edit: If you read the comments you'll learn that my analysis has limits, mainly due to my inability to carry out extensive tests and lack of understanding of a crucial game mechanic regarding cannons. However, it seems the first half of the post still remains valid and I recommend it to people who want to know the best unit types for western technology. I'm planning on writing a revised version with further tests to supplement the analysis, but until then please read this with a grain of salt. Introduction
Hello, all. A mod that I saw a few days ago sparked my curiosity about unit types, unit stats, and how they work. At first I thought the mod wouldn't be much of a use for me since I've been playing EU4 for quite some time and since I had read Zwirbaum's unit guide before and have been playing according to it since. But to my surprise the mod's unit suggestions were not what I was expecting, which led me to realize that, in fact, I know nothing about the actual implementation of unit stats in-game. I then nagged one of the mod creators with questions and was able to get this valuable information out of it.
This piece of information was crucial to my effort to accurately measure the value of cavalry, and I thank @Jarvin for sharing it with me. Now with both physical and morale damage equations acquired, I tried to evaluate how much stronger (or possibly weaker) cav actually is compared to infantry. However, I soon found out that things are much more complicated than I thought, and from there an entire project of its own began. I'm here to share what I've discovered along the way and to receive feedback and check if I haven't made any mistake.
How Unit Damage Is Calculated
In order to properly measure unit strength, we need to first understand how land combat works in EU4. Not the basic rules that we already know of, but the exact interactions of various combat modifiers. To do so, let's take a look at the kill casualties formula.
Kill Casualties:
If you take a close look, you'll find that every variable is multiplied to one another. This means that it's better to focus military modifiers to one type of damage, e.g. fire or shock. To put the formula into words it'd be something like this:
Unit fire/shock damage = (dice roll + general pip - enemy general pip + unit offense pip - enemy unit defense pip - terrain penalty) x (percentage of soldiers alive in a regiment) x (fire/shock multiplier from mil tech) x (discipline, combat ability, fire/shock damage dealt) x (length of battle in days) x (1 - enemy fire/shock damage reduced) / (enemy tactics)
Now, because everything is multiplied, we can hypothesize an equal condition for both sides of the battle and simplify the formula to this:
Unit fire/shock damage = (average dice roll +/- unit pip difference) x (regiment strength) x (tech multiplier) x (length of battle) / (enemy tactics)
Morale casualties work pretty much the same way as physical damage. This means that everything that boosts physical damage also boosts morale damage, which can be simplified to this:
Unit morale damage = (daily base morale damage) + (average dice roll +/- unit pip difference) x (regiment strength) x (tech multiplier for fire/shock) x (length of battle) / (enemy tactics)
Okay, great. Now we can calculate and figure out how much stronger a cav is compared to an infantry, right? Not quite. The values we get from the formulas are only the damage output of a single combat day. Knowing that, for example, a cav does 20% more damage than an infantry on the first day doesn't tell us anything about the overall strength comparison of the two units. This is because of the two following reasons.
1. Regiment strength (unit man count) affects damage. The more you kill today, the less damage you take tomorrow. This doesn't mean, however, that offensive stats are better than defensive stats. In fact, in a 1 vs 1 situation, they're pretty much the same thing. More on that later. So now you have no idea how big of an impact the initial advantage you have will end up snowballing into.
2. Morale damage is affected by physical damage. Morale appears to be a separate area of its own, but because regiment strength is also calculated for morale damage, casualties caused by physical damage lowers both physical and morale damage output of the enemy. This makes everything too complicated to handle with pencil and paper.
So what do we do? Well, if I had the skills I would've coded a proper combat simulation program, but because I'm a lowly liberal-arts major with only basic mathematical capabilities required for college, I relied on Windows Excel to create something you could barely call a simulator. This is how it looks.
