Bang per buck: Melee cavalry

[Miracle]

Yeah there's a lot more things to consider when computing value:

- Likelihood of weapon/armor upgrades and guild/building exp bonuses
- AP weapons
- Speed
- Mass
- Stamina
- Terrain bonuses and penalties

Recruitment cost is almost as important as upkeep cost as well. Melee cavalry gain exp fairly quickly, but will always take casualties in the process. Retraining becomes essential if you want to preserve an experienced cavalry force.

Also, in the late game value doesn't matter as much as other factors because you're usually swimming in cash. Bang-for-the-buck estimates really matter only for early and mid-game cavalry (castle or fortress-level).

[Shahed]

Having played MTW/VI and used Yas's tools in the past years I can clearly understand what these figures represent.

These figures are clearly intended as ballpark figures, not precise algorithms. The establishment of which is, impossible, on a broad level.

[Doug-Thompson]

If somebody has a better calculation than Yas' has, let's hear it.

Allow me to repeat a few key phrases from my first post:

"very generally speaking" ... "This very crude calculation shows a very rough picture" ... "Buyer beware"

If anybody want to explain why his favorite cavalry unit is so much better than these numbers reflect, that would be fruitful.

[Miracle]

If somebody has a better calculation than Yas' has, let's hear it.

Alright lemme give it a try:

Value =

TotalCharge*SecondaryAttack*TotalDefense*Speed*(Morale^0.75)*(Mass^0.6)
0.25*RecruitmentCost + UpkeepCost

If...

• Secondary weapon is AP: Add 3 to SecondaryAttack
• Unit is not Hardy or Very Hardy: Multiply by 0.9
• Unit is untrained: Multiply by 0.9
• Unit capable of padded armor upgrade: Add 3.75 to TotalDefense
• Unit capable of light mail armor upgrade: Add 0.6 to TotalDefense
• Unit capable of heavy mail armor upgrade: Add 0.75 to TotalDefense
• Unit has combat bonus in desert: Subtract 0.2 from TotalCharge, SecondaryAttack, and TotalDefense
• Unit does not have combat bonus in desert: Subtract 0.1 from TotalCharge, SecondaryAttack, and TotalDefense
• Faction is Muslim, Spain, Portugal, or Denmark: Add 0.5 to TotalCharge, SecondaryAttack, and TotalDefense
• Faction can build jousting lists: Add 0.5 to TotalCharge, SecondaryAttack, and TotalDefense (knight units only)
• Faction can build fortress-level swordsmen: Add 0.75 to TotalCharge and SecondaryAttack

Note: General's Bodyguards and Citadel/Huge City-level cavalry should not be used with this formula, since value isn't a very important factor for them.

Speed values:

slow = 415 metres/minute
normal = 525 metres/minute
fast = 600 metres/minute
(measured by CBR)

Mass values:

camel 1
eastern armoured horse 2
armoured horse 2
barded horse 2
mailed horse 2
pony 1.25
fast pony 1.25
heavy horse 1.75
elephants 40

[IrishArmenian]

What if the faction can build a horse-breeders guild?

[Miracle]

What if the faction can build a horse-breeders guild?

This is taken into account:

Faction is Muslim, Spain, Portugal, or Denmark: Add 0.5 to TotalCharge, Attack, and TotalDefense

These are the only factions that can get HB's guilds early on.

it might be worthwhile considering considering where these units show up in terms of availability based on the tech tree. A high "value" unit on that list may not be as worthwhile if it only shows up at tier 5 in a city.

This thread is mostly about performance/price which is independent of availability.

Discussion about the "best" units belongs in another thread.

[Whacker]

This thread is mostly about performance/price which is independent of availability.

Discussion about the "best" units belongs in another thread.

He didn't say that it was exclusive of availability. You can have a wonderful melee cav unit that you can't get until you have a citadel or a huge city cranking them out, which can take a very long time and most likely you'll be so far in the lead it'd be pointless. Discounting availability is not a good thing to do. I'll leave that up to Doug, this is his thread.

[Miracle]

you'll be so far in the lead it'd be pointless.

Which is why value only really matters in the early/mid game. This also happens to be the period where there are low building requirements for every unit and therefore high availability.

Discounting availability is not a good thing to do.

If you're talking about the "best" units, of course that's true. But Doug was talking about "bang per buck," "bargain," and "maintenance."

