Travian Calculations & Formulae

[Woden]

I got bored, so I decided to compile all the defense bonus listings I've found so far.

Blacksmith & Armoury upgrades
Note: These upgrades apply to all soldiers trained in that village, both before and after the upgrade.
Formula: 1.015 ^ x; x = upgrade level
Lv = Bonus __ Change
_1 = + 1.50% _+1.50%
_2 = + 3.02% _+1.52%
_3 = + 4.57% _+1.55%
_4 = + 6.14% _+1.57%
_5 = + 7.73% _+1.59%
_6 = + 9.34% _+1.61%
_7 = +10.98% _+1.64%
_8 = +12.65% _+1.67%
_9 = +14.34% _+1.69%
10 = +16.05% _+1.71%
11 = +17.79% _+1.74%
12 = +19.56% _+1.77%
13 = +21.36% _+1.80%
14 = +23.18% _+1.82%
15 = +25.02% _+1.84%
16 = +26.90% _+1.88%
17 = +28.80% _+1.90%
18 = +30.73% _+1.93%
19 = +32.70% _+1.97%
20 = +34.69% _+1.99%

City Wall (Romans)
Formula: 1.03 ^ x; x = level
Lv = Bonus ___Change
_1 = + 3.00% _+3.00%
_2 = + 6.09% _+3.09%
_3 = + 9.27% _+3.18%
_4 = +12.55% _+3.28%
_5 = +15.92% _+3.37%
_6 = +19.40% _+3.48%
_7 = +22.98% _+3.58%
_8 = +26.67% _+3.69%
_9 = +30.47% _+3.80%
10 = +34.39% _+3.92%
11 = +38.42% _+4.03%
12 = +42.57% _+4.15%
13 = +46.85% _+4.28%
14 = +51.25% _+4.40%
15 = +55.79% _+4.54%
16 = +60.47% _+4.68%
17 = +65.28% _+4.81%
18 = +70.24% _+4.96%
19 = +75.35% _+5.11%
20 = +80.61% _+5.26%

Palisade (Gauls)
Formula: 1.025 ^ x; x = level
Lv = Bonus ___Change
_1 = + 2.50% _+2.50%
_2 = + 5.06% _+2.56%
_3 = + 7.68% _+2.62%
_4 = +10.38% _+2.70%
_5 = +13.14% _+2.76%
_6 = +15.96% _+2.82%
_7 = +18.86% _+2.90%
_8 = +21.84% _+2.98%
_9 = +24.88% _+3.04%
10 = +28.00% _+3.12%
11 = +31.20% _+3.20%
12 = +34.48% _+3.28%
13 = +37.85% _+3.37%
14 = +41.29% _+3.44%
15 = +44.82% _+3.53%
16 = +48.45% _+3.63%
17 = +52.16% _+3.71%
18 = +55.96% _+3.80%
19 = +59.86% _+3.90%
20 = +63.86% _+4.00%

Earth Wall (Teutons)
Formula: 1.02 ^ x; x = level
Lv = Bonus ___Change
_1 = + 2.00% _+2.00%
_2 = + 4.04% _+2.04%
_3 = + 6.12% _+2.08%
_4 = + 8.24% _+2.12%
_5 = +10.40% _+2.16%
_6 = +12.61% _+2.21%
_7 = +14.86% _+2.25%
_8 = +17.16% _+2.30%
_9 = +19.50% _+2.34%
10 = +21.89% _+2.39%
11 = +24.33% _+2.44%
12 = +26.82% _+2.49%
13 = +29.36% _+2.54%
14 = +31.94% _+2.58%
15 = +34.58% _+2.64%
16 = +37.27% _+2.69%
17 = +40.02% _+2.75%
18 = +42.82% _+2.80%
19 = +45.68% _+2.86%
20 = +48.59% _+2.91%

Heroes
Each point of Def-Bonus will add +0.2% (max +20.0%) to the defense of troops owned by the same player that are located in the same village

All above bonuses are additive, not multiplicitive. For example, a unit with a level 16 Armoury upgrade, behind a level 10 Palisade, will have a total bonus of (26.90 + 28.00 = +54.90%), as opposed to (126.90% × 128.00% = 162.43%).