This is one of the four different Excel files I made to simulate battles in different settings, the rest being '1 vs 1 w/ artillery support,' '1 vs 2 consecutive battles,' and '1 vs 2 consecutive battles w/ artillery support.' I made these to analyze units statistically, but please understand that I spent most of my time sleeping during my Statistics 101 class, and therefore what I'm about to present may seem rudimentary to many.
Deciding Which Units to Compare
If we are to run a cavalry vs infantry combat simulation we need to first decide which of the many unit types we're going to use. So naturally I had to figure out which units are the best among their counterparts. Let's start with (western) infantry.
*Blue: more men remaining / Red: more morale left / Purple: both men and morale superiority
*Use 'A-B' values on the right side for comparison. Positive # means advantage for Unit A, negative # for Unit B.
*Keep in mind that these calculations aren't precise representation of actual in-game numbers. I tried to replicate identical in-game settings as closely as possible to see if they're accurate. The numbers weren't always identical, but they were close enough.
Notice how every battle is won by depleting the opponent's morale. Also, higher tech doesn't equal to higher kill counts because defensive stats and morale stats are affected by various modifiers just the same as offensive stats. In most cases (if not all), units with higher morale total (regardless of the pip distribution) win whereas units with higher fire/shock value gets better kill/death ratio. It is also important to note that, in a 1 vs 1 situation, only total fire/shock/morale pips matter, e.g. Galloglaigh Infantry (0,0/1,0/2,0), Longbow (0,0/1,0/1,1), and Men at Arms (0,0/0,1/1,1) are all dead even despite the difference in pip distribution. For the best units I chose morale winners, i.e. units that win battles, because the cost for the trade off in the most extreme case would be 45*40=1800 manpower for Blue Coat infantry, but usually winning a full on head to head battle grants you easy kill on late reinforcements and gives you many other strategic advantages. Even when you resort to attrition warfare against a larger foe, you will have to be able to win battles to lift enemy sieges so even then you want morale.
Before we move on, by analyzing the above chart we can deduce pip priority for infantry units, which we need to break stalemates. First thing to look at is Charge Infantry (1,2/3,1/3,2) vs Maurician Infantry (2,2/2,1/3,2). At tech 15, infantry fire multiplier is 1.1 while shock multiplier is 1.15. Since the two have identical morale pips, the slight advantage that Maurician Infantry shows over the Charge Infantry comes from its 1 offensive fire pip despite the lower multiplier value. This is a first hint at fire>shock that will be much more apparent when artillery comes into the mix.
So we know that, in general, morale>fire>shock applies for infantry. Also, although in a 1 vs 1 situation offensive and defensive stats are basically the same because they're both always in use either by myself or the enemy, in a real battle frontline troops are prone to flanking and artillery fire, which means defensive stats are to be preferred for infantry units. Based on what we have so far, we can pick out the best unit types for all tech levels except one, tech 26.
For tech 26, Blue Coat Infantry seems to be the obvious pick, but we don't know for sure. Blue Coat Infantry (3,3/3,3/4,4) has the most total morale pips but Red Coat Infantry (3,4/3,3/4,3) does have one more defensive fire pip. Who knows? defensive fire pip might be better against infantry+artillery armies. So I tested it out and you can see that Blue Coat still wins. I'll talk about this later when explaining artillery, but because artillery lends half of its fire/shock defensive pips to the front row but not its morale defensive pip (at least according to what I can tell from the wiki; this needs confirmation) and because artillery usually has the same number of offensive fire and offensive morale pips, morale defense remains the most important stat for infantry even against artillery back row.
On a side note, morale stats are used twice as more frequently as fire/shock stats, but that doesn't necessarily mean that morale is twice as important. This is because physical damage causes actual loss of soldiers which in turn reduces enemy's damage output, whereas morale damage has no effect on the ongoing battle until it completely depletes enemy unit's morale pool. However, that doesn't change the fact that, for infantry, morale is the most important among the three, especially since infantry needs to stay around for as long as possible to protect artillery.
That said, my list of best western infantry is as follows.
