Convergent point is one of the most important concepts in understanding how to play a good macro game. I have posted about it in the Heart of the Swarm era (part 1 and part 2), and I believe it is a good time to post an improved version with some updates based on Legacy of the Void.

There are forum posts occasionally asking about the number of production buildings (a recent example on /r/allthingsterran), and these questions can be answered through the understanding of convergent points. This post aims to be a stand alone piece, so you don’t need to read the two previous posts on convergent points before you read this.

First and foremost, I want to be clear that I did not create “convergent points”, but I simply provide a systematic explanation based on observation from countless number of games. Also, I am not saying I am the first to observe it, but it just happens that my posts on this topic have been picked up and accepted by many. You may have been applying the concept of convergent points in your game without noticing it anyway.

Basics of convergent points

What is it?

A convergent point refers to a benchmark in terms of the number of production buildings you should have based on the number of mining bases you own in order to have an optimum production.

If you compare many professional games of different players in the same match up at the say 10:00 point, you will notice that they have more or less the same number and type of production structure (assuming they use the same type of composition and nothing drastic happened). This is because that production building set up (both quantity and type) is considered the most efficient to spend your resources based on the number of mining bases you have. I just come up with a random time stamp of 10:00 as that is probably the time that the players have at least three mining bases, and they have already reached the mid-to-late game convergent point.

While these games have more or less the same production structures later in the game, they probably have used a wide range of openings and build orders. However, even if you know they have different openings and build orders, it is almost impossible to tell what have been used because they now basically have the same set up. This suggests that no matter what opening and build order you choose, you will eventually converge back to what is considered the most efficient production set up (e.g., X number of Barracks). Such most efficient production set ups provide check points for players to know what to build. These check points are convergent points.

Practical applications

There are several important practical applications. At the basic level, it provides a guide for how many production buildings should be added based on the number of mining bases. If you have more buildings than the convergent point benchmark, not all buildings are producing. If you have fewer buildings than the convergent point benchmark, resources will start to bank up. Therefore, by knowing what the convergent points are, you have the optimum set up to spend the resources.

The other important implication is to provide a check point for which converge you converges your build order towards, and this explains the name “convergent point”. You may have faced the below situation before.

You have found a build online through a build order guide or a professional game vod, and you try to execute it in your game. While you have a decent idea of what to build and what to do within the boundary of a specific build order, you may find that your plan is limited to what is stated in the build order notation. What do you do after you have done all that you have written on your build order? How many Barracks should you add and when?

As I have discussed earlier, the convergent points remain the same for most, if not all, build orders. Thus, you can use the convergent points as a guide to build additional production structures based on the build order you have selected. This is also what I called the build order block concept, but I will focus on the convergent points in this post.

Assumptions and limitations

It is important to note that convergent point assumes constant production from every building including the Command Centres. There is little meaning to convergent points if you do not produce constantly, because it implies that you can stop production to add X number of production buildings as you like and then produce units from all of them at once. Then, there is no point in discussing the optimum number of production buildings based on the number of mining bases.

Constant production is an unique feature of Terran due to the linear production mechanism. Consequently, the concept of convergent points should be limited to Terran.

Zerg do not have to add production buildings as the number of mining bases increases, so it is obvious that there is no convergent point for Zerg. However, although Protoss do not exactly have the similar linear production of Terran, their production mechanism is comparable. In fact, some have applied this concept to Protoss, but I will restrict my discussion to Terran only.

Production saturation

Although I described a convergent point as the optimum number of production buildings based on the number of bases, it does not mean there is no “overflowing” of mineral and gas if you produce from these buildings constantly. If there is no “overflowing” of resources, you cannot build an additional Command Centre to expand. Thus, I further categorise convergent points into two “paths”. One is you plan to play a normal macro game whereby you continue to expand when you can (i.e., unsaturated). The other is you plan to stay at a certain number of bases and not expand (i.e., saturated).

If you do not plan to expand after a certain number of bases (e.g., two base all-in), you should pick a convergent point that saturate the production. In other words, when you constantly produce units, you should not have extra mineral to build a Command Centre.

On the other hand, if you plan to expand accordingly, the number of production buildings for the convergent points should not be saturated. That is, as you constantly produce from these production buildings, the residual mineral will slowly pile up to allow you to squeeze out a Command Centre and expand.

The convergent points I discuss below will take this into consideration.

Common convergent points

One base

Strictly speaking, there is no convergent point on one base, because you don’t converge to one base. But for the sake of being comprehensive, I will briefly go through it, and explain its implications for the subsequent two base convergent points.

Unsaturated

Due to the accelerated economy in the early game of Legacy of the Void, there are countless way to play this out. This essentially includes every build order that takes an expansion.

Saturated

It is extremely rare to stay on one base in Legacy of the Void. The most extreme case I have come across is proxy four Barracks cheese, which is comparable to proxy two Barracks in Heart of the Swarm and Wings of Liberty.

