LotV Economy: Worker Pairing

Read the original post and discussion on TeamLiquid.net

If this Blog piece sparked your interest on the economy of StarCraft, be sure to read the secondary and more thorough piece wrote by TL’s Strategy Team:
A Treatise on the Economy of SCII



Did you knew that Lalush actually spends time watching old development videos calculating the time workers take to mine a single Mineral pallet?

Economy is boring for the majority, but Economy is everything, specially in Starcraft, a good amount of issues and problems that we see nowadays, things such as the Swarm Host can be more or less be fixed with the economy of the game.

What was the whole point of the Swarm Host? To slowly chip away at highly fortified positions while being both cost and supply efficient, but there are two problems with that, first the SH is a unit that to work best it needs to exist in a good amount, just like Carriers a single Swarm Host will probably not do much at all, but eight or twelve of them will, and the second issue is why does it need to be supply and cost efficient at all? The reason for this lies in the economic system of the game, if players were allowed to make inefficient trades, not just one or two, but as many as his strategy allowed the Swarm Host would be obsolete, replaced by more mobile and DPS effective Hydra-Roach-Viper based compositions, same thing could be said of Terran Bio compositions versus Heavy Protoss Deathballs, this sounds interesting doesn’t it? Now how could this be achieved? and why does the SH exist? Well the biggest reason for the existence of the Swarm Host is because of something you do in the early game but it affects you in the entire game, Worker Pairing.

The economic system of Starcraft II is build in such a way that if you want to be as supply efficient as possible while collecting resources you will need 16 workers per base mining Minerals and other 4 mining gas, this sums to 20 workers per base. In an average Starcraft game you for the most part will want to have around 80 workers in the later stages of the game, now what does this means? Well if a single bases needs 20 workers to be as supply efficient as possible, you will not want to have more than 4 bases at a time. Now if we got rid of Worker Pairing, and Worker Pairing only, meaning that the most supply efficient amount of workers per Mineral patch was 1 instead of 2, the number of bases would rise to a staggering 8, have you ever had 8 mining bases in a single Starcraft game? Just think about it a bit, just picture Life vs MMA with 8 mining bases each on Whirlwind, Frost, or Deadwing.

Now lets show a different picture, below are the mining rates for Starcraft II, there is a lower bound and a higher bound depending on the relative distance of the Mineral patches, all data courtesy of Liquipedia.


Minerals/Minute Min/min | MineralsPerWorker/Minute MinW/min
Gas/minute Gas/min | GasPerWorker/Minute GasW/min

Minerals

  • 1 Worker – 39/45 Min/min – 42 Avg Min/min – 42 MinW/min
  • 2 Workers – 78/90 Min/min – 84 Avg Min/min – 42 MinW/min
  • 3 Workers – 102 Min/min – Max Saturation -18 MinW/min

Vespene

  • 1 Worker – 33/42 Gas/min – 37.5 Avg Gas/min – 37.5 GasW/min
  • 2 Workers – 66/84 Gas/min – 75 Avg Gas/min – 37.5 GasW/min
  • 3 Workers – 101-114 Gas/min – 107.5 Avg Gas/min – 32.5 GasW/min
  • 4 Workers – 114 Gas/min – Max Saturation, 4 workers are only needed on inefficient diagonal geysers

Disclaimer: For the most part we are going to be focusing on Minerals and Averages to save up time, if anyone wants he’s free to make the math for every other Mineral configuration or amount.


Now that we have some numbers we can play around a bit, how much does a supply efficient base mine per minute?

  • 2 Workers * 8 Mineral patches = 84 Min/min * 8 = 672 Minerals Per Minute

And a fully saturated Mineral line?

  • 3 Workers * 8 Mineral patches = 102 Min/min * 8 = 816 Minerals Per Minute

Okay we have some interesting stats, we will be leaving out Vespene completely to save up time and we will think that each base has 6 workers mining gas.

