Bang per buck: Melee cavalry

Hi folks, I thought I should just drop by to add some comments.

Let me emphasize that my equation is for computing the value of conventional early/mid game melee cavalry only.

That means no bodyguards, elephants, Christian Guard, etc.

I don't think value is important for later cavalry units because their cost/upkeep relative to your treasury/income is minuscule. The more important factors to consider for their period are aesthetics/fun factor, raw performance, availability and replenishment rates.

Muslim, Spanish, Portuguese and Danish units get an experience bonus because their factions can build cavalry at the Minor City level without any other guilds. This allows them to obtain a Horsebreeder's Master's Guild early enough for it to be considered in the value equation. Other factions get it too late for it to affect value when it matters most.

Factions with jousting lists available get an experience bonus for knight units. This is halved because you don't get the lists until you get fortresses, and not every fortress will have a list. Thus, this bonus is intended as an average.

Factions with fortress-level swordsmen can build Swordsmith's guilds early enough to be considered in the value equation. Weapons upgrades give more than the +1 offensive bonus indicated, but since you can't always get the upgrade, the bonus is reduced to 0.75.

For cavalry, the marginal differences between hardy/very hardy and trained/highly trained are too small to warrant any separate multiplier. Not having these traits makes a noticeable difference though, but not much. That's why there's only a 10% penalty for not having them.

Discipline doesn't matter much for human-controlled cavalry. Most of the time you are actively controlling them thus preventing any unruly behavior. It matters much more to slow infantry and AI-controlled units. For a great example of this, try the Battle of Tannenberg historical battle, and see how the AI knights unwisely charge your faster HA.

Speed and mass are not exactly inversely proportional. A simple multiplication shows this:

Fast: 600*1.25 = 750
Normal: 525*1.75 = 919
Slow: 415*2.00 = 830

In addition, there are two 525-type cavalry with ponies, namely scouts and hobilars. They have a speed-mass of 656, which is pretty bad. But camels, with an approx. speed-mass of 400, are the worse.

These are the regular speed-mass^0.6 values according to my formula:

Fast: 600*1.25^0.6 = 686
Normal: 525*1.75^0.6 = 734
Slow: 415*2.00^0.6 = 629

Notice how fast movers are better in this calculation, but medium horses are still be best.

Assigning ratings for each unit based on role sounds pretty good. You could modify the equation for each role to emphasize certain variables like speed, charge or cost.

Examples:

Bargain Bin Cavalry for Extremely Tight Budgets:

TotalCharge*SecondaryAttack*TotalDefense*Speed*(Morale^0.75)*(Mass^0.6)
0.25*RecruitmentCost^4 + UpkeepCost^3

This is likely to put Hobilars in a whole new light.

Standing Melee Monsters

(TotalCharge^0.5)*(SecondaryAttack^1.5)*(TotalDefense^1.5)*(Speed^0.5)*(Morale^1.5)*(Mass^0.25)
0.25*RecruitmentCost + UpkeepCost

Norse War Clerics and Huscarls will be propelled to the top by this one.

Cheap supplementary router chasers

(TotalCharge^0.5)*(SecondaryAttack^1.25)*(TotalDefense^0.5)*(Speed^1.5)*(Morale^0.5)*(Mass^0.3)
0.25*RecruitmentCost^2 + UpkeepCost^1.5

Obviously Border Horsemen are going to like this one.

If you notice, the difference is entirely on emphasis. You can modify the exponents for any variable based on your particular needs. Want an awesome charge and don't care about speed? Crank up TotalCharge and Mass. Need something that won't rout every time a Mongolian sneezes? Focus on morale. Need a good, all-around unit? Well, you should probably use the original formula or something close to it. https://forums.totalwar.org/vb/images/icons/icon6.gif

Very good !

Outstanding. The explanations on the factors make sense — especially since I'm having withdrawl pain on race tracks while playing the trackless Hungarians. At least Hussars are militia cavalry. They also must be the best militia cavalry one can get.

Got rid of elephants, bodyguards and the Monastic Knight Orders because they have more than one hit point and/or are obtained in strange and/or expensive ways.

I cut the AP bonus from 3 to 2. I thought the bonus of 3 was too low until I tried alt+charge.

Kept my cost formula.

Haven’t added in the sword or stable bonuses in yet.

