# Boni

**Boni**

**wall**: gives extra bonus percent to defense, up to +80%**basic defense**: adds some absolute value to defense, +10**palace**: adds some absolute value to defense, up to +800**moralebonus**: defender could have up to +50% bonus, if his account's total population is less than attacker's total population**upgrades**: depends on stats of units, +20–30% for offense/defense average, but may be higher in some rare cases

**2.a. Wall**

Wall gives to defender extra percent-based bonus, which depends on race of wall:

1.020^L for Teutonic Earth wall;

1.025^L for Gallic Palisade;

1.030^L for Romans City wall.

where L is level of corresponding building.

E.g. roman city wall 15th level gives next bonus: 1.03^15 = 1.558 or 55.8%. At 20th level bonus is a bit more than 80%. Therefore wall is a "cornerstone" in village's defense.

Consider 150 swordsmen attacking 100 praetorians and 25 legionnaires behind 15th level city wall.

Since swordsmen are infantry we will use only defense against infantry values.

offense points will be: 150 · 65 = 9750

defense points will be: 25 · 35 + 100 · 65 = 7375

But we have a wall, which could greatly increase defense points: 7375 · 1.558 ≈ 11490

11490 is greater than 9750 so in this example defender will win.

casualties = 100% · (9750 / 11490) ^ 1.5 = 78.17% which result in 78 praetorians and 20 legionnaires loss.

If there's no wall attacker would win. You may check it with combat simulator.

**2.b. Basic village defense**

Even empty village with no fortification, has some small defense value, equals 10. Moreover, this value is also affected by other boni like wall. I was not completely honest with you, omitting this value in previous calculations. This was done for the sake of simplicity and because such small value hardly can affect result of average combat.

E.g. 2 phalanx attacks empty village.

offense is 15·2 = 30

defense is 10

2 · (10/30)^1.5 ≈ 0.385 which leads to no casualties.

But if we build in empty (I mean no troops) roman village a 5th level wall, combat result will change.

defense become 10·1.03^5 or 12 points

2 · (12/30)^1.5 ≈ 0.506 which will be rounded to 1 and will mean 1 died phalanx.

Also there's one extra tricky moment. There's known phenomena, that one unit will always die against even empty village if he was not a strong cavalry. It could be described by basic defense, but if it's so, why one imperian with 70 offense points die and 2 phalanx with total 30 offense points don't die?

There's an extra check for every combat with lone attacker.

If unit's offense points are less than 83, unit will die disregarding of defender's losses. This check is applied for both attack types: normal attack/raid. Also this value (83) could be affected by moralebonus and unit's offense is counted considering upgrades.

You may read below in this section about exact formulas for upgrades and moralebonus.**2.c. Residence/Palace**

Residence/Palace (we will use just "Palace" hereinafter, since both buildings are equal in their defending abilities) could also help in combat, but its contribution isn't much. Palace doesn't add percent-based bonus, but just gives some absolute defense value: e.g., on 20th level Palace will give only 800 defense points (both against infantry and cavalry). This addition could be expressed as next formula:

where n is level of palace.

As we could see, first levels give you nearly nothing. E.g., 1st level Palace adds only 2 points, 2nd level — 8pts, 3rd level — 18pts, etc.

For greater armies even 800 points is a tiny value, but against small squadrons it may be useful. If 10 imperians attack village with 20th level palace, they all die! (700 < 800+10). Of course, it is not easy to obtain benefits from these buildings, since even 5th level residence isn't very cheap. And when you have enough resources, armies is far more stronger than 10 imperians.*Nevertheless, in the beginning of one Russian server I made top-50 in defense, using no troops! Of course, it was done due to residence's defense. Residence is especially effective against noobs attacking with phalanx or spearmen =)***Hint**: Defense given by palace and basic village defense **is** affected by wall bonus as well as troops.

15 phalanx attacks village with 6th level residence and 6th level roman wall.

offense is 15 · 15 = 225

defense is (Residence + base defense) · Wall bonus = (2·6^2 + 10) · (1.03^6) ≈ 82 · 1.194 ≈ 98

Attacker wins, but residence couldn't be destroyed by regular troops, so attacker despite of his/her win, looses something and defender looses nothing.