Residence/Palace defense bonus
Formula: 2 * (level ^ 2)
Lv = Def. Change
_1 = __2 _+ 2
_2 = __8 _+ 6
_3 = _18 _+10
_4 = _32 _+14
_5 = _50 _+18
_6 = _72 _+22
_7 = _98 _+26
_8 = 128 _+30
_9 = 162 _+34
10 = 200 _+38
11 = 242 _+42
12 = 288 _+46
13 = 338 _+50
14 = 392 _+54
15 = 450 _+58
16 = 512 _+62
17 = 578 _+66
18 = 648 _+70
19 = 722 _+74
20 = 800 _+78

Note: The Palace/Residence defense is the same for both Infantry and Cavalry; e.g., at level 10, it offers 200 Infantry Defense and 200 Cavalry Defense. This is affected by walls. These values are not listed at either the Wiki or the FAQ; I inferred them from one of the third-party combat calculators.

[Woden]

-= Roman units =-
Legionnaire: .. 40 Off/wheat, 35/50 Def/wheat,. 6 speed, carries 40/wheat, costs 440/wheat
Praetorian: ... 30 Off/wheat, 65/35 Def/wheat,. 5 speed, carries 20/wheat, costs 460/wheat
Imperian: ..... 70 Off/wheat, 40/25 Def/wheat,. 7 speed, carries 50/wheat, costs 600/wheat
E. Imperatoris: 40 Off/wheat, 22/17 Def/wheat, 14 speed, carries 33/wheat, costs 470/wheat
E. Caesaris ... 45 Off/wheat, 20/26 Def/wheat, 10 speed, carries 18/wheat, costs 543/wheat
E. Legati: .................. 10/ 5 Def/wheat, 16 speed, ................. costs 180/wheat

-= Teuton units =-
Maceman: . 40 Off/wheat, 20/ 5 Def/wheat,. 7 speed, carries 60/wheat, costs 250/wheat
Spearman:. 10 Off/wheat, 35/60 Def/wheat,. 7 speed, carries 40/wheat, costs 340/wheat
Axeman: .. 60 Off/wheat, 30/30 Def/wheat,. 6 speed, carries 50/wheat, costs 490/wheat
Paladin: . 28 Off/wheat, 50/20 Def/wheat, 10 speed, carries 55/wheat, costs 503/wheat
T. Knight: 50 Off/wheat, 17/25 Def/wheat,. 9 speed, carries 27/wheat, costs 508/wheat
Scout: ................. 10/ 5 Def/wheat,. 9 speed, ................. costs 360/wheat

-= Gaul units =-
Phalanx: .. 15 Off/wheat, 40/50 Def/wheat,. 7 speed, carries 30/wheat, costs 315/wheat
Swordsman:. 65 Off/wheat, 35/20 Def/wheat,. 6 speed, carries 45/wheat, costs 535/wheat
T. Thunder: 45 Off/wheat, 13/20 Def/wheat, 19 speed, carries 38/wheat, costs 545/wheat
Druidrider: 23 Off/wheat, 58/28 Def/wheat, 16 speed, carries 18/wheat, costs 545/wheat
Haeduan: .. 47 Off/wheat, 17/55 Def/wheat, 13 speed, carries 22/wheat, costs 655/wheat
Pathfinder: ............. 10/ 5 Def/wheat, 17 speed, ................. costs 190/wheat

Analysis (by race)
The best attackers: Imperian; Swordsman; Axeman
The best looters: Maceman; Imperian; Swordsman
The best infantry defenders: Praetorian; Druidrider; Paladin
The best cavalry defenders: Spearman; Haeduan; Legionnaire
The best overall defenders: Praetorian (100); Spearman (95); Phalanx (90)
The fastest strong attacker: T. Thunder; E. Imperatoris; T. Knight
The fastest strong defender: Druidrider (86 @ 16); Paladin (70 @ 10); Praetorian (100 @ 5)
Fastest raiders: T. Thunder (38 @ 19); E. Imperatoris (33 @ 14); Paladin (55 @ 10)


Most efficient attackers (top 5)
1) T. Thunder: ... 45 * 19 = 855
2) Haeduan: ...... 47 * 13 = 611
3) E. Imperatoris: 40 * 14 = 560
4) Imperian: ..... 70 *. 7 = 490
5a) E. Caesaris: . 45 * 10 = 450
5b) T. Knight: ... 50 *. 9 = 450


Most efficient looters (top 5)
1) T. Thunder: ... 38 * 19 = 722
2) Paladin: ...... 55 * 10 = 550
3) E. Imperatoris: 33 * 14 = 462
4) Maceman: ...... 60 *. 7 = 420
5) Imperian: ..... 50 *. 7 = 350

[Gondeath]

One of the bigger decisions of the game is what Tribe to choose. I calced out attack and defense rates of the units to determine which set of troops are best; Roman, Gaul, or Teuton.

