Bang per buck: Melee cavalry

[Doug-Thompson]

Take a unit’s maintenance cost from R'as al Ghul's unit guide. Divide that by the combat value given in YAS’ TOOLS. That yields a number: The lower the number, the more combat value per florin per turn — very generally speaking.

This very crude calculation shows a very rough picture of what’s a bargain and what’s not. Buyer beware: A unit that routs in front of a better, more expensive unit is no bargain at all. Also, the combat value for charging with the primary weapon was used in the calculation. Some units are much better in sustained melee.

Anyway, here’s the results from best to worse:

Best in Category: 2.5 florins per combat point.
Mercenary Elephants

The “4s” (4.2 to 4.6)
All bodyguard units

The 5s (5.4 to 5.8)
Italian Cavalry Militia
Polish Retainers
Hussars

The 6s (6.3 to 6.8)
Huscarls
Chivalric Knights
Polish Knights
Quapukulu
Druzhina
Mamluks
Sipahi Lancers
Royal Mamluks
Teutonic Knights
Khan's Guard
Christian Guard
Conquistadores
Eastern Chivalric Knights
Knights Hospitaller
Knights of Santiago
Knights Templar
Norman Knights
Arab Cavalry
Mounted Sergeants
Border Horse
Serbian Hussars

The 7s
Armored Clergy
Scouts
EE Cavalry Militia
Demi Lancers
Portuguese Knights
English Knights
Imperial Knights
Feudal Knights
Stradiots
Albanian Cavalry
Greek Militia Cavalry
Latinkon
Kataphractoi
Crusader Knights
Serbian Knights
Tsars Guard
Granadine Lancers
Mailed Knights

The 8s
Bedouin Cavalry
Alan Light Cavalry
Byzantine Lancers
Noble Knights
Polish Guard
Lancers
Royal Banderium
Gothic Knights
Italian MAA
Famiglia Ducale
Hobilars

The 9s
Armenian Cavalry
Mercenary Frankish Knights
Merchant Cavalry Militia
Gendarmes
Kwarizmian Cavalry

The 10s
Mercenary German Knights
Broken Lances
Mercenary Knights
Tuareg Camel Spearmen

And in a category all their own:
Condottieri — 13.8

[Foz]

This means very little without an attached in-depth explanation of how exactly YAS's "combat value" is arrived at and what it means. If I may be so bold, it'd be nice if someone would add one

[Doug-Thompson]

Attack + Defense + (Charge +Armor+Morale)/2

Whether it means anything is in the eye of the beholder.

[Shahed]

Good work ! It is useful as an indicator of bang per buck.
Is it entirely complete ? Khan's Guard is not there, for example. Just mentioning it.

The calculation is from MTW/VI. We don't know exactly what the calculation is in M2. I emailed Yas about this and posted his reply in the "Total War Korea" (keyword = korea) thread.

[Doug-Thompson]

Is it entirely complete ? Khan's Guard is not there, for example. Just mentioning it.

You are correct, sir. I don't know what else is missing, but Khan's Guard's "score" is 6.5, right in Teutonic Knight range.

Do you have a link to that reply from Yas?

[Shahed]

Yeap I just bumped it here. You might get his attention if you post queries there, or otherwise you can email him, he'll surely respond.

[Doug-Thompson]

Much thanks. Here's the relevant section, with some copyediting:

"The calculation for combat rating is very simple. (just same as it in MTW1)

: (attack + defence * HP + armour + shield)+(morale+charge)/2

I know it's not perfect. There are many factors that the ratings can't cover. The combat logic of M2TW is so complicated (it's difficult) to cover (in) the whole factor. If you have any idea about that, please advise me."

[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?

[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.

[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.

[IrishArmenian]

Ah, but the Russians (Militia Cavalry recruitable from Tier 4 Barracks, I believe), too, may get a Horse Breeders guild. I've gotten one with the French too, but that was after I built a Military Academy and trained Gendarmes.

[Miracle]

Yeah the Italians can build Militia Cavalry too but only from Large Cities. To get a HB master's guild in the early/mid game you need to be able to build cavalry from Minor Cities.