Took out the “1.1” bonus for “Highly Trained” and “Very Hardy,” which made a bigger difference than I would have thought. In fact, it gave us a new champ:

Unit name ... "Bang per Buck"

Hussars ... 159.75
Christian Guard ... 154.42
Polish Knights ... 154.36
Conquistadores ... 152.71
Norman Knights ... 152.71

Chivalric Knights ... 149.99
Quapukulu ... 146.14
E Chivalric Knights ... 143.42
Royal Mamluks ... 140.11

Serbian Knights ... 138.89
Serbian Hussars ... 136.93
Crusader Knights ... 133.52
Tsars Guard ... 129.66
Polish Guard ... 128.22
Demi Lancers ... 126.41
Noble Knights ... 125.19
Royal Banderium ... 122.32

Lancers ... 117.83
Gothic Knights ... 116.22
Huscarls ... 112.16
Famiglia Ducale ... 104.47
Polish Retainers ... 101.96

Druzhina ... 98.97
Mamluks ... 96.64
Imperial Knights ... 94.58
Sipahi Lancers ... 90.93
Latinkon ... 90.63

Armored Clergy ... 89.85
English Knights ... 88.95
Kataphractoi ... 82.96
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
Broken Lances ... 58.35
Albanian Cavalry ... 56.87
Stradiots ... 56.87
Kwarizmian Cavalry ... 54.45

Alan Light Cavalry ... 49.50
Italian Cavalry Militia ... 48.90
Mounted Sergeants ... 39.17
Arab Cavalry ... 38.42
Mercenary German Knights ... 37.62
Byzantine Lancers ... 37.24
Italian MAA ... 34.02
Mercenary Knights ... 32.62

Condottieri ... 28.76
Bedouin Cavalry ... 27.05
Border Horse ... 25.95
Tuareg Camel Spearmen ... 19.70
EE Cavalry Militia ... 14.64
Greek Militia Cavalry ... 13.54
Scouts ... 10.10
Merchant Cavalry Militia ... 9.61
Hobilars ... 6.94

Hit it and quit it

Any cavalry unit that can “pump” — charge, break free and charge again — should do so, as a rule of thumb. However, this is more important — and possible — for some units than others.

Any cavalry unit can batter infantry in this fashion. Doing the same thing against opposing cavalry is more problematic.

This is a ranking of units whose primary attack plus its charge is more than 1.5 times as powerful as their melee attack value, even after any anti-armor bonus for the melee attack is applied. Note is also made of their speed. Bodyguard and Monastic Order knights are not included:

Condottieri — normal
Italian MAA — slow
Mercenary Knights — slow
Polish Retainers — normal
Latinkon — normal
Broken Lances — normal
Portuguese Knights — slow
Gendarmes — slow
Alan Light Cavalry — fast

Next comes units whose charge is 1.5 times as powerful as their melee, and which have normal speed:

Christian Guard
Serbian Knights
English Demi Lancers

1.5 charge, slow speed:

Mercenary German Knights
Imperial Knights
Polish Knights
Chivalric Knights
Eastern Chivalric Knights
Polish Guard
Noble Knights
Royal Banderium
Lancers
Famiglia Ducale

Stay and Play

At the opposite end of the spectrum, we have units that should “pump” against infantry but should never allow enemy cavalry to break away and charge again. They should get a grip on their cavalry enemies and never let go. They have a “pump rate” of 1.33 or less:

Albanian Cavalry — fast
Stradiots — fast
Mamluks
Merchant Cavalry Militia
Kataphractoi — slow
Armored Clergy — slow
Huscarls
Quapukulu — slow
Royal Mamluks — slow
Druzhina

Here’s some more that should consider just slugging it out as an option, with a “pumping” rate of 1.4 or less. All have normal speed unless indicated otherwise:

Gothic Knights — slow
English Knights — slow
Hussars
Conquistadores
Norman Knights
Serbian Hussars
Crusader Knights
Tsars Guard — slow

What's left?

Here are the units that have no clear-cut option in this particular category, ranked in order of the superiority of their charge over their melee factor. Speed other than normal is noted:

Mailed Knights
Granadine Lancers
Mercenary Frankish Knights
Armenian Cavalry
Sipahi Lancers
Feudal Knights — slow
Kwarizmian Cavalry — slow
Tuareg Camel Spearmen — very slow
Border Horse — fast
Italian Cavalry Militia
Byzantine Lancers
Mounted Sergeants
Arab Cavalry
Bedouin Cavalry
EE Cavalry Militia
Greek Militia Cavalry
Scouts
Hobilars

Nice work. Do you intend to do a missile cav classification ?