I used 12 crops and tried to find out which units are the best for their tribe, and then what combinations are the best for an overall balanced effect. These calculations where done regardless of the unit's cost.

Overall I think the Gauls are the best race (not counting traps in there).
- They are the best raiders, speed attackers, and melee defenders
- Overall they are ~28% stronger than the Romans, and ~33% stronger than the Teutons.

Romans have the best attacker unit (Imperians), and Teutons have the best cavalry defense unit (Spearfighters).

The best set ups (if you are equally concerned with attack, defense and speed) are -

Romans:
- 12 Legionnaire
- 12 Praetorian
- 12 Imperian
- 8 Equites Imperatoris

Gauls:
- 12 Swordfighters
- 12 Theutates Thunder
- 6 Druidrider
- 4 Haeduan

Teutons:
- 12 Axefighters
- 12 Spearfighters
- 12 Paladins
- 4 Teuton Knights

This guide does not include which is the cheapest though, so while Gauls may be stronger overall (per crop) a Teuton may be able to recruit faster, and have a better army (in two Teuton villages vs. one Gaul village).

Village for village, crop per crop; Gauls are the best.

₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪

Headings:
- # : Number of units you can get for 12 crops
- A : Attack value (based on # x attack)
- Ra : Raid value (based on # x speed x res carried)
- A/Sp : Attack for Speed (based on # x attack x speed)
- MD : Melee Defense (based on # x melee defense)
- CD : Cavalry Defense (based on # x cavalry defense)
- Unit Name : (the name of the unit)

# - A - Ra - A/Sp - MD - CD - Unit Name

12 480 2880 02880 420 600 Legionnaire
12 360 1200 01800 780 420 Praetorian
12 840 4200 05880 480 300 Imperian
04 480 5600 06720 260 200 Equites Imperatoris
03 540 2100 05400 240 315 Equites Caesaris

# - A - Ra - A/Sp - MD - CD - Unit Name

12 180 2520 01260 480 600 Phalanx
12 780 3240 04680 420 240 Swordfighter
06 540 8550 10260 150 240 Theutates Thunder
06 270 3360 04320 790 330 Druidrider
04 560 3380 07280 200 660 Haeduan

# - A - Ra - A/Sp - MD - CD - Unit Name

12 480 5040 03360 240 060 Clubswinger
12 240 3360 00840 420 720 Spearfighter
12 720 3600 04320 360 360 Axefighter
06 330 6600 03300 600 240 Paladin
04 600 2880 05400 200 600 Teuton Knight


₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪

Headings:
- SpVa Specific Value (The stat specific value)
- TV : Total Value, (The total value of their [att + m/c def] x units for 12 crop)
- ModV : Modified Value, (SpVa + TV showing 2x the stat they will be most used for)
- Unit Name (the name of the unit)

Best Attackers:
SpVa - TV - ModV - Unit Name
00840 1620 02460 Imperian
00780 1440 02220 Swordfighter
00720 1440 02160 Axefighter

Best Raiders:
SpVa - TV - ModV - Unit Name
08550 0930 09480 Theutates Thunder
06600 1260 07860 Paladin
05600 0940 06540 Equites Imperatoris

Best Attackers for Speed:
SpVa - TV - ModV - Unit Name
10260 0930 11190 Theutates Thunder
06720 0940 07660 Equites Imperatoris
05400 1100 06500 Teuton Knight

Best Melee Defenders:
SpVa - TV - ModV - Unit Name
00790 1290 02080 Druidrider
00780 1560 02340 Praetorian
00600 1170 01770 Paladin

Best Cavalry Defenders:
SpVa - TV - ModV - Unit Name
720 1260 1980 Spearfighter
660 1420 2080 Haeduan
600 1500 2100 Legionnaire

₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪ ₪

Total Power (12 crops for each unit that is the best of their tribe)

Rome: 21100
Imperian - 12 for attack
Equites Imperatoris - 4 for raids
Equites Imperatoris - 4 for speed attacks
Praetorian - 12 for melee defense
Legionnaire - 12 for cavalry defense

Gaul: 27050
Swordfighter - 12 for attack
Theutates Thunder - 6 for raids
Theutates Thunder - 6 for speed attacks
Druidrider - 6 for melee defense
Haeduan - 4 for cavalry defense

Teuton: 20270
Axefighter - 12 for attack
Paladin - 6 for raids
Teuton Knight - 4 for speed attacks
Paladin - 6 for melee defense
Spearfighter - 12 for cavalry defense