Everyone says that Starcraft II suffers from a 3 base problem, but we have the math, we know better than that and we also know that players will want more or less 80 workers, but is that true about the base number? Lets play safe and say that we are Protoss players and we have 3 bases but we are scared of taking a fourth because of the map, so we save up all of our workers and fully saturate our bases, that’s 30 workers per base, how much Mineral income is that? We’ll straight up remove 18 gas workers from the equation, that leaves us 64 Mineral workers, which would give us an income of around (8163) – (72-64)18 Min/min = 2304 Min/min, that’s quite a bit. Now how does our Zerg enemy fare? He’s a good Zerg so he’s ahead of us by a base, and he’s being supply efficient with his workers (16 workers per Mineral line), he is collecting 2688 Min/min with 64 workers.

Wait a moment… Our opponent has an extra base, a whole saturated base, and he’s getting slightly over 15% income from it while having the same worker count on Minerals as us? No wonder people do not expand more.

Maybe a fluke? After all SC is a complex game, what does it happen if I had a supply efficiently saturated my 3 bases and my opponent had 6 bases with 8 workers each instead of 3×16? Well our income would be of 2016 Min/min (672*3), and the income from our Zerg opponent would be of… 8 Workers *42 Min/min * 6 Bases = 2016 Minerals per Minute.

So what we can get from our calculations is that there is No Mineral income advantage to expanding if you can’t fill all of your bases up to 16 workers each, AND the income from 3 fully saturated bases falls behind the income of 4 supply efficient bases by 384 Minerals per Minute, or 16%, this is without taking into account the 6 extra workers that the 4 basing player would need to invest into collecting gas from his 7th and 8th Vespene geysers, or the intangible inherent weakness that being covering a bigger area implies.


Okay, now that we know more or less does having Worker Pairing means how would the game work if Worker Pairing was to be removed? Well to start you wouldn’t be able to pair workers so when you have 2 workers in a single mineral patch both of them mine at 100% efficiency, instead you would have 1 worker mining at 100% and the second one added to the mineral patch would mine at a lesser percentage, such as 75%, these percentages could be tweaked easily to allow for a greater or lesser worker scaling/most efficient amount of workers per base, you could want to make the ideal amount of worker be 8 or be 30, these values would be dependent in how you want the economy in a large scale to behave.

I should note that this thread is in no way saying that the maximum possible amount of workers per base (24 as it stands now in HotS) should be lowered, only that two bases with 8 workers each should mine more minerals that 1 base with 16 workers, this can be achieved without affecting much the maximum amount of possible workers that can be mining on a mineral line.

One must think of the average income per minute per worker. That graph looks something like this.


(Graph 1) This graph showcases Starbow/BW like mining vs Standard SC2 mining and a new mining system called Double Harvesting which we’ll talk about later.

In our little graph things show to be the same amongst the three different systems and this is the cornerstone i want to get across before continuing, the income and as such the game would not need a extremely hardcore re-balance if a thing such as the Worker Pairing was to be removed, because the total income per base would stay more or less the same.

As it happens this graph tends to be more or less useless other than to showcase the parity between the income systems, and this is why we have the following graphs:

  • Benefit of 2 bases over 1.


(Graph 2)

From Double Mining TeamLiquid Thread:
Even at as few as 10 workers, adding an expo can give noticeable benefits, for both Starbow and Double Harvesting models. Starbow oscillates around constant 25% benefit, while Double Harvesting gradually grows from 10% to Starbow’s levels.
Standard falls behind a lot. Expo starts to kick in only at above 20 workers.

At higher worker counts (24+), second expo is a must for all models. Double Harvest however grows slower by few %.

  • Benefit of 3 bases over 2.


(Graph 3)

From Double Mining TeamLiquid Thread:
The decision of taking third base is probably more important. Standard gives no noticeable benefit until you reach around 40 worker count, and then grows very quickly.

Starbow has a strange peak around 25 worker count, caused by the odd behavior around 10-12 worker in single base.
Apart from that, Starbow and Double Harvesting shows similar benefit of 10-15% when taking 3rd base at 20-40 worker count.

At higher worker counts 3rd is important for all models. Double Harvest however is the lowest – which is good: it penalizes the loss of such base the least.

  • Benefit of 4 bases over 3.


(Graph 4)

From Double Mining TeamLiquid Thread:
This is where Standard fails the most: You don’t really need 4th mining base until you are really high on the worker count. In practice, given that some workers mine gas instead, you usually don’t have 60 workers mining minerals.

For Starbow and Double Harvesting, the benefit starts much earlier, giving you additional 5-15% income.