Tech 3 - Latin Medieval Infantry
Tech 5 - Men at Arms
Tech 9 - Landsknechten Infantry
Tech 12 - Tercio Infantry
Tech 15 - Maurician Infantry
Tech 19 - Reformed Tercio
Tech 23 - Line Infantry
Tech 26 - Blue Coat Infantry
Tech 28 - Square Infantry
Tech 30 - Drill Infantry
Now lets move on to finding the best western cavalry.
Same general principle applies to cavalry, but, as you can see in the chart above, there were two particular cases that had me uncertain. First is tech 23. If we take a look at the stat distribution of the three options for tech 23, you'll see why I had to further test them out.
Armee Blanche Cavalry (1,1 / 5,3 / 5,3)
Latin Dragoons (1,1 / 4,4 / 4,4)
Latin Hussars (1,2 / 4,3 / 4,4)
Note how all three of them have 8 total morale pips. Armee Blanche Cav have one more offensive pip instead of a defensive pip, and since cavs are frontline troops after all, it might seem like a reason for disqualification. But what if, unlike infantry, offense oriented distribution of pips actually benefit cavs? Armee Blanche Cav does go 50:50 against Latin Dragoons after all. Or what if cavs turn out to be utter garbage and therefore Latin Hussars' one extra fire defense pip becomes preferable to a shock pip?
Further tests against same tier infantry with and without artillery support proved that Armee Blanche and Latin Dragoons fight well enough against fire troops to justify not taking Latin Hussars. Latin Hussars do perform the best against those troops, but it loses the cav match ups, and since the AI does field some cav, I thought it would be best to go with an option that wins all match ups, and so I chose Latin Dragoons based on performance. But now that I review it as I'm writing this, Latin Hussars lose to other cavs by a very small margin. I think I should've tested cav vs cav with artillery support which I think Latin Hussars would've probably won. But, whatever the case, the difference is small enough not to invalidate other tests.
edit: Latin Hussars barely win against Latin Dragoons with artillery on both sides. It's really close, but they win. In my opinion, this makes Latin Hussars the best unit for tech 23, but tests I've done using Latin Dragoons shouldn't be too off.
Tech 28 is also a tricky one.
Latin Chasseur (2,1/4,4/5,5)
Latin Cuirassiers (1,2/5,4/4,5)
Latin Lancers (0,2/6,4/5,4)
Based on cav fights, Latin Chasseur should be the winner, particularly with it's 10 total moral pips. But I really didn't like the fact that it was the only one with a single defensive fire pip. I also noticed how Latin Lancers inflicted heavy losses to Latin Chasseur despite suffering defeat. Moreover, if you look at the stat line, Latin Lancers waste no pip for fire offense and have a whopping 6 offensive shock protected by 2 defensive fire pips. However, lack of a morale defense pip is a big flaw, so I did additional tests and eventually selected Latin Lancers for my infantry vs cavalry comparison, as it was the only unit to achieve a full victory over infantry w/ artillery support and had good performance overall.
So now we have the list for best western cavalry.
Tech 3 - Western Medieval knights
Tech 10 - Schwarze Reiter
Tech 14 - Latin Caracole Cavalry
Tech 18 - Gallop Cavalry
Tech 23 - Latin Hussars
Tech 26 - Reformed Latin Hussars
Tech 28 - Latin Lancers
Infantry vs Cavalry
Before I begin, I'd like to point out that cavalry doesn't have to be 2.5 times stronger than infantry to be worth the cost. Without premium, elite units would be straight up OP. Of course there's the issue of whether cavs are actually elite, but at least theoretically that's how it should be. Let's take a deeper look into the game system of EU4 to see if the 'pay extra for performance' rule could be applied the same.
