This post was originally going to be an EffortPost™ in the Suggestions subforum, but it got complicated and frankly more interesting than I expected, so instead I am posting it as a mechanics post. This post was originally motivated by complaints made in the Bugs Thread that planetary invasions were fundamentally broken and unfun as a gameplay mechanic. I wanted to analyze the mechanics of invasions, initially to serve as the basis for suggestions to improve invasions. However, things quickly became complicated, and in the process I learned some things which led me to rethink planetary invasions and to question the initial premise - are planetary invasions in fact broken and unfun gameplay?
The basic idea here is to analyze what it actually takes to carry out a planetary invasion, in an effort to quantitatively assess the complaints many people have about planetary invasions being too prohibitive and/or unfun gameplay. My hope is to accomplish a few things here: (1) to provide something generally-informative for the player base, (2) to give some insights on how to effectively go about playing your game to prepare for eventual planetary warfare, and (3) to gain some insightful basis for looking at the question of whether or not planetary invasions are actually problematic or poor game design.
In a broad sense, a planetary invasion consists of four stages: (i) building a lot of troops, (ii) shipping them to the nearest NPR homeworld, (iii) shooting things, and (iv) maintaining supply lines until the battle is over. Of these, step (ii) is fairly well-understood and I'm not going to spend much time on it, as I think most players know how to build 200,000-ton assault dropships and point them at the enemy. I'm also not going to cover the naval aspects such as eliminating STOs or conducting preliminary orbital bombardments, as I think most players know how to point and shoot. The remaining aspects, however, correlate with common complaints which are raised about planetary invasions, thus are worth analyzing in detail to assess the validity of those complaints - and what, if anything, can be done to mitigate those issues which so many players struggle with.
Without further ado, we begin with...
Building Ground ForcesTo get a sense of how long it actually takes to build the several million tons of ground troops we need to go conquer someone, let's make some simplifying assumptions:
- The build cost of a ground formation is very nearly (neglecting HQs) equal to the size of the formation in HS (tons/50) times the average armor level of the elements in that formation. A 5,000-ton battalion of infantry (1 armor) costs about 100 BP to build, while 5,000 tons of medium tanks (4 armor) costs 400 BP. I'm going to assume that the balance of infantry and armor in our army is such that the average armor level is 2, so that every 5,000 tons of ground forces will cost 200 BP.
- Ground Force Training Facilities (GFTFs) start off with 250 BP/year capacity, if I recall correctly, and the techs to improve this are relatively cheap. I will assume an average of 500 BP/year tech level which I think is reasonable for the early game (say, first 25-50 years).
- A GFTF costs 2400 BP to build with planetary industry. At the start of a typical 500m pop game (the default), the player race has 400 factories producing 4000 BP/year, so if a player gives 20% of their industry to GFTF construction (an optimistic estimate, but we'll go with it) they can build a new facility every 3 years. Of course this can be accelerated with technology, new factory construction, and good planetary governors, all of which are difficult to model in a simple way, so I'm going to make a rough approximation that we build a new GFTF every two years on average.
- Assuming a default 500m pop start, we begin the game with 4 GFTFs in service.
This means that we generate a total of (based on our assumptions) 4000 BP in the first two years, 5000 BP the next two years (9000 total), and so on. After ten years we have produced 30,000 BP of ground forces, after 25 years we will have built 122,000 BP, and after 50 years a nice 400,000 BP. Again, rough estimates here.
Recalling that our assumptions give us 25 tons of ground forces per BP, this means that after ten years we can build 750,000 tons of ground forces. After 25 years we can build 3,050,000 tons, and after 50 years we can have an impressive ten million tons of ground forces. Now I do want to emphasize that I am making some fairly generous assumptions here, but in any case it looks like we should be able to build a nice, big invasion army in 25 to 50 years - of course, this neglects the need to, for example, upgrade old formations with new equipment, or to build enough garrisons and defensive troops to secure our expanding stellar empire. But don't bother me with trifles, we have a 10,000,000-ton invasion army and I am going to use it!
Note that an important part of this assessment is that we actually build a lot more GFTFs. If I had only used my initial four facilities, and not built any more (because I had more important things to build like, I dunno, mines or labs or whatever), I would only be able to produce 100,000 BP of troops - a "mere" 2.5 million tons - in 50 years. That's nothing to sneeze at, but it's also not terribly impressive when trying to invade a planet defended by multimillion tons of enemy ground troops.