Quote:

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Originally Posted by Sinan

Do you intend to do a missile cav classification ?

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Yes, but I don't know when.

Cool, no problem. Was just asking so I know if that's somewhere in the future, should be interesting too.

OK. Used most of Miracle's formula again to calculate the charge and melee estimates for missile cavalry. Note that this estimate include sno aspect of missile attack. This is a pure melee value, with charge added in for primary weapon.

Once again, the Mongols and Timurids are left out.


Dvor Cavalry, 118.98
Reiters, 116.12
Polish Nobles, 111.55
Mamluk Archers, 77.57
Vardariotai, 75.07
French Mounted Archers, 69.23
Hungarian Nobles, 65.29
Boyar Sons, 59.84
Cossack Cavalry, 49.44
Sipahis, 41.41
Jinetes, 39.30
Lithuanian Cavalry, 36.55
Granadine CB Cav, 30.97
Granadine Jinetes, 26.89
Strzelcy, 22.16
Desert Cavalry, 21.96
Byzantine Cavalry, 13.97
Mounted Crossbowmen, 12.61
Camel Gunners, 10.80
Turkomans, 8.91
Bedouin Camel Riders, 8.20
Turkomans Mercs, 7.78
Magyar Cavalry, 7.67
Turkopoles, 6.96
Kazaks, 6.49
Turkish Horse Archers, 6.34
Skythikon, 5.74
Akinjis, 5.71
Cuman Horse Archers, 5.05

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Note how Mamluk Archer and Vardariotai have as high a value in this formula as Feudal Knights, despite the lack of a powerful lance charge and higher cost. The biggest surprise for me, though, was the relatively low standing of the Turkish Sipahis. In the formula, this was caused by the lower morale compared to Mams and Vards, and lack of the "hardy" trait.

The rest of it jives with my experiences in the game. As a rule, nothing below a Camel Gunner on this list needs to get in a melee, and the Camel Gunner's included only because it has the camel anti-horse bonus.

@ Miracle

Can this formula, or some varient of it, be applied to melee infantry?

Quote:

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Originally Posted by Doug-Thompson

Can this formula, or some varient of it, be applied to melee infantry?

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It would have to be heavily modified for each infantry class (spearmen, S&S infantry, etc.).

For example, the formula for S&S infantry would emphasize stamina and speed a lot more than the one for spearmen.

However, the infantry running speeds need to be precisely quantified before anyone can compose any formulas.

Re: Lack of running speed data.

Amazing what we're not told, isn't it?

Would be interesting if you could make another list, this time not taking into account the cost. I'm interested to know which to build for bang per buck but also which to build if I have tons of cash and just wanna own something.

Also, "hardy" is high stamina?

Yes, hardy is high stamina.

Here's the "Bang" index, with the combat value divided by 1,000 instead of by each unit's cost:


Christian Guard 49.72
Serbian Knights 49.72
Quapukulu 48.96
Tsars Guard 48.23
Conquistadores 47.80
Norman Knights 47.80
Crusader Knights 47.80
Polish Knights 47.70
Chivalric Knights 47.70
Polish Guard 47.70
Noble Knights 47.70
Royal Mamluks 46.24
Gothic Knights 45.09
E Chivalric Knights 44.89
Royal Banderium 44.89
Lancers 44.89
Hussars 42.18
Serbian Hussars 42.18
Famiglia Ducale 39.28
Demi Lancers 37.29

Huscarls 28.94
Imperial Knights 28.37
English Knights 27.66
Latinkon 27.01
Armored Clergy 26.95
Mamluks 26.19
Mercenary Frankish Knights 25.61
Armenian Cavalry 25.61
Druzhina 25.53
Kataphractoi 25.22
Gendarmes 24.38
Sipahi Lancers 24.01
Portuguese Knights 23.41
Feudal Knights 23.12
Polish Retainers 22.69
Mailed Knights 22.41
Granadine Lancers 22.41
Broken Lances 21.07