[Woden]

Hero bonus: +25% Attack, +67% Defense (game rounds to nearest 5)

Attack/Defense Points (game rounds to nearest 5)
This section lists the average bonus per point of Attack or Defense.
-=ROMAN=-
Legionnaire:.... 54.0 Attack,.. 49.0 /. 62.5 Defense
Praetorian:..... 47.5 Attack,.. 74.5 /. 47.5 Defense
Imperian:....... 74.0 Attack,.. 57.0 /. 42.0 Defense
E. Imperatoris: 107.5 Attack,.. 72.0 /. 59.5 Defense
E. Caesaris:... 147.5 Attack,.. 79.0 /. 99.0 Defense
-=TEUTON=-
Maceman:........ 54.0 Attack,.. 59.5 /. 24.0 Defense
Spearman:....... 34.0 Attack,.. 48.0 /. 70.5 Defense
Axeman:......... 67.5 Attack,.. 47.5 /. 47.5 Defense
Paladin:........ 64.0 Attack,. 100.0 /. 49.5 Defense
T. Knight:..... 127.5 Attack,.. 58.5 /. 80.0 Defense
-=GAUL=-
Phalanx:........ 37.5 Attack,.. 53.0 /. 62.0 Defense
Swordsman:...... 71.0 Attack,.. 54.0 /. 38.0 Defense
T. Thunder:..... 87.5 Attack,.. 42.0 /. 57.0 Defense
Druidrider:..... 57.5 Attack,. 108.5 /. 60.5 Defense
Haeduan:....... 121.0 Attack,.. 55.0 / 145.0 Defense

Figures were obtained using the Herocreator by calculating the difference between 10 points and 0 points, then dividing by 10.

Break-evens (before Blacksmith/Armoury bonuses):
This section lists the total strength of an army needed for points in Off-Bonus or Def-Bonus to have a larger effect than points is Attack or Defense.
-=ROMAN=-
Legionnaire:... 27,000 Attack / 55,750 Defense
Praetorian:.... 23,750 Attack / 61,000 Defense
Imperian:...... 37,000 Attack / 49,500 Defense
E. Imperatoris: 53,750 Attack / 65,750 Defense
E. Caesaris:... 73,750 Attack / 89,000 Defense
-=TEUTON=-
Maceman:....... 27,000 Attack / 41,750 Defense
Spearman:...... 17,000 Attack / 59,250 Defense
Axeman:........ 33,750 Attack / 47,500 Defense
Paladin:....... 32,000 Attack / 74,750 Defense
T. Knight:..... 63,750 Attack / 69,250 Defense
-=GAUL=-
Phalanx:....... 18,750 Attack / 57,500 Defense
Swordsman:..... 35,500 Attack / 46,000 Defense
T. Thunder:.... 43,750 Attack / 49,500 Defense
Druidrider:.... 28,750 Attack / 84,500 Defense
Haeduan:....... 60,500 Attack /100,000 Defense

E.g.: To break-even between an Imperian's Attack and Off-Bonus, the attacking army (I'll use Imperians-only for the example) would need to have a total pre-Hero, pre-Blacksmith Attack of 37,000 points. That would be (37,000 / 70 = ~529 Imperians) before the Off-Bonus becomes a better value than Attack.

[Woden]

----- Normal Attack -----

(Note: Attacker's defense values are not used; defender's attack values are not used.)

Cavalry%: Attack value of cavalry / total attack value of attacking army

Total defense: (Total infantry defense * [1-Cavalry%]) + (Total cavalry defense * Cavalry%)

Loser's casualties: 100%
Winner's casualties: (loser's strength / winner's strength)^1.5 * 100%

----- Raid -----

As Normal Attack, but "winner's casualties" is now "modifier"

Winner's casualties: modifier / (modifier + 1) * 100%
Loser's casualties: 100% - winner's casualties

----- Scouting -----
(Note: This is not the exact formula, but it provides a close approximation.)

Attacking scouts are considered to have 35 attack (subject to all the normal modifiers). Blacksmith upgrades give ~2.1% bonus per level instead of ~1.5% bonus per level.
Defending scouts are considered to have 20 attack (subject to all the normal modifiers). Armory upgrades give ~3.0% bonus per level instead of ~1.5% bonus per level.

Defender's casualties: 0%
Attacker's casualties: (defense strength / attack strength)^1.5 * 100%
If defense strength is higher than attack strength, then all attacking scouts die.