There are other close-to-saturation convergent points, for example, three Barracks Reaper and some variations of 1-1-1. These builds still expand eventually but the Command Centre is delayed drastically.

Two bases

Unsaturated

The most common one is

1x Barracks

1x Factory

1x Starport

2x Main composition building

If the main composition is bio, then the two main composition buildings are Barracks. Thus, it will be a 3-1-1. Similarly, this applies to mech and air composition, whereby the convergent points are 1-3-1 and 1-1-3 respectively. This is arguably the most important convergent point as it generally marks the end of a build order, and it is the convergent point that almost every build converges to.

Saturated

This is perhaps the only noteworthy saturated convergent point. A simple way to think about it is how much more production you can squeeze out from the above unsaturated convergent point.

For bio composition, you can have two more Barracks, and this results in 5-1-1. It is less clear for mech and air compositions, because these two compositions always plan to expand beyond two bases. Hypothetically, if you want to stay on two bases with these two compositions, I suppose you can only add one additional main composition building instead of two.

Just to be clear, it is still possible to add a third Command Centre by cutting production temporarily and transit to a macro game on multiple bases.

Three bases

When you take a third base, it is safe to assume that you plan to play a standard macro game and expand as much as you can. Thus, it is unnecessary to consider the saturated convergent points.

There are two stages. The first is as follow,

1x Barracks

1x Factory

1x Starport

4x Main composition building

To put it simply, it is 5-1-1 for bio, 1-5-1 for mech and 1-1-5 for air. Subsequently, you add additional buildings based on your composition goal in the second stage, while you build more Command Centres accordingly.

For example, Tank is an important unit in the Terran mirror match composition, so a second Factory is usually added right after you have converged to the above check point. It will be a 5-2-1. What to add next depends on the situation, play style and game plan. For instance, TY usually stays on 5-2-1 for a long time, and he spends the resources on more Command Centres. Other players may prefer to add more production buildings and move towards 8-2-1 or 7-3-1. If you need to transit to sky Terran to compete against opponent’s air composition, you will need to make adjustments accordingly by adding more Starports.

Another example, Liberator and Medivac can be key units in TvP, so the subsequent convergent point is 5-1-2. The same logic applies, and the usual go-to convergent point is 8-1-2 in the end. There is more room for flexibility after you have reached the standard convergent points.

All in all, the rule of thumb is generally a maximum of twelve total production buildings (assuming you produce from all simultaneously), and the set up is dependent on match up, composition and preference.

Convergent point selection and flexibility

The last section only describes what the convergent points are in regards to the quantity of production buildings, and I will explain how you can be flexible with the convergent points based on your selected build.

Let’s use some common examples for illustration.

Cure opened up with a Command Centre first into three Barracks build order in the above vod, so he had a 3-0-0 on two bases. Intuitively, he should converge to the standard two base convergent point of 3-1-1, and he did that by building the necessary structures (i.e., Factory and Starport).

In the vod below, Cure opened up with a more aggressive one base 1-1-1. As discussed earlier, there is no practical one base play, so there should be a delayed expansion. In the game, he did expand after a 1-1-1 opening on one base, and he placed two more Barracks afterwards when he could afford. This converged back to the two base 3-1-1 convergent point. Therefore, as shown in these two games, you can have different openings and builds, and still can eventually converge back to the “next” convergent point.

While it seems conveniently intuitive to assume the “next” convergent point is the default choice, there is more room for strategic flexibility. Often, we see players go for an early third Command Centre for an economic advantage, but this also means that there are three bases before the two base convergent point is reached.

Let’s use the above vod as an example, TY used a standard one Reaper expand opening into 1-1-1 build, then built a third Command Centre. This is perhaps the most common TvZ build right now.

Due to strategic choices, TY put down a third Command Centre before he even reached the standard two base convergent point of 3-1-1. I must make it clear that there is nothing wrong with this. This simply means that he delayed the 3-1-1 convergent point to spend the resources on a third Command Centre before he converged back to a standard convergent point. Indeed, TY later added two more Barracks to move back to the 3-1-1 convergent point, then added another two more for 5-1-1. After TY had reached 5-1-1, he added two more Barracks for 7-1-1. Eventually, he added the second Factory for a 7-2-1. Like I had said, there is more room for flexibility and preference after the 5-1-1 convergent point, and the rule of thumb is to not have more than twelve production building for optimum resource expenditure.

Is it alright to build a production building that is beyond what is required for the standard 3-1-1 or 5-1-1 convergent points?

Yes. For example, you can go for a Reaper expand into two Factory blue flame Hellions with a 1-2-0. Clearly, you can converge to 1-3-1 for mech with this build, and 1-3-1 is just the mech version of 3-1-1. But the point is, you can still go for bio with a 1-2-0 build structure, even though you cannot exactly go back to 3-1-1 because you have two Factories. You can still build two more Barracks and a Starport to move back to 3-1-1 with an extra Factory, and play out the game as per normal.