I'll leave that up to Doug, this is his thread.

It's pretty clear what this thread is about.

[Whacker]

Doug, since this is the SP forum, one thing I would also offer is that it might be worthwhile considering where these units show up in terms of availability based on the tech tree. A high "value" unit on that list may not be as worthwhile if it only shows up at tier 5 in a city.

[Doug-Thompson]

Alright lemme give it a try:

Value =

TotalCharge*SecondaryAttack*TotalDefense*Speed*(Morale^0.75)*(Mass^0.6)
0.25*RecruitmentCost + UpkeepCost

Excellent.

Not being that keen on math, however, let me make sure I read this correctly:

1. "Total Charge" is primary attack plus the charge bonus
2. "Total Defense" is armor, shield and defensive skill combined.
3. "Speed" confuses me. If we multiply by meters per minute, for instance, that's going to make quite a difference in points between units. I agree totally that speed is wonderful, but that wonderful?
4. I'm stuck at the <> stage here. What does ^ mean, as in Morale ^ 0.75, and where did 0.75 come from.
5. Ditto on mass.
6. 25 percent on recruitment cost, added to one turn of upkeep cost. That reflects a pretty high rate of attrition. I was thinking more along the lines of [Recruit + (9 * upkeep)]/10. While cavalry has to be retrained often, it also gains experience, making it a better unit.

As for adding three to an AP secondary weapon, doesn't AP halve a target unit's armor? Perhaps there should be a separate, lessened figure giving the target's defensive value against AP attack. Ditto on reducing or increasing values for deserts, etc.

[Miracle]

Thanks for the reply Doug.

1. TotalCharge is the spear/lance's attack value + charge bonus. This may sound weird but the spear attack and the secondary attack are sometimes different. For example, Mailed Knights are listed with 10 attack and 6 charge but their sword attack actually has 11 attack.

2. TotalDefense is correct.

3. Speed is VERY important for melee cavalry. It determines:

- how many volleys of arrows/bolts you receive before charging
- how effectively you can chase archers/routers
- how quickly you can retreat, reform, and recharge

To give you an idea of how important it is, compare Mailed Knights with Feudal Knights. With MK you can successfully give chase to bodyguards and therefore have a chance of catching a high-ransom family member. With FK's it's impossible to catch up to them, losing a prisoner potentially worth thousands of florins.

4. ^ means "to the power of". Morale^0.75 means, "5 to the power of 0.75" if the unit in question has 5 morale. The 0.75 part is to de-emphasize morale a bit since it isn't as important as the other factors. Note that if the exponent went to zero it would have no effect on the formula.

5. Mass partly determines how powerful your charges will be. But since it isn't as important as TotalCharge I have de-emphasized it using ^0.6.

6. I admit I didn't give enough attention to the denominator. I will give serious consideration to your method.

7. The +3 attack was derived from a theoretical (largely untested) formula I used:

Chance to Hit = (Attack^2)/(Attack^2 + TargetDefense^2)

If a soldier's attack is 11 and the target's defense is 10, his chance to hit is 55%. Let's say the target is wearing light mail with no shield. With an AP weapon his CtH is now 68%. To get the same CtH with a non-AP weapon, the soldier would need +5 extra attack. Since some units have shields which de-emphasize AP weapons a bit, I have lowered the bonus to +3 as an average.

Obviously this won't be completely precise, especially since this formula is pure speculation. But it's a pretty good educated guesstimate that should approximate the real, CA-written formula.

Actually now that I think about it, here's a better formula:

CtH_1 = (Attack^2)/(Attack^2 + (TargetDefenseSkill + TargetShield)^2)

This computes a soldier's chance to get past his opponent's weapon parrying and shield blocking. If CtH_1 is successful, CtH_2 is commenced. If not, the soldier attacks again.

CtH_2 = (Attack^2)/(Attack^2 + TargetArmour^2)

This computes the soldier's weapon's chance to penetrate the opponent's armour. If CtH_2 is successful, the opponent dies. If not, he is covered in blood and the soldier attacks again.

CtH_true = CtH_1 * CtH_2

This is the true and final chance the soldier has to kill his opponent. To utilize the 11-10 example from last time, the soldier's CtH is now 69%. If his weapon was AP, the CtH is 79%. That is equivalent to +3 attack. If I used this formula the AP bonus will probably be +2.

But since I can't prove any of these formulas I'm open to suggestion.