Shooting the Other Guy's Ground Forces, Repeatedly and with Great VigorSo I've found a nearby NPR, blown up their ships, shot all their STOs from orbit, and shuttled ten million tons of troops to the planet surface in dropships. However, the local NPR has decided to fight me instead of surrendering, and this is going to take a while.
To find out how long this war is actually going to take, we need to somehow estimate the casualty rates with math. As it happens, we have a reasonable way to estimate this in the form of Lanchester's Law, which takes the form of:
dA / dt = -beta * B
dB / dt = -alpha * A
Terms:
A : Strength of Force A (attackers), here in units of tons
B: Strength of Force B (defenders), here in units of tons
alpha: Kill rate of Force A firing at Force B
beta: Kill rate of Force B firing at Force A
t: time, here in units of ground combat increments (GCI)
This system of equations can be solved to obtain a rather unwieldy expression for the time dependence of A and B, or integrated numerically; in either case, the results are not much different at least in the case of Aurora.
The kill rates are essentially the product of the hit rate, the average shots per ton, the probability of scoring a kill when a shot hits, and the average tonnage destroyed per kill. The hit rate is generally known, except for commander bonuses. For the attackers, the hit rate is the product of the base 20% hit rate and the terrain to-hit modifier, divided by the effective fortification modifier; for the sake of example, I will use Mountain terrain, which has a fortification modifier of 2x and a to-hit modifier of 0.5x, and assume the defending force includes INF and STA elements as well as enough CON to bring the entire force to a maximum fortification of 6x (12x with terrain modifier), giving an estimated hit rate of 0.833%. For the defenders, the hit rate is the product of the base 20% hit rate, the terrain to-hit modifier, and the effective evasion stat of the attacking force which I will assume to be 0.6x (INF and VEH elements), giving an estimated hit rate of 6.0%. I will further assume that the average shots per ton is 0.2, taking this as representative for a mix of PW (0.2), CAP (0.5), and MAV (0.03) weapons, and that the kill probability for a hit is 50%, which is a fair approximation if both forces are made up of an even split by tonnage between infantry and armored elements. Finally, making the same approximation about force composition, I estimate the tonnage destroyed per kill at about 10 tons. This gives values of alpha = 0.00833 and beta = 0.06.
Now let's take my big, impressive 10,000,000-ton army and land it on the planet of my local NPR opponent, the Haplessians, who only have 2,000,000 troops to defend themselves with, and see what happens:
So we will win handily, and it will take us less than ten days to do so. The time it takes to win is important, as discussed below, because it will directly influence how many supplies we will need to build to accompany our army.
Before we move on, I would like to try a few other cases:
(1) What if we invade with, say, 5,000,000 tons of troops? For reasons to be discussed below, this is a relevant question as we may not be able to deploy all 10,000,000 tons of the troops we've built as combat forces (we will need some logistics). In this case, we...okay, actually, we would lose horribly. But if we attack with
5,500,000 tons of troops, we can still win, but it will take us much longer, about a month (100 GCI = about 30 days), and we will lose most of our army in the process.
(2) What if the enemy has a nice, rolling prairie planet with few if any natural defenses (fortification modifier 1.0x, to-hit modifier 1.0x)? Surely it will be easy to kill them even with only five million tons of troops? Under these conditions, we have alpha = 0.33%, beta = 1.2%, and as it turns out we can now comfortably destroy our enemies with only moderate losses. We could even win with a mere four million tons of troops, if we really needed to, but with very high casualties. This takes only about five days.
(3) On the other hand, what if the enemy has a harsh, foreboding Jungle Mountains homeworld? With a fortification modifier of 3x and a to-hit modifier of 0.125x (alpha = 0.000139, beta = 0.0015) there's no way we can take this planet with five million soldiers...what about ten million? As it turns out, the answer is yes, but it will take about two months.
Okay, okay, that's enough math for now. So far, what we've learned today is that if we outnumber the enemy badly enough (for the curious, this condition is met when alpha * A^2 > beta * B^2 initially), we can take their planet from them. It might take fifty years to build a big enough army to do this, but it can be done. However, there is one other major consideration we need to deal with.