In EU4, there are four main factors that limit the player's military capabilities: force limit, combat width, manpower, and money. So, for example, if you decide to build 25 infantries instead of 10 cavalries, you may be paying the same amount of money, but you're costing yourself 2.5 times more of the other three resources. This is why I think the above mentioned principle applies the same in EU4. If given that cavalry is better than infantry, by trying to save some money with infantry you might put yourself at risk of losing battles against armies with cavalry. If you have to reinforce your infantry-only army with the extra troops you've earned, then that defeats the whole purpose of taking infantry over cavalry. But, if it turns out that you can spare some of the extra troops for separate missions while still ensuring victory of your main army, then it might be worth the cost of force limit space and manpower. Mercenary is basically trading money for manpower so it shouldn't change things much. In the end, it all comes down to how cavalry performs against infantry, so let's see the test results.
Before I began entering numbers into the "simulator," I had decided to base my measurement of cavalry strength on that of two infantries, because cavs have the advantage of flanking which gives you higher chance of stack-wiping outnumbered enemies, and I thought that could be counted as 0.5 ducats worth of value (and for the sake of easier comparison too). But that assumption turned out to be unnecessary because of what you can see above.
The results were no where close to what you'd expect from a unit twice as expensive as an infantry (if you justify the remaining 50% cost for its flanking ability and with the 'elite unit' logic). At certain tech levels cavs even lose against their infantry counterparts. But remember the snowballing effect I mentioned earlier that makes simple comparisons difficult and inaccurate? I thought the same might be the case here so I tested a consecutive 1 vs 1 battle using the results I got from the initial test. I went for consecutive two 1v1s instead of a simultaneous 1 vs 2 battle, because combat width works against the numerically superior side. And to save myself from meaningless labor, I picked one with the best performance per each cav unit type.
Turns out even at its peak a cav unit can only route one infantry unit and take the second one down to three-quarters of its numbers before breaking. Latin Hussars would've done slightly better than Latin Dragoons, but the results are so lopsided that it wouldn't even matter. With artillery support things get even worse.
Now, even if I were to try and defend cavalry with the 'pay premium for elite unit' argument, it would only be applicable in very specific time periods of the game (tech 11, tech 17~19, tech 23~26, and even less depending on how you look at it, but before tech 16, or possibly tech 22, artillery is severely cost-inefficient, so using cav in tech 4 and tech 10~13 may also be justifiable).
This is how much of an impact artillery makes in the infantry vs cavalry match up.
If you look at the 'Artillery Effect' on the right side of the chart, you can confirm that artillery mostly favors infantry, obviously. But before we conclude that cavalry is inviable, let's give it one last chance and compare it with artillery. After all, artillery is even more expensive than cavs but no one ever complains about them. Yes, they do serve a crucial role of speeding up and sometimes even enabling sieges, but pure combat-wise it might turn out that they're just as inefficient as cavalry.
Measuring the Combat Strength of Artillery
As I mentioned before, simply comparing the results of 'infantry vs infantry' with that of 'infantry vs infantry + artillery' doesn't really tell us much about the power of artillery due to the snowball effect. If, e.g. artillery gives you 100 more kill differential and 0.5 more morale differential, how strong is the artillery itself? It's tough to say, so, again, I went with the 'two consecutive 1 vs 1s' method.
In terms of cost-efficiency, artillery should be able to fight 3 infantries to be worth it. But I'm sure everyone would agree that that's not a smart way of comparing things. In my opinion, if an infantry and an artillery can win against two infantries (consecutively, because combat-width), then even purely combat-wise artillery is worth the buck. Otherwise, it might be arguable that, at least for battles, it's better to allocate the manpower and the force limit to an additional infantry unit than an artillery. This is also why I said that the threshold for artillery becoming useful in battle may possibly be tech 22 and not tech 16. But then again, artillery is three times more expensive but no one complains about that. In my opinion, it's not just because of their siege pips, since if that was the only reason then people should be claiming that you should only get the minimum amount of cannons required for maximum siege bonuses and go all-infantry. But most people I see on the internet say that you should fill up the back row with as many cannons as you can. There seems to be an inconsistency when evaluating the usefulness of cavalry and artillery, which is probably only apparent now that I have a way to measure their combat performance. So now with this new understanding in mind, I believe we can finally come to an objective conclusion about the viability of cavalry.