8. The bonuses/penalties due to buildings, desert, etc. were carefully chosen based on a number of factors:

- While a unit can be upgraded, it can't always
- It costs something to get those upgrades, devaluing them a bit
- Weapons upgrades tend to give more than the +1 bonus indicated
- Desert units will encounter snow at some point
- Non-desert units will encounter desert at some point
- Frontiers for desert units tend to be non-desert
- Desert units have large penalties in snow
- Snow only appears every other turn
- Snow covers more traversable non-coastal land area than desert
- Some units are neutral to desert and snow (don't know exactly which ones)
- There are no melee cavalry units with bonuses in snow which means all cavalry units have low or no penalties in desert
- All cavalry should avoid fighting in wooded areas

As you can see, in the overall scheme of things terrain bonuses don't matter much for melee cavalry. In fact there are only two desert melee cavalry units: Tuareg Camel Spearmen and Bedouin Cavalry, both of which aren't used much if at all.

I may not be able to respond to future posts due to commitments so if you have any questions please ask them later.

[ninjahboy]

a very good ROUGH indication of price v performance ratios

[Doug-Thompson]

@Miracle

It would take somebody better at math than me to fully critique your formula, but at least the variables show real reasoning behind them and are all out in the open.

Time permitting, I'll calculate some values with your formula and we'll see what we get.

@ninjahboy

Thanks.

@Caliburn
Hey, I'm a big HA fan too (click my signature pix for the link, if you haven't seen it already). However, I don't plan to get to them for a while.

Of course, if somebody want to beat me to it ... (wink wink, nudge nudge, say no more.)

[Shahed]

That's a good attempt, miracle.
If you can do this for all units and make a website out of it, hats off.

It's time to get Yas in here.

Personally I think you can never arrive at the perfect and complete formula, specially given the criteria in the initial suggestion (terrain etc).

[Agent Smith]

If somebody has a better calculation than Yas' has, let's hear it.

Allow me to repeat a few key phrases from my first post:

"very generally speaking" ... "This very crude calculation shows a very rough picture" ... "Buyer beware"

If anybody want to explain why his favorite cavalry unit is so much better than these numbers reflect, that would be fruitful.

Actually, couldn't you simply just do two categories: attack + charge per florin and defense per florin? Those are the two main numbers you are looking for. You want to simply find which has the most attack compared to its cost, and likewise defense for its cost. You can even simply add the numbers together and combine it by florins. Adding any other numbers, especially morale, makes it more and more subjective and less concrete, because morale is completely subjectively based depending on the situation the unit is in. In optimum conditions (large army, flanks protected, etc.) morale isn't even entirely an issue, whether it is 3 or 10. Likewise, armor piercing is completely subjective depending on the defender's armor. If they aren't wearing any, then the armor piercing value is meaningless.

Also, like someone mentioned, you could also come up with a raw number by adding up the total number of florins, barring any other improvements, required to make the unit available. So, if you need just a castle, it would have the value of just the wooden castle + castle upgrade. If it requires a Knight's Stable, which can only be built at a castle, then it would be wooden castle + castle + stables + knight's stables, etc. Then you can come up with a "total cost for availability number" and further compare that to the attack + defense per florin number.

[andrewt]

Isn't mass and speed inversely related, though? I don't have the time right now to check the formula but they could cancel each other out.

[Doug-Thompson]

Well, that was loads of fun.

The numbers below use Miracle's formula, with lapses:

1. Armored upgrade potential was left out, for now.
2. Desert Bonus too.
3. The added factors for being Muslim, Spainish, Portugeuse or Danish are not in there yet.
4. Jousting and swordsmen are left out for now.

Also, there are no Mongol/Timurid melee cavalry on this list. I'm working on it.

=========

Keep in mind several things here. This is not a "best to worst" list. This is a fighting value per unit of money estimate.

Adding in an armor-piercing secondary weapon made big differences in the final outcomes.

While valid points have been raised about morale being somewhat subjective, it is also very important. A formula that includes some indicator of that value is more accurate than one that leaves it completely out.

Speed and mass may have an inverse realtionship, but at worst including them both will do no harm while leaving them out might make some difference.