What these graphs are displaying is how much income advantage do you get from taking a base, as I have previously stated in the SC2 Mining system you do not receive many economic advantages if at all from taking a base if you cannot at least fill up all of you bases up to 16 workers each, so maynarding 8 workers from your 16 workers third base to your new fourth base will not give you an economic advantage other than not mining out your third as quickly. In the case of Starbow and Double Harvesting you will receive an income advantage from doing this and depending on the way the system is put in place one can control the pacing of the game, and the rate at which players will want to take bases or respond to his opponent’s new base.


Beating a dead horse?

So what in general does utilizing an income system that does not use worker pairing looks like? Well if we look at Starcraft II’s income system we can see parallels with what might be a Fastest Possible Map, this would be obviously an exaggeration, but the parallels are still there, in Starcraft II given that the max supply cap is of 200 you will not want to have more than 40% to 45% of your entire supply into workers, this as i have said many times now that the max theoretical base count would be of around 4 bases with 16 workers in minerals and ~4 on gas, but given that a 4 basing player does not get that much of an incentive to expand in the first place the game revolves for the most part around a smaller base count of 3.

In general High Ground Advantage is looked down upon because it reinforces turtling, none the less this is in an environment where the Starcraft II economy reigns and 3 basing tends to be the norm. But in a place where the theoretical base cap is of 7 or 8 instead of 4 it becomes quite clear that a player that is facing a turtler will be able to out expand him fairly easily and because his workers are more efficient than his ~3 basing opponent he will be able to overcome the turtle player by sheer numbers and macro.

The premise I’m trying to make here is that in an economy where aspiring to take 8 bases is the norm, games could become very snowbally if there isn’t a strong defenders advantage to counteract the economy, this was more or less the case in Broodwar and this is also more or less the case in Starbow, because of this it is important to be careful while adding economic modifications to a game, but it also means that if the homework and investigation are done you can end up with an incredibly interesting game, as i have said while showing the Income graphs, if a system were to be implemented big overarching changes in the unit stats wouldn’t need to happen for the most part, but deeper considerable changes in the game mechanics or macro mechanics may be necessary to counteract the more active economy.


I have many times read about things such as using 6 Mineral patches instead of the normal 8 or using the new LotV economic system, the truth about said systems is that even when they do a better job than the current system does in Heart Of The Swarm, it is still pretty lacking compared to the Double Harvesting system or the BW mining, the 6 mineral patches per base was tested quite a bit under FRB (Fewer Resources per Base) and what it did is that instead of players ending up with 3 bases they ended up with 4, so in that regard it only shifted the income slope closer to Starbow or Double Mining systems, but the core is that as long as a strong Worker Pairing is active any system that simply reduces the Mineral patch amount per base will not fully succeed.

The case of the new LotV mining scheme is that it will force players into expanding more by being aggressive with the depleting mechanic, this is a very interesting way of trying to fix the issue the previous iteration of the LotV economy had, which is that as one expanded along the map one was leaving empty carcasses of bases without a real strategic value, and because there weren’t any changes to the Worker Pairing mechanics one could see the players 3-4 mining bases shift on the map as the game progressed. Because the new LotV mining system doesn’t try to alleviate the core problems of HotS economy there are still problems with the 3 base cap, but that’s not everything, the design view of Starcraft II is that the game must be very easy to read, mineral patches that have 750 minerals mixed in with patches that have 1500 on a single base is something very hard to read at a quick glance, specially because mineral patches have 10 different models, and each model has 4 different states depending how much minerals there are left on the patch. Now I ask, to which patch will you land your mules? There are 7 maps in the map pool and each map and base has a different mineral setup, will Terran players need to memorize every single mineral patch for every map so they know where to land their mules?

This problem can be circumvented, nonetheless it will mean that a new colored mineral patch model be introduced to the game, but I’m afraid that there might still be other problems, such as the game becoming more punishing to new players/noobs, I have faced many times while playing custom games in the Open Games section LotV mods but without the economy changes and this is because new players naturally want to turtle up and play a NR20 game, I’m not saying that the game be shaped to fully please bronze and lower players, but a system that forces expanding, and alienates bad or new players meanwhile bringing little advantages over other systems such as BW like economies is not the route to go, the shift of mining bases that the Blizzcon build of LotV had will still be there only slower and not as sharp, a player that has 16 workers in a single base vs a player that has 16 divided on two will still get the exact same income, same thing with a player 3 basing player that has 16 workers per base vs a 6 basing player that has his 48 workers evenly split.


