>.
If we can arrive at a consensus I will update the Gorge guide with the numbers.
If we can arrive at a consensus I will update the Gorge guide with the numbers.<!--QuoteEnd--></td></tr></table><span class='postcolor'><!--QuoteEEnd-->
I've sent Nazgul the Excel spreadsheet with the numbers punched through.
I don't think there's any easy way to make a "proof" of the minimum time to second hive without running through some iterations, much the same way that you can't build a mandelbrot set without running the numbers. I think the numbers are correct, but there could be an extra factor we're missing. Only the developers know for sure, and I wonder if they've done the same calculations.