Supplying Ground ForcesGround elements have a GSP value, which is determined by their weapons and indicates how many supplies that unit needs to fight ten rounds of combat (3 1/3 days). Therefore, for every 10 GCI while we are engaged against the Haplessians, we will need some amount of LOG to sustain our troops.
As a
very rough estimate, I have found that for my own combat formations the total GSP for all elements in a formation tends to be about 30% of the tonnage - in other words, a 5,000-ton battalion will carry about 1,500 GSP. Extrapolating this recklessly, our ten million ton army will require 3m GSP every 10 GCI, or since one month is 90 GCI about 27m GSP per month.
We have two options to provide this GSP. We can use INF logistics units, which provide 10 GSP per ton or, more importantly, 500 GSP per build point as long as we don't slap any power armor on them. However, these can only resupply the formations they are attached to, meaning our front line formations will be less combat-effective per ton, and are vulnerable to enemy fire on the front lines. Fortunately, with the new unit series and replacement mechanics we can manage the supply situation reasonably well with these. The other option are LVH+LOG, which are logistically much easier to use (just slap them into an Army-level HQ and let them do their jobs), but provide only 8 GSP per ton due to the LVH tonnage overhead, and even worse
provide only 200 GSP per build point because they are an armored unit! This may end up being a serious problem if we need to build a lot of supply elements to keep our offensive moving.
Returning to our big, scary army, which demands 27,000,000 GSP per month: with infantry logistics elements this comes out to 54,000 BP needed to supply our offensive, just for one month. Remember that our total ground forces BP over the past 50 years has been a whopping 400,000. We will need more than one-eighth of this just to keep our army supplied for one month.
Now, remember our initial invasion plan of Haplessian Prime, in which our ten million tons of soldiers could defeat two million tons of enemy soldiers in ten days? We will need 18,000 BP worth of logistics elements to keep our soldiers in supply for that time period, which isn't too bad actually. On the other hand, if we were to send only 5 million tons of soldiers, we would need half as many supplies per month (13,500,000 GSP per month, or 27,000 BP) but we would actually need supplies for a whole month. However, we only built half as many soldiers in the first place, so the overall cost in BP is lower (the cost to replace all of our losses, however...).
The extreme case, however, would be our assault into the Jungle Mountain terrain, which requires supplying our ten million tons of troops for nearly two months - requiring roughly 100,000 BP of supplies on top of the 400,000 BP we used to build our army. That's a lot to put it bluntly, however do we really need that many supplies? Consider the following:
- The defending force will have the same problem - they, too, will run out of supplies unless they have dedicated 30% of their production to logistics, which at the very least no NPR ever does as far as I know.
- Formations which are "out of supplies" are not combat-ineffective - they will still fight, but each element will have only a 25% chance to fire in each GCI.
Therefore, we really only need enough supplies to at least match the defending force, and once both forces have run out of supplies they will continue fighting on equal footing at a much lower intensity - the net effect here is that out invasion will take roughly four times longer than we had initially planned. If we really want to splurge, we can try to land on the planet with
more supplies than the defenders have, which gives us more GCI of full-efficiency fighting while the defender is only at 25% efficiency, potentially allowing us to gain a big advantage. This point would become more important if we had a smaller force (at equal tech, we need around 6,600,000 tons to break even), in which case the battle would take much longer.
All this being said, having ~20-25% of our force composition as logistics elements is not too onerous, one might even say it is realistic. I have also neglected the fact that supply demands will decrease as we lose troops, which further reduces the actual needs.
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So to conclude, let's return to my earlier stated goals:
(1) What information has been provided to the player base? First of all, with a reasonable investment into ground forces (which is, as we have seen, very necessary if you want to mount a planetary invasion), a player can build roughly ten million tons of ground forces over a 50-year period. This would scale approximately linearly with the starting population at least within a reasonable range. Further, a planetary invasion under relatively favorable conditions will still require multiple months to complete, and under more marginal conditions can take a year or more. Finally, to execute a planetary invasion can impose a significant logistics burden, but as a fraction of our total force composition it turns out to not be too onerous under most conditions.