[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

[Caliburn]

I believe that ranged horse units have the most bang per buck, more than any of the formulas seen on this thread. After all, HA can empty their quivers before charging, causing morale penalties and huge casualties, thus their overall damage potential is greatly increased.

Does anybody have any ideas how to factor in the missile attack? On another note, could this be utilized in creating a more balanced unit training for the AI? I have no idea how the AI prioritizes its unit training.

[Kobal2fr]

Miracle, you forgot one hugely important factor in your calculation : stamina. As in "bodyguards can charge around all day because they have good stamina" :P

[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).

[Doug-Thompson]

It's time to get Yas in here.

No argument there.

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

We're going to wind up with more than one number here, I'm betting:

Charge value, melee value, melee value against a unit with armor-piercing attack, resistance to missiles, and so forth.

[Doug-Thompson]

For now, I'm going to use the normal cavalry speed calculated by CBR of 525 meters a minute as 1. that would make the multiplier for a fast cavalry unit 1.14 and a slow one 0.79.

[Edited P.S.: I've come around to Miracle's way of thinking about speed. I greatly affects attrition rates in a campaign and is a serious tactical consideration in battles. All other things being equal, a slow unit is going to lose more when defeated and not capture or kill as many when victorious. The opposite is true for fast ones. Even against another fast unit, time of exposure while running for the map edge is reduced.]

OK. Let's try this for Arab Cavalry, step by step. The only purpose of this exercise is to see if I have the steps right:

1. Total Charge = 9+4 = 13
2. Secondary attack, which I presume does not include the charge bonus, is 9
3. Total Defense is 13
4. Speed multiplier is 1
5. Morale is 5, so applying the factoring makes the multiplier 3.34
6. Mass is heavy horse, giving a multiplier of 1.75
7. No AP bonus, so no multiplier
8. Not hardy, making the multiplier 0.9
9. Trained -- no penalty
10. Upgradable armor -- can go all the way to Heavy Mail. Add 5.1 to Total Defense.

I may dispute this one. I think separate values should be given for each armor upgrade, but we'll go with it for now.

11. No Desert bonus -- This one I am going to leave out. I think a separate number for desert combat should be included, especially since the heat penalty should be accounted for within that.

12. The unit is Muslim. Therefore, add 0.5 to Total Charge, Secondary Attack and Total Defense. (Explanation, please?)

13. Jousting list (Explanation, please) No modifier.
14. Fortress-level Swordsman (Explanation, please, although I remember this being debated earlier in the thread and may look it up myself.)

The modified value for Total Charge is 13.5
The modified value for Secondary attack is 9.5
The modified value for Total Defense is 13.5

I'm going to use my figure for cost, but with the understanding that the topic is wide open to debate: [Recruitment cost +(9*upkeep cost)]/10. In this case, that's [510+(9*175)]/10 = 208.5

[Edited P.S.: This is basically a reflection of attrition rates, and could vary widely from player to player and situation to situation. Players who don't have a lot of finesse in their tactics or anybody caught in a series of tough situations would be better off with an expensive, hard-to-kill unit than a good value one.]

======

13.5 * 9.5 * 13.5 *3.34 * 1.75 / 208.5 = 48.53

Now, if I have the mechanics right, I can put that formula into a spreadsheet (Bless you, R'as al Guhl, for using Excel). Then we can see if there are any absurd aberrations.

[Shahed]

Good work ! Would be interesting to see how this turns out.

[Doug-Thompson]

Man, this is a bigger bear to wrestle than I thought. However, progress is being made.

I came around again to Miracle's way of thinking when I tried to leave out the anti-armor bonus. Then I ran across the Danish Armored Clergy, for example. Not only do they have an anti-armor bonus for their secondary attack, but they have the same bonus for their primary attack because the only weapon they carry is a mace.

This unit isn't the fastest peasant-killer out there, but if you leave out the anti-armor capability you skew the deadliness of that unit very badly, and that's just the most extreme example.

So I'm adding anti-armor bonuses in, adding three points to attacks that have it. Notice that means the Armored Clergy get a lot of points added, but I still think its more accurate than just leaving it out.

[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.