100% · (98/225) ^ 1.5 ≈ 28.7% or 4 phalanx

**2.d. Moralebonus**

This bonus is applied only to defender when his/her population is less than population of attacker. For example, if attacker's population is 500, and defender's one is 600, there will be no bonus. If attacker's and defender's populations are 700 and 150 correspondingly, defender will receive a bonus.

Accounts population is used! Though, on travianwiki.com is said, that population of "village" (aldea) is taken, it is wrong.

Formula for moralebonus is simple: M^0.2, where

M is attacker's population / defender's population.

E.g. 500 swordsmen from account with 2500 pop attacks 500 praetorians from account with 1000 pop.

(2500/1000)^0.2 ≈ 1.2 or 20% bonus

losses are 100% · (65·500 / 65·500·1.2) ^ 1.5 = 76.0% or 380 praetorians

Moralebonus never goes higher than +50%, even if defender have zero population.**Note:** Unoccupied oasis has its own population, which is 500. And moralebonus works for nature as usual. For occupied oases owner account's population is used.

//This formula is also applied to loyalty descending.

Furthermore, if attacker has fewer points than defender (including all boni, except moralebonus itself), and has more population, formula become a bit more complicated:

moralebonus = M^{0.2·(offense points/defense points)}

Such case could occur for example with WW village on small account, but WW villages are completely unaffected by moralebonus.

E.g. 1500 swordsmen from account with 2500 pop attacks 2500 praetorians on account with 1000 pop.

offense points = 1500 · 65

defense points = 2500 · 65

As offense points are less then defense points and attacker's population is bigger, complicated formula is used:

moralebonus = M^{0.2·(offense points/defense points)} = (2500/1000) ^ {0.2 · 1500/2500)} = 2.5 ^ 0.12 ≈ 1.116

Also total amount of troops (4000) taking part in battle is more than 1000, so it is immense battle, use (5).

K = 2 · (1.8592 – 4000^0.015) = 2 · (1.8592 – 1.1325) = 2 · 0.7267 = 1.4534

defender wins and his/her losses conclude: 100% · (offense points / defense points·moralebonus) ^ K

losses = 100% · (1500·65 / (2500·65 + 10)·1.116) ^ 1.4534 = 40.57% or 1014 praetorians

**2.e. Upgrades**

This part of Travian combat mechanics have most various zoo of formulas spread over the Internet.

BASE_VALUE · 1.015^LEVEL

BASE_VALUE · (1 + 0.015 · LEVEL)

(А · UPKEEP + 0.015 · BASE_VALUE) · LEVEL / 2, where А is a constant ≈ 0.641627,

But full correct formula is a bit more complicated:

It is correct for every stat (offense, def. against infantry, def. against cavalry) and for any unit.

I've obtained this formula in summer 2007 and published it on ru-forum.

As said on travianwiki.com, Nicolas Cirigliano ElCiri also obtained this formula, but it doen't said, when he did it. Nevertheless, since two persons obtained the same formula independently, so it counts in favor of last formula.**Note**: Base upkeep is always used. Neither artifacts, nor WW village, nor Horse drinking trough could affect upgrades.

As always, consider some example.

20,000 clubswingers, fully upgraded in blacksmith (lvl20) attacks 12,000 non-improved praetorians.

According to formula (7)

improved_value = 40 + (40 + 300 · 1 / 7) · (1.007^20 – 1) ≈ 40 + (40 + 42.8571) · 0.149713 = 52.4048

offense points will be: 20,000 · 52.4048 = 1,048,096

defense points will be: 12,000 · 65 = 780,000

total amount of troops is 32,000, so according to (5) immensity of battle will be

K = 2 · (1.8592 – 32,000^0.015) = 2 · (1.8592 – 1.1684) = 2 · 0.6908 = 1.3816

losses will be 100% · (780,000 / 1,048,096) ^ 1.3816 = 66.486% or 13297 clubswingers.

so then you will absolutely get pleasant knowledge.