Kwarizmian Cavalry 18.78
Albanian Cavalry 14.22
Stradiots 14.22
Alan Light Cavalry 13.86
Mercenary German Knights 12.68
Condottieri 11.85
Mercenary Knights 10.70
Italian MAA 9.63
Italian Cavalry Militia 9.24
Byzantine Lancers 8.90
Mounted Sergeants 8.01
Arab Cavalry 8.01

Tuareg Camel Spearmen 6.50
Bedouin Cavalry 5.55
Border Horse 4.52
EE Cavalry Militia 2.49
Greek Militia Cavalry 2.26
Merchant Cavalry Militia 2.17
Scouts 1.78
Hobilars 1.13

What about Teutonic Knights? I expected them to at least make the top five.

The spreadsheet I used didn't have the Monastic Orders in them.

I'll post again tonight. Real life is interfering.

Thanks. I'm playing the Moors right now. Between good initial economy, Christian Guard, dismounted Christian Guard (which I assume would be up there as well on both bang per buck and just plain bang on infantry) and Camel Gunners, the campaign is a lot of fun. I'm about finished, though.

An early spreadsheet without all the details.

Notice that speed makes a big difference in the formula, making the Order Knights a little lower than one could expect.

Quapukulu 63.19
Christian Guard 60.16
Royal Mamluks 59.68
Tsars Guard 53.06
Conquistadores 52.58
Norman Knights 52.58
Polish Guard 52.47
Teutonic Knights 50.79
Serbian Knights 49.72
Knights Hospitaller 49.38
Knights of Santiago 49.38
Knights Templar 49.38
Royal Banderium 49.38
Gothic Knights 48.10
Crusader Knights 47.80
Polish Knights 47.70
Noble Knights 47.70
Chivalric Knights 47.70
Lancers 44.89
E Chivalric Knights 44.89
Famiglia Ducale 43.21
Hussars 42.18
Serbian Hussars 42.18
Demi Lancers 37.29
Huscarls 33.00
Mamluks 31.21
Armored Clergy 31.03
Imperial Knights 30.74
Kataphractoi 30.05
English Knights 29.79
Druzhina 27.50
Latinkon 27.01
Mercenary Frankish Knights 25.61
Armenian Cavalry 25.61
Gendarmes 24.38
Sipahi Lancers 24.01
Portuguese Knights 23.41
Feudal Knights 23.12
Polish Retainers 22.69
Mailed Knights 22.41
Granadine Lancers 22.41
Broken Lances 21.07
Kwarizmian Cavalry 18.78
Albanian Cavalry 15.40
Stradiots 15.40
Mercenary German Knights 13.95
Alan Light Cavalry 13.86
Condottieri 13.03
Mercenary Knights 10.70
Byzantine Lancers 9.79
Italian MAA 9.63
Italian Cavalry Militia 9.24
Mounted Sergeants 8.01
Arab Cavalry 8.01
Tuareg Camel Spearmen 7.15
Bedouin Cavalry 6.10
Border Horse 4.52
EE Cavalry Militia 2.49
Greek Militia Cavalry 2.26
Merchant Cavalry Militia 2.17
Scouts 1.78
Hobilars 1.13

What's that last list? It seems similar from plain bang but some units jumped up.

Quote:

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Originally Posted by andrewt

What's that last list? It seems similar from plain bang but some units jumped up.

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The first list has several more factors built in and is more refined. For instance, the second list includes Monastic Order knights but gives a bonus for anti-armor secondary weapons that was too high, IMO.


I'll redit this post after making some more adjustments.

[edited P.S.]

Well now, that was interesting.

Before giving these rankings, a couple of disclaimers:

1. Speed mattered. Seven of the top 10 had normal speed, which is faster than most knights.

2. The difference between the top of this "best of" list and the bottom is very close. Every one of these is a tough unit. Also, look at how many of these are scores are tied.

3. One point of armor between Chivalric Knights and Order Knights made the difference.

So, here it is: Christian Guard 49.72
Serbian Knights 49.72
Quapukulu 48.96
Tsars Guard 48.23
Conquistadores 47.80
Norman Knights 47.80
Crusader Knights 47.80
Polish Knights 47.70
Chivalric Knights 47.70
Polish Guard 47.70
Noble Knights 47.70
Royal Mamluks 46.24
Gothic Knights 45.09
E Chivalric Knights 44.89
Royal Banderium 44.89
Lancers 44.89
Knights Hospitaller 44.89
Knights of Santiago 44.89
Knights Templar 44.89
Teutonic Knights 43.29

2 more questions if you don't mind:

1. How is the sand/snow/etc. bonus/penalty computed in?
2. What is trained? Does that just affect morale or is it something else?