[Woden]

This is the raw production (that is, before all other modifiers) of each field at a given level. The value is the same for each field type.

Level . Production . Increase
.0 . ... 2 / hour ... -----
.1 . ... 5 / hour ... +.. 3 / hour
.2 . ... 9 / hour ... +.. 4 / hour
.3 . .. 15 / hour ... +.. 6 / hour
.4 . .. 22 / hour ... +.. 7 / hour
.5 . .. 33 / hour ... +. 11 / hour
.6 . .. 50 / hour ... +. 17 / hour
.7 . .. 70 / hour ... +. 20 / hour
.8 . . 100 / hour ... +. 30 / hour
.9 . . 145 / hour ... +. 45 / hour
10 . . 200 / hour ... +. 55 / hour
11 . . 280 / hour ... +. 80 / hour
12 . . 375 / hour ... +. 95 / hour
13 . . 495 / hour ... + 120 / hour
14 . . 635 / hour ... + 140 / hour
15 . . 800 / hour ... + 165 / hour
16 . 1,000 / hour ... + 200 / hour
17 . 1,300 / hour ... + 300 / hour
18 . 1,600 / hour ... + 300 / hour

Then all bonuses from bonus buildings (such as the Brickworks and Flour Mill) and Oases are added together, then applied to the raw production listed above.

For example, if you had a level 5 Brickworks (+25% Clay production) and one Clay oasis (+25% Clay production), then a bonus of 50% would be added to your Clay production.


Next, the bonuses from any Gold production bonuses you have activated get applied.

For example, if you had 4 level 10 Clay Pits (800 total production before bonuses) and a level 5 Brickworks (+25% Clay production; increases the total production to 1,000), then activating the Gold bonus for Clay would increase the 1,000 production to 1,250 production.


Finally, for Wheat only, your population and the wheat consumption of your army is subtracted from your production.

[Woden]

Here is some data on scout defenses:

(All of these are assuming equal populations; if you are smaller than the attacker, you will be more successful in defending.)

With 5 non-upgraded scouts and no wall, you can detect any scouting attempts from up to 96 non-upgraded scouts or 27 fully-upgraded scouts; you can completely kill scouting attempts of up to 3 non-upgraded scouts or 2 fully-upgraded scouts.

With 10 non-upgraded scouts and no wall, you can detect any scouting attempts from up to 757 non-upgraded scouts or 217 fully-upgraded scouts; you can completely kill scouting attempts of up to 6 non-upgraded scouts or 4 fully-upgraded scouts.

With 15 non-upgraded scouts and no wall, you can detect any scouting attempts from up to 2,544 non-upgraded scouts or 729 fully-upgraded scouts; you can completely kill scouting attempts of up to 8 non-upgraded scouts or 6 fully-upgraded scouts.

With 5 fully-upgraded scouts and no wall, you can detect any scouting attempts from up to 544 non-upgraded scouts or 156 fully-upgraded scouts; you can completely kill scouting attempts of up to 5 non-upgraded scouts or 3 fully-upgraded scouts.

With 10 fully-upgraded scouts and no wall, you can detect any scouting attempts from up to 4,316 non-upgraded scouts or 1,238 fully-upgraded scouts; you can completely kill scouting attempts of up to 10 non-upgraded scouts or 7 fully-upgraded scouts.

With 15 fully-upgraded scouts and no wall, you can detect any scouting attempts from up to 14,527 non-upgraded scouts or 4,166 fully-upgraded scouts; you can completely kill scouting attempts of up to 15 non-upgraded scouts or 10 fully-upgraded scouts.

To approximate the results with a wall, multiply the number of attacking scouts listed above by the defense bonus of your wall.

[Nickster]

Got bored before my bedtime. So I did these Calc's.
Note: Multiply by 3 to get Speedserver Bonus Product.

Romans:
Carrying Capacity: 500
Multiply 110% = 550
Multiply 120% = 600
Multiply 130% = 650
Multiply 140% = 700
Multiply 150% = 750
Multiply 160% = 800
Multiply 170% = 850
Multiply 180% = 900
Multiply 190% = 950
Multiply 200% = 1000
Multiply 210% = 1050
Multiply 220% = 1100
Multiply 230% = 1150
Multiply 240% = 1200
Multiply 250% = 1250
Multiply 260% = 1300
Multiply 270% = 1350
Multiply 280% = 1400
Multiply 290% = 1450
Multiply 300% = 1500
Level 20 Marketplace capacity + Level 20 Trade Office = 30000