If your army composition requires a Reactor on the Factory (e.g., Widow Mine), you can now just use the two Factories without add-on instead of adding a Reactor. Alternatively, if your army composition requires a Tech Lab on the Factory, you can simply don’t produce from the second Factory. Eventually, you will move beyond the 3-1-1 and 5-1-1 convergent points whereby you need to add a second Factory (e.g., 7-2-1), then you can just utilise that second Factory again.

Other considerations

Upgrade and add-on

There is this general understanding that the number of upgrade buildings (e.g., Engineering Bay) depends on the production saturation choice. If you plan to play a macro game and use unsaturated convergent points, you should have two upgrade buildings for the main unit composition (e.g., two Engineering Bay for bio). Conversely, if you plan to stay on two bases, it is usually a better choice to have only one.

This can be more dynamic than an either/or option. For example, way back in Wings of Liberty and Heart of the Swarm, it is normal to have 3-1-1 on two bases with one Engineering Bay for +1 attack upgrade in TvP. The second Engineering Bay is added after the the third Command Centre is built. Consequently, the bio attack and armor upgrades are not in sync, and it is often +2/+1 –> +3/+2 instead of +1/+1 –> +2/+2.

Add-ons have little to no effect on the convergent points, because the expenditure cost of a production cycle with a Reactor versus a Tech Lab is quite close. There can be exceptions, which I have brought up in the last section regarding the two Factories in a 1-2-0.

Extreme late game situations

At times, you reach an extreme late game situations when you bank up resources after you have already max out and taken as many bases as realistically possible. The convergent points should not be a factor in your game any more at that stage, because the assumption of constant production is not upheld.

You should consider adding more production buildings beyond the rule of thumb threshold, because it is the production “speed” that matters when you have a huge bank of resources. You want to re-max as quickly as possible after you have traded your max out army. It is difficult to pin point what buildings and how many should be added, as there is hardly any framework for extreme late game situations. It is down to individuals’ understanding and experience, and this also explains why players who truly understand the game well beyond mere mechanics ability excel in the late game.

Legacy of the Void economy

The above discussion has taken the new economy into account, but there are other interesting observations worth mentioning.

The 2-1-1 has become a standard build in TvP, and it is an interesting Legacy of the Void twist to the old TvP build order choices. In Heart of the Swarm, Terran have two main build variations (not openings),

Multiple Barracks first (three Barracks)

Tech first (1-1-1)

The key is that they are mutually exclusive due to the limitation of resource, and the player has to pick one. This results in the choice of favouring earlier mid game bio strength (i.e., multiple Barracks) or early harassment potential (i.e., tech). Unlike Heart of the Swarm, Legacy of the Void allows you to tech up and have multiple Barracks at the same time. Therefore, 2-1-1 has become a unique convergent point in the match up in Legacy of the Void. Most importantly, while it is a “new” convergent point, it still converges back to the main convergent points I mentioned above. It is normal to add the third Barracks to converge back to the standard 3-1-1.

The second interesting observation is the shortened gap between the two base (i.e., 3-1-1) and three base (i.e., 5-1-1) convergent points for certain builds. When you chose a 1-1-1 into three Command Centre build variation, you will add two more Barracks to reach the 3-1-1 convergent point (I use bio as an example). Subsequently, you will then add another two Barracks to reach 5-1-1 convergent point. However, due to the mining rate, you can afford to put down the fourth and fifth Barracks while the second and third are still building. As a result, you are actually building four Barracks at the same time. Nevertheless, the logic of convergent points still stands.

The third observation, and also the most important one, is how the Legacy of the Void mine out rate affects the converging process beyond 5-1-1. In Heart of the Swarm, players almost always converge to 8-2-1 or something comparable on three bases in all match ups (again, I use bio as an example), before they decide to build the fourth Command Centre. This is because the Heart of the Swarm economy favours the three base paradigm, and hence, it is more rewarding to operate on a close-to-saturated three base convergent point before expanding further. In contrast, in Legacy of the Void, your main is about to mine out when your third has started mining. If you move from 5-1-1 to say 8-2-1 on three bases, the decreasing total mining rate (due to a low efficient mining main base) will not allow you to produce from all eleven production buildings. Therefore, it is more common to stay on 5-1-1, 5-2-1 or 5-1-2 longer and expand, before eventually converging towards an eleven or twelve production buildings converging point after the total mining rate is back to at least three efficient bases.

Summary

A convergent point refers to a benchmark in terms of the number of production buildings you should have based on the number of mining bases you own in order to have an optimum production.

The key convergent points are 3-1-1 and 5-1-1 for two and three mining bases respectively. There is more room for flexibility after you have reached 5-1-1.

You can have build orders that do not follow these convergent points strictly, but they should converge to them eventually.

This article is translated and posted on scboy.com by 知識と日陰の少女.

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