Assessing the viability of Cavalry
Since deploying full stacks of cannons becomes viable at tech 22, before that it would be fair to compare cavalry with infantry alone since most of the time there wouldn't be enough artillery to cover the edges of formation. If you feel like your opponent, whether an AI or a human, brings full artillery stacks before that time period, then you can use the charts above to judge for your own.
If we are to use the same standards as artillery, a cavalry is worth the cost if it can guarantee victory against an infantry. You could argue that artillery has much more use outside of battles, and while cavalry does give you a better chance of stack-wiping weaker enemies and act as a win-more mechanic, those two are just not comparable to siege bonuses of artillery, not to mention that artillery can flank as well. But, again, that doesn't explain why people get more than what they need for maximum siege bonus. I do expect this to be a controversial argument so let me explain this one more time. In terms of combat, artillery starts to give you advantage over an all-infantry opponent at tech 22, and even after that it never allows you to win 2 vs 3 despite costing three times more than infantry. But people still field them in numbers even before tech 22, because they understand intuitively that the price of victory isn't directly proportional to cost-effectiveness. Also, since infantry spam is penalized by force limit and combat width after a certain point, it's only logical that you pay premium for elite units, in this case elite unit being either cavalry or infantry upgraded by artillery. If you think of it that way, paying a bit less than artillery to be able to secure victory in a 1 vs 1 combat is worth it, even though you would never be able to win 1 vs 2. Therefore, when evaluating cavalry, the most important thing is whether it can get you the W. And besides, cavalry takes only a small portion of army comp, so the burden on your economy is limited to a certain amount.
Then, in the charts above, we can obviously exclude cavs that lose to infantry, but what about close wins? If the enemy gets better RNG then those cavs would lose to infantries and waste the extra gold you've spent on them. But, on the flip side, if cav can win despite bad RNG, then I'd say I'm getting my money's worth. So let's run the simulation one more time to see how cavs perform when the opponent starts the battle with a 9 and you a 0 (remainder of the battle calculated with the same 4.5 dice rolls, if you're unluckier than that just lose, Kappa).
I added a 'good RNG' version at the bottom as a reference. I'm not sure what to make of this other than that 9 vs 0 in the first fire phase is devastating with cannons, often leading to a stack-wipe. I still think it's reasonable to use cavalry during their peak, but it's up to you to decide, and eventually they become in-viable since at tech 32 they straight up lose to Drill Infantry even without artillery.
Or there's another approach you can take. You can argue that cannons are overrated and that people should build minimum number of artillery required for full siege bonuses and fill the rest of the force limit with infantry only. It's certainly not a far-fetched idea, and I think the answer is to understand the pros and cons of the two opposing approaches and selectively use them according to your in-game situation. (Edit: This is wrong. To prevent double morale damage you should make sure you have enough artillery to fill up the back row.)
Conclusion
So there you have it. You can't really tell whether cavalry is viable or not with a yes or no, and even though generally most would say they're on the weaker side, during their peak (tech 11, 17~19, 23~26) I think they're worth it. However, this thread wasn't just about cavalry but all unit types in general. We also found out that morale is king. And of-course, all of the above can change depending on technology type and combat modifiers. If you're curious and feel like you're up to some manual work, then please feel free to use the attached Excel files to test things yourself. I'll be glad to read the results you get if you care to share. You can find all the info you need here: https://eu4.paradoxwikis.com/Technology#Cumulative_mil_tech_effects_to_army, https://eu4.paradoxwikis.com/Land_units#Unit_groups, https://eu4.paradoxwikis.com/Land_warfare#Kill_Casualties, https://forum.paradoxplaza.com/foru...offensive-or-defensive.1331399/#post-26267711.
Also, as a bonus, here's a power spike chart that I made for western unit type.
Thank you for reading this all the way and let me know what your thoughts are!