(2) What helpful insights have we gained for conducting planetary invasions? Aside from basic conclusions such as "build a lot of troops" and "build a lot of logistics elements", this requires some interpretation of the data. One major takeaway here is to maintain a significant technological advantage. Because the kill rate scales roughly quartically with technology - i.e., as (attack / armor) ^ 4 - a tech edge has a very strong effect. In practice, this is less likely to improve your own kill rate very much if you are starting from equal tech compared to your opponent, because of overmatching effects, however if you have better armor than your opponent's weapons their own kill rate will drop off
dramatically, which allows you to (a) use fewer troops, and/or (b) prosecute a campaign with poorly-supplied troops, since being out of GSP only reduces your damage output by 75% (since out-of-supply formations only have 25% of their units firing in any GCI).
This is an important point, since as we have seen, in some extreme cases it may be untenable to keep an invasion force
supplied for the duration of an invasion, although in our favor, the defenders will have the same problem - the net effect of this is most likely going to be an extreme lengthening of the campaign by a factor of ~4x. And now we know why the game is called "Aurora 4x"!
rimshot Additionally, the role of orbital bombardment can be considered in quantitative terms. We can estimate the level of enemy forces we can comfortably defeat with our own forces, and attempt to orbitally bombard the enemy down to that number. This will still inflict some collateral damage, but hopefully less than just nuking them to zero from orbit, leaving
something for our boots on the ground to conquer.
(3) Are planetary invasions fundamentally broken?
This is a difficult question to answer. In most cases, the answer seems to be "no" since aside from requiring a lot of troops the burden on the attacker is not too extreme in terms of e.g. supply requirements. In some cases, such as attacking with marginal forces or into harsh terrain, the supply requirements can be significant; however, as we have seen, this is not as problematic as it appears, because we really only need enough supplies to last until the defenders run out of supplies, at which point we are fighting on even footing just at a lower intensity. This leads us to realize that the purpose of providing an invasion force with extra LOG elements is not to keep them supplied indefinitely, but only to keep them on even footing with the defenders, or perhaps to gain a brief advantage which can snowball into a big victory.
In these extreme cases, we may be subjected to multiple months (or even years?) of 8-hour increments even if we have nothing else going on in our empire and would really rather be clicking the five-day button. Is this a problem? Well...maybe not? Aurora after all has always been a game for patient people, dating back to the VB6 days of hitting "next turn" and grabbing a good book to read for the next few minutes. In all honesty, it is pretty likely that by the time you're mounting a planetary invasion (remember, 50 years to build all of these troops...), your empire will be busy enough that something is happening most of the time - frankly, I recommend turning your construction increment down to one day or even eight hours so that you have something to do after every few button clicks.
So with the logistics problems settled reasonably, and the problem of eight-hour increments for months or years of game time admittedly handwaved with exhortations to patience and serenity, what else is left? Some people will complain about the amount of troops required, or how long it takes to build them. There is some merit to this, perhaps, but at the same time Aurora is fundamentally a game about the long-term, and the player frankly
should be punished or rewarded for having the foresight to plan several decades into the future. It is ultimately a question of taste, but personally I do not see a problem with this aspect of the game design aside from my own impatience, and for those who do take issue we have SpaceMaster mode.
I will, however, note one important caveat here, which is that the enemy can also build ground forces. This is, in theory, a problem, as an alien race can simply build enough troops to match an invasion force (given the foresight to do so well in advance, of course), thus effecting a stalemate at the strategic level. In practice, however, a race consigned to their homeworld by a superior power will eventually fall behind, as they will be starved of the TNEs needed to build research labs to develop better technologies as well as GFTFs to keep up with the production of their enemy, not to mention
eventually running out of the Vendarite needed to build any troops in the first place. More pragmatically, of course, the NPRs just don't build up their defenses that well anyways, so with dedication and focus the player can rather easily outbuild most NPRs which precludes much of the issue anyways. Where multiple player races are concerned, it is up to the player to devise a solution that they personally find most satisfying.
So to answer the question: No, I do not believe that planetary invasions are fundamentally broken. They do, however, require the player to break out of certain misconceptions and rely on very astute long-term planning to actually make them possible. Hopefully, this post has contributed in some way to help players do exactly that.
Have fun shooting things, folks!
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EDIT: I have corrected some errors in the kill rates due to neglecting the tonnage-per-kill term. This significantly changes the analysis compared to the first version of this post, since campaigns take much less time and supplying armies thus is much more feasible. Please be aware of this when referencing the earlier points of discussion.