Teutons:
Carrying Capacity: 1000
Multiply 110% = 1100
Multiply 120% = 1200
Multiply 130% = 1300
Multiply 140% = 1400
Multiply 150% = 1500
Multiply 160% = 1600
Multiply 170% = 1700
Multiply 180% = 1800
Multiply 190% = 1900
Multiply 200% = 2000
Multiply 210% = 2100
Multiply 220% = 2200
Multiply 230% = 2300
Multiply 240% = 2400
Multiply 250% = 2500
Multiply 260% = 2600
Multiply 270% = 2700
Multiply 280% = 2800
Multiply 290% = 2900
Multiply 300% = 3000
Level 20 Marketplace capacity + Level 20 Trade Office = 60000

Gauls:
Carrying Capacity: 750
Multiply 110% = 825
Multiply 120% = 900
Multiply 130% = 975
Multiply 140% = 1050
Multiply 150% = 1125
Multiply 160% = 1200
Multiply 170% = 1275
Multiply 180% = 1350
Multiply 190% = 1425
Multiply 200% = 1500
Multiply 210% = 1575
Multiply 220% = 1650
Multiply 230% = 1725
Multiply 240% = 1800
Multiply 250% = 1875
Multiply 260% = 1950
Multiply 270% = 2025
Multiply 280% = 2100
Multiply 290% = 2175
Multiply 300% = 2250
Level 20 Marketplace capacity + Level 20 Trade Office = 45000

[Hellraiser]

Sure! I've now thrown all my calculations into an Excel worksheet and discovered quite a few transcription and calculation errors that I made using pen, paper and calc.

Basically, I was penalizing praetorians as I had their cost as 600 rather than 460. On the other hand, I was rewarding 24/7 roman hammer armies, as now they are the second least efficient (most costly) hammer behind teutons building maces + TKs.

Feel free to edit as you see fit:

================

How valuable is the superior wheat efficiency of romans?

On the total cost of ownership, per 100K defense generated, assuming a 50/50 inf/cav attack, which is the most likely attack mix for hammer attacks:

Teuts 100K = 2105 spears @ a cost of 716K in 111 hrs
Gauls 100K = 2222 phalxs @ a cost of 700K in 108 hrs
Roms 100K = 2000 praets @ a cost of 920K in 165 hrs
Roms 100K = 2353 legos @ a cost of 1.04M in 176 hrs

A praetorian defense will break even with phalanxes and spears on cost for the same amount of defense if they live longer than, respectively, 41.25 and 80.83 days. If the inf/cav attack ratio breaks more towards infantry, which it often will, then the romans will do relatively better (i.e. - break even faster).

On the total cost of ownership, per 100K defense generated (assuming a 100/0 inf/cav attack):

Teuts 100K = 2857 spears @ a cost of 971K in 150 hrs
Gauls 100K = 2500 phalanxes @ a cost of 788K in 122 hrs
Roms 100K = 1538 praets @ a cost of 708K in 127 hrs
Roms 100K = 2857 legos @ a cost of 1.26M in 214 hrs

Praets win from the outset and just pile on from there.

On the total cost of ownership, per 100K defense generated (assuming a 0/100 inf/cav attack):

Teuts 100K = 1667 spears @ a cost of 567K in 88 hrs
Gauls 100K = 2000 phalanxes @ a cost of 630K in 98 hrs
Roms 100K = 2857 praets @ a cost of 1.31M in 236 hrs
Roms 100K = 2000 legos @ a cost of 880K in 150 hrs

Spearmen win from the outset and just pile on from there.

Lessons learned:

Praetorians are slow and expensive to build initially. However, due to their wheat efficiency and because most attacks (other than cavalry raids) will be significantly skewed towards infantry attack for cost efficiency reasons, they usually end up being the most cost effective defenders. Still, build your city wall to protect your upfront investment in praetorians. The longer they live, the cheaper they become relative to the other primary defenders.

Romans need to build+tech defense production in more (1.5x) cities in order to produce the same amount of defense per unit time because of relatively longer build times.

Romans and teuts should trade praets for spearmen (or, less preferably, use legos) to even out their inf/cav defense ratios. I recommend a 3:1 or higher ratio of praets:spears as many attack armies will be heavily skewed towards infantry in total attack, due to infantry's cheaper cost. Basically, you want just enough spears (or legos) to make all cavalry raids too expensive. Gauls can get by on just phalanxes, but if you find a roman that will trade at some multiple (e.g. - 9:10 praets for phalanxes), it could be a good idea to up your infantry defense.