Removing Worker Pairing from the game will not magically “fix” everything everyone considers “broken” in the game, Worker Pairing generates very specific issues, such as players not wanting to expand over a certain threshold, meaning that without Worker Pairing players will want to take more bases and split themselves more, creating more weak points in the defense which aggressive players can take advantage of, but these scenarios will not happen when players only have two bases, they will happen when players have +4. In that regard changing the way the economy works does not affect the great majority of games, but when economy comes into play then it can be seen clearly.

Without Worker Pairing SC2 will continue to be SC2, as I said previously the removal of Worker Pairing is not a magical “fix” to everything and it will not magically transform the game to BroodWar, most timing attacks will continue to exist, same with unit compositions and such, these things are ingrained into unit design, not the economy of the game for the most part. The removal of Worker Pairing also does not mean that players will not be able to turtle, turtle strategies will continue to exist but it will allow the aggressive player to actually take more bases and get an advantage out of it by being more supply efficient with his workers than his opponent, which in turn will allow him to make supply inefficient trades, where the turtling player with his limited income of resources will need to be as efficient as possible with his units.

The removal of WP does not mean that the income per base changes drastically, a 1 fully saturated base with Double Harvesting or SC:BW based Mining will still mine around the same Minerals per minute than a SC2 fully saturated base with the same amount of harvesters, what it changes is the amount of income per supply as the number of harvesters go into the single digits. This is clearly showcased in graph nº1.

The complete removal of Worker Pairing means the need of “dumb workers”“, as the Double Harvesting system showcases this is not entirely true, it is possible to achieve a good supply/income curve without the need of BroodWar worker trains, this is the point Double Harvesting attempts to showcase, even when by SC2 standards they will be considered dumb, it must be understood that “smart workers” does not equal the existence of Worker Pairing, in the same sense that Worker Pairing does not mean smart or better workers and economics.


To allow further testing I have made a couple extension mods based on the Starbow/BW economy systems and imported the Double Harvesting system into an Extension Mod, so both systems can be tried out on any Melee map, both systems are also open to editing for anyone that wishes to know the necessary changes to remove Worker Pairing. It should be noted that for this to be achieved there is no need for the use of triggers with the necessary manpower and correct math into the data editor. This is not a blog to sell these mods, this is a blog to showcase the damage Worker Pairing is causing into the economy of StarCraft II. And basically any system where workers have a gradual decline in efficiency starting from the first worker forwards will be better than the current system where the first and second workers mine at the same 100% efficiency. Further additions to allow for better worker bouncing, or worker trains à la BW will help, but are not strictly necessary, as the Double Harvesting mod showcases.

Both Extension Mods can be found under NoWorkerPairing or NWP tag in any of the four servers. If any bug or problem is spotted just post in this thread and I’ll do my best to take care of it.

It should be noted that because of the high efficiency of the first worker compared to the normal SC2 workers, players will tend to mine more minerals at the start of the game. Because of this the game will be accelerated slightly in the early game, meaning that you will need to speed up your build order by around 2 to 3 workers, like the initial steps of Brood War build orders would be.


TeamLiquid Thread Thread

Reddit Thread

Lalush’s, small background behind AI and worker pairing

Scientifically Measuring Mining Speed

Ideal Mining Thoughts (BW Income Values)

Mod Double Harvesting Better Saturation Curve

Starbow Economy Explained (Video)

Mod Fewer Resources Per Base (FRB)

LotV Economy Discussion

Starcraft 2 BroodWar

Some Issues with Turtle Playstyles in Starcraft 2

Breaking 3 Base Establishing Asymmetrical Mining

Worker Count Gas Based on Korean Commentators

Breadth of Gameplay in SC2

Onegoal a Better SC2 Project hub

Why Protoss is Frustrating to Play or Play Against

In Defense of Mech

Gold Minerals Evaluated

Worker Transfers

SC2 Liquipedia; Mining Minerals

SC2 Liquipedia; Resources

SC2 Liquipedia; MULE

BW Liquipedia; Resources

BW Liquipedia; Mining

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