Unit name, "Bang per Buck"

Elephants, 643.01
Quapukulu, 188.62
Christian Guard, 186.84
ME Late Bodyguard, 182.63
Royal Mamluks, 180.84
EE Late Bodyguard, 175.80
Greek Bodyguard, 170.09
NE Late Bodyguard, 168.17
SE Late Bodyguard, 168.17
Conquistadores, 167.98
Norman Knights, 167.98
EE Bodyguard, 163.72
NE Bodyguard, 160.85
SE Bodyguard, 160.85
Hussars, 159.75
ME Bodyguard, 159.57
Teutonic Knights, 158.73
Knights Hospitaller, 157.77
Knights of Santiago, 157.77
Knights Templar, 157.77
Polish Knights, 154.36
Chivalric Knights, 149.99
E Chivalric Knights, 143.42
Tsars Guard, 142.62
Polish Guard, 141.04
Serbian Knights, 138.89
Serbian Hussars, 136.93
Royal Banderium, 134.55
Crusader Knights, 133.52
Huscarls, 127.90
Demi Lancers, 126.41
Noble Knights, 125.19
Gothic Knights, 123.97
Lancers, 117.83
Mamluks, 115.16
Famiglia Ducale, 114.92
Druzhina, 106.58
Armored Clergy, 103.42
Imperial Knights, 102.46
Polish Retainers, 101.96
Kataphractoi, 98.86
English Knights, 95.79
Sipahi Lancers, 90.93
Latinkon, 90.63
Portuguese Knights, 79.35
Feudal Knights, 77.58
Mailed Knights, 76.47
Granadine Lancers, 74.69
Mercenary Frankish Knights, 74.65
Armenian Cavalry, 73.16
Gendarmes, 66.80
Albanian Cavalry, 61.61
Stradiots, 61.61
Broken Lances, 58.35
Kwarizmian Cavalry, 54.45
Alan Light Cavalry, 49.50
Italian Cavalry Militia, 48.90
Mercenary Knights, 43.49
Mercenary German Knights, 41.39
Byzantine Lancers, 40.96
Mounted Sergeants, 39.17
Arab Cavalry, 38.42
Italian MAA, 34.02
Condottieri, 31.64
Bedouin Cavalry, 29.76
Border Horse, 25.95
Tuareg Camel Spearmen, 21.67
EE Cavalry Militia, 14.64
Greek Militia Cavalry, 13.54
Scouts, 10.10
Merchant Cavalry Militia, 9.61
Hobilars, 6.94

[Shahed]

GREAT work !
How do you feel this compares to your orginal list and how is it superior ?
BTW Royal Banderium are Hungarian Nobles I assume ? Just noticed Quapakulu are top of the list.. wow.

[Doug-Thompson]

How do you feel this compares to your orginal list and how is it superior?

It simply takes so many more factors into account. Whether it takes them into account correctly is what the debate should be all about. However, there is a rational basis for each of the estimates in Miracle's formula, at least.

I think the first, simple list overstated the value of cheap cavalry. Cheap cavalry make very good router chasers, but don't have the all-round value of the knight units. The second formula looks much closer to being right in my highly subjective judgement. For instance, notice how much lower Arab Cavalry is on this list. I love Arab Cavalry, but realize that it is successful largely because it ususally attacks units already softened up by Mamluk archers, at least in my campaigns in my campaign.

Having a mace may be overvalued in this formula. Or not.

The formula should include a discipline modifier. Also, I'm tempted to make "highly trained" a 1.1 modifier along with "very hardy," but need to hear from Miracle first.

BTW Royal Banderium are Hungarian Nobles I assume?

They are Hungarian, but a knight unit available in the Late era.

Just noticed Quapakulu are top of the list.. wow.

That's mainly because of their mace, and many other fine qualities.

=======

@Phog

I'll get back to your questions ASAP, but have to make some concessions to real life now.

[Phog]

Wow.....that was a tough read.

Thanks guys for doing all the math and figuring for the rest of us that absolutely suck at math. Doug-Thompson and Miracle, well done! My brain would have been pudding after all that. Great work guys and quite a handy list. There are many Cav units listed that I haven't had a chance to try at all, mostly bacause I play strictly SP and don't really mess around with the custom battles.

Time to delve it that a bit.


- Phog

[Phog]

Can't edit my posts yet *grumble* *grumble*

Never shoud have let my old username lapse....oh well.

Anyway! Question, in your research which Cav units stand up better than most in sustained meele? And did better meele stats affect their charge attack rating at all?

And you don't have to do any math for this one I am just looking for opinions.


- Phog