Legos, paladins, druidriders and haeduans are expensive for pure defense. If you build these units, then they should be built for other purposes as well (i.e. - raiding, mobile defense, attack, etc.).

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What about wheat efficiency for attack infantry?

Teuts 100K = 2500 MCs @ a cost of 625K in 84 hrs
Teuts 100K = 1667 AXs @ a cost of 817K in 94 hrs
Gauls 100K = 1538 SWs @ a cost of 823K in 104 hrs
Roms 100K = 1429 IMs @ a cost of 857K in 129 hrs
Roms 100K = 2500 LGs @ a cost of 1.10M in 188 hrs

Imperians will break even with maces, axes and swords on a cost basis for the same amount of offense in 9.0, 7.1 and 12.9 days, respectively. These are significantly better break even times than the defensive infantry.

Axes will break even with maces in just 9.6 days. Note, however, that if resource cost is not a constraint then macemen are preferable for 24/7 building due to their higher att/min, speed and carrying capacity (see below).

Lessons learned:

Imps are cheap in total cost of ownership, although slow to produce, relative to other attack infantry.

Macemen cost (a lot) more than axemen if they stick around for more than about ten days. However, teutons should build macemen rather than axemen when resources are not an issue due to higher att/time production (see below).

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What about attack cavalry?

100K = 667 TKs @ a cost of 1.02M in 93 hrs
100K = 714 HDs @ a cost of 1.40M in 104 hrs
100K = 1111 TTs @ a cost of 1.21M in 129 hrs
100K = 833 EIs @ a cost of 1.18M in 103 hrs
100K = 556 ECs @ a cost of 1.21M in 92 hrs

ECs break even with EIs after 4.6 days. HDs break even w/ ECs after 104 days.

Lessons learned:

It is far cheaper to produce the same amount of attack w/ infantry versus cavalry. Most offensive armies will skew significantly toward infantry attack power for exactly this reason. Therefore, your defenses should also skew towards defending against infantry.

ECs are actually cheaper than EIs for the same amount of attack. If you want to raid and/or have speed then EIs can make sense. For pure attack power go ECs.

On an att/cost basis, ECs and TTs are almost exactly identical.

TKs are always cheaper per attack than any other attack cavalry.

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Eventually, you will build a hammer army, which is BY FAR your biggest offensive army, that you should house in your 15c capital. For hammer armies, resource costs are largely unimportant as your entire empire will fund the building in this single city. Note, that you DO NOT build your hammer in your capital, but preferably a nearby (e.g. - adjacent) city. You do this because you cannot build Great Barracks or Great Stable in your capital and because you won't have enough space there for all the desirable military buildings due to granaries and warehouses taking up so much space.

Build times are what dominate how good your hammer army can be, so we want to maximize att/time here, with some thought given towards wheat efficiency to maximize the size of your hammer relative to your empire. In a hammer city producing 24/7 in lvl 20 barracks and a lvl 20 stable (13.5% of default build time).

Teuts MCs can produce 1185 att/hr @ a cost of 7.4K rsrc/hr
Teuts AXs can produce 1067 att/hr @ a cost of 8.7K rsrc/hr
Gauls SWs can produce 963 att/hr @ a cost of 7.9K rsrc/hr
Roms IMs can produce 778 att/hr @ a cost of 6.7K rsrc/hr
Roms LGs can produce 533 att/hr @ a cost of 5.9K rsrc/hr

Roms EC can produce 1091 att/hr @ a cost of 13.3K rsrc/hr
Teuts TK can produce 1081 att/hr @ a cost of 11.0K rsrc/hr
Roms EI can produce 970 att/hr @ a cost of 11.4K rsrc/hr
Gauls HD can produce 957 att/hr @ a cost of 13.4K rsrc/hr
Gauls TT can produce 774 att/hr @ a cost of 9.4K rsrc/hr

Totaling up and using best att/time units we get:

Teuts MCs + TKs can produce 2266 att/hr @ a cost of 18.4K rsrc/hr
Teuts AXs + TKs can produce 2148 att/hr @ a cost of 19.7K rsrc/hr
Gauls SWs + HDs can produce 1920 att/hr @ a cost of 21.4K rsrc/hr
Roms IMs + ECs can produce 1869 att/hr @ a cost of 19.8K rsrc/hr

If you can afford both GB and GS (you better!), then double the amount of att/hr while quadrupling the rsrc/hr. The inf/cav ratio will remain the same.

Lessons learned:

Teutons can produce significantly more att/hr than the other races at superior cost, even when wheat efficiency is taken into consideration (see below).