Quote:

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Originally Posted by andrewt

1. How is the sand/snow/etc. bonus/penalty computed in?

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It's not — yet. It's hard to work in that variable because, for instance, I have some Knight Templars in my current game who have not and will not leave Europe.

Quote:

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2. What is trained? Does that just affect morale or is it something else?

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Doesn't rout if they see untrained units routing, IIRC.

Now, a big list with everybody on it, including melee values for missile cavalry units:

Christian Guard 49.72
Serbian Knights 49.72
Quapukulu 48.96
Tsars Guard 48.23
Conquistadores 47.80
Norman Knights 47.80
Crusader Knights 47.80
Polish Knights 47.70
Chivalric Knights 47.70
Polish Guard 47.70
Noble Knights 47.70
Royal Mamluks 46.24
Gothic Knights 45.09
E Chivalric Knights 44.89
Royal Banderium 44.89
Lancers 44.89
Knights Hospitaller 44.89
Knights of Santiago 44.89
Knights Templar 44.89
Teutonic Knights 43.29
Hussars 42.18
Serbian Hussars 42.18
Famiglia Ducale 39.28
Demi Lancers 37.29
Reiters 36.81
Dvor_Cavalry 36.29
Polish_Nobles 30.01
Huscarls 28.94
Imperial Knights 28.37
English Knights 27.66
Latinkon 27.01
Armored Clergy 26.95
Mamluks 26.19
Mercenary Frankish Knights 25.61
Armenian Cavalry 25.61
Druzhina 25.53
Kataphractoi 25.22
Gendarmes 24.38
Sipahi Lancers 24.01
Portuguese Knights 23.41
Feudal Knights 23.12
Vardariotai 22.90
Polish Retainers 22.69
Mailed Knights 22.41
Granadine Lancers 22.41
Mongol_Heavy_Archers 21.64
Mamluk_Archers 21.64
Broken Lances 21.07
French_Mounted_Archers 20.21
Kwarizmian Cavalry 18.78
Hungarian_Nobles 17.24
Boyar_Sons 15.32
Albanian Cavalry 14.22
Stradiots 14.22
Alan Light Cavalry 13.86
Mercenary German Knights 12.68
Condottieri 11.85
Mercenary Knights 10.70
Cossack_Cavalry 10.14
Sipahis 9.67
Italian MAA 9.63
Italian Cavalry Militia 9.24
Byzantine Lancers 8.90
Mongol_Horse_Archers 8.53
Jinetes 8.23
Mounted Sergeants 8.01
Arab Cavalry 8.01
Lithuanian_Cavalry 7.58
Granadine_CB_Cav 6.67
Tuareg Camel Spearmen 6.50
Granadine_Jinetes 6.04
Bedouin Cavalry 5.55
Polish_Shooters 4.62
Border Horse 4.52
Camel_Gunners 4.19
Desert_Cavalry 4.15
Byzantine_Cavalry 2.94
Bedouin_Camel_Riders 2.73
Mounted_Crossbowmen 2.58
EE Cavalry Militia 2.49
Greek Militia Cavalry 2.26
Merchant Cavalry Militia 2.17
Scouts 1.78
Turkopoles 1.68
Turkomans 1.66
Turkomans_Mercs 1.66
Magyar_Cavalry 1.52
Hobilars 1.13
Kazaks 1.12
Turkish_Horse_Archers 1.12
Skythikon 1.12
Akinjis 1.01
Cuman_Horse_Archers 1.01

Quote:

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Originally Posted by Doug-Thompson

It's not — yet. It's hard to work in that variable because, for instance, I have some Knight Templars in my current game who have not and will not leave Europe.

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I meant how is it computed by the game. If something gets a -2 to sand, do they get -2 to attack, defense skill or both?

Quote:

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Originally Posted by andrewt

I meant how is it computed by the game. If something gets a -2 to sand, do they get -2 to attack, defense skill or both?

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Wow. I don't know.

I'll post a thread on the topic.