Romans can output offensive points nearly as fast as the other races if they build ECs 24/7. If they try to skew heavily towards imps to minimize cost, then they can have a significantly more efficient, but MUCH smaller and longer to build/repair hammer.

A 24/7 roman hammer army will be skewed towards cavalry in total attack points at 58.4% cavalry, gauls will almost be even at 49.8% and teuts will be slightly skewed towards infantry at 47.7% (macemen) or almost even at 50.3% (axemen).

If you can't afford to keep both your GS + GB going 24/7, then favor keeping your GB running as we saw infantry has far better att/rsrc ratios. Because of this fact, hammer armies may be more skewed towards infantry in practice than the theoretically optimal numbers above.

As your hammer approaches the maximum size that your empire can support, superior wheat efficiency really begins to matter. In this case, teuts should build axemen rather than macemen. In general, production should shift more towards infantry than cavalry due to better overall cost and wheat efficiency.

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On the total cost of ownership, using the 24/7 hour build per 100K offense generated:

Teuts will spend 812K and consume 2261 wh/hr. Build time: 1.84 days. (Macemen)
Teuts will spend 917K and consume 1834 wh/min. Build time: 1.94 days. (Axes)
Gauls will spend 1.11M and consume 1840 wh/min. Build time: 2.17 days.
Roms will spend 1.06M and consume 1892 wh/min. Build time: 2.23 days.

Teuts building axes will immediately do better than breaking even with both Romans and Gauls. They will break even on cost w/ a Teut building macemen after 10.3 days.

Gauls will break even in 29.7 days w/ Teuts building macemen. They will break w/ Romans after 41.5 days.

Romans will break even in 28.0 days w/ Teuts building macemen.

Lessons learned:

Teutons building axes have the cheapest / most efficient and fastest growing 24/7 hammer armies.

Romans get boned because imperians have such long build times. They need to build ECs to keep up in total offensive output, but ECs have poor wheat efficiency leaving a 24/7 roman hammer w/ the 2nd worst total cost of ownership behind teuts building macemen.

[Hellraiser]

May be redundant with other things you've already posted:

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The following are the cheapest attackers and defenders (vs 50/50 inf/cav total attack) in initial production cost on a per 1000 resource cost basis.

Use this as your production guide when resources are tight or you want maximum stats per resource spent.

Attack points per 1000 rsrcs (higher is better):

Roms IM produce 116.7
Roms LG produce 90.91
Roms EI produce 85.11
Roms EC produce 82.95
Roms PT produce 65.22

Gauls SW produce 121.5
Gauls TT produce 82.57
Gauls HD produce 71.25
Gauls PH produce 47.62
Gauls DD produce 41.28

Teuts MC produce 160.0
Teuts AX produce 122.5
Teuts TK produce 98.36
Teuts PD produce 54.73
Teuts SP produce 29.41

Defense points per 1000 rsrcs under 50/50 inf/cav attack (higher is better):

Roms PTs produce 108.7
Roms LGs produce 96.59
Roms IMs produce 54.17
Roms ECs produce 42.63
Roms EIs produce 41.67
Roms SPY produce 40.78

Gauls PHs produce 142.9
Gauls DDs produce 77.98
Gauls HDs produce 54.71
Gauls SWs produce 51.40
Gauls SPY produce 39.47
Gauls TTs produce 29.82

Teuts SPs produce 139.7
Teuts PDs produce 69.65
Teuts AXs produce 61.22
Teuts MCs produce 50.00
Teuts TKs produce 40.98
Teuts SPY produce 20.83

Lessons learned:

Macemen are far and away the cheapest attackers in initial cost, although they fall quickly behind in total cost when wheat efficiency is taken into account (see below).

The other infantry attack units cost roughly the same, but imps will be slightly cheaper over time due to wheat efficiency (see below).

Praetorians are quite expensive initially when compared to other races' primary defensive units => build your city wall so you don't lose them before their wheat efficiency can make them cost relatively less (see below).

Legos aren't quite as useless as they might seem. If you actually use them for both offense and defense, then they can be worth their cost. If you only use them for one or the other, then stick w/ the specialists. In particular, legos probably should not be in your hammer army (see below) and since most of your other empire's army should be defense, their only real place is acting as raiders + secondary defenders (evening out inf/cav defense ratios, see below).

Paladins, druidriders and haeduans are quite expensive for the defense they provide. You should hold off on building these unless you intend to attack/raid with them or have a mobile defense to help other cities.

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