1.a. Offense and defense points
In Travian every unit has some levels of attack and defense. His offense points are his attack skill. The more offense points () unit has, there more enemies he will kill, when used in attack. The same is true for defense, except there're two types of it: defense against infantry () and defense against cavalry ().
E.g. praetorians (65/35 def) are better against infantry, just as spearmen (35/60 def) are better against cavalry.
In combat only offense points of attacker, and defense points of defenders are taken into account. Attack with praetorians isn't effective despite their high defense value. Similarly clubswingers are worse units in defense. So use your troops wisely, only for purposes, they're well-suited. Otherwise you'll loose easily!
Despite of knowledge about units' stats, you cannot easily predict combat result, because combat system is neither simple nor trivial.
Players with Travian plus turned on could find rather good warsim in their rally point. This extended version allows them taking into account almost all values affecting battle result. Players w/o plus have limited version of combat simulator, which doesn't allow to take into account some factors like wall level, moralebnonus, leading to inaccurate results. Since new Т3.6 version all players have the same full functionality, though.
There're several free combat simulators online. One of the most famous free warsim is mine one. It has almost equal set of features as full in-game warsim and even more: convenient hero using, traps in Gallic village, battles with Natars, some artifacts and two targets for catapults.
Also my warsim have one useful feature: it "remembers in URL" which units you have input. If you copy URL from address bar and send it to somebody, after opening this URL, he or she will go to the simulator's page, where all troops are already set to the same values as you just done. All examples in this article will be accompanied by "try it" link, so you'll be able to check example by yourself.
1.b. Raid / normal attack
Here I describe common combat w/o any boni like walls, upgrades, etc. As mentioned, we only take offense points from attacking army and defense points from defender's army.
First of all, count total offense and defense points. Total points are just amount of troops multiplied by corresponding unit stat.
For instance, we attack with 100 imperians and 50 legionnaires. Their attack values are 70 and 40 respectively, so total offense points will be:
100 · 70 + 50 · 40 = 9000 (1)
Let defender has 150 phalanx. As all attacking troops in our example are infantry we will use only defense against infantry, 40. In this case total defense points are:
150 · 40 = 6000 (2)
Consider firstly normal attack, combat is going on till one side will be completely destroyed. We determine looser by comparing total offense and defense points. In our example 9000 (1) is more than 6000 (2), so defender will loose.
Winner's casualties are determined by next formula:
100% · (looser_points / winner_points)^1.5 (3)
since defender looses this battle, looser_points = 6000 and winner_points = 9000.
100% · (6000 / 9000)^1.5 ≈ 100% · 0.5443 = 54.43%
54.43% of attackers will die. This fraction is the same for all different types of troops. Since attacker had 100 imperians and 50 legionnaires, he/she lost 100 · 0.5443 = 54.43 (54 rounded) imperians and 0.5443 · 50 = 27.21 (27 rounded) legionnaires.
Amounts are rounded for each type of troops separately.
For raid formula changes a bit, losses will be:
100% · x / (100% + x)
where x is determined by formula mentioned above (3).
This is losses of winner. Losses of another side will be (100% – winner's losses).
Consider another example: 100 imperians raiding 100 praetorians. Offense points (7000) are greater than defense ones (6500), so attacker wins again.
x = 100% · (6500 / 7000)^1.5 ≈ 89.479%
100% · 89.479% / 189.479% ≈ 47.22%
So 47.22% from 100 or just 47 imperians will die. Defender will loose 100% – 47.22% = 52.78% of his/her army, i.e. 53 praetorians.
try it and don't forget to choose "raid"
When greater armies taking part in combat, disposition changes a bit, bringing winner more casualties. Instead common formula (3), another one is used:
100% · (looser_points / winner_points)^K (4)
where K depends on how much soldiers were involved in combat. Really, large, immense battles should differ from small battles between hundreds of soldiers.
К is determined by next formula:
2 · (1.8592 – N^0.015) (5)
where N is total amount of units, taking part in battle (amount, and not their total upkeep).
1.2578 ≤ К ≤ 1.5: When total amount of units is one thousand or less K = 1.5, and if total amount is larger than billion (not exact) K = 1.2578.
E.g., 2000 haeduans attacks 1400 phalanx. N = 2000 + 1400 = 3400
К = 2 · (1.8592 – 3400^0.015) = 2 · (1.8592 – 1.1297) = 2 · 0.7295 = 1.459
So formula for losses will look like (attacker wins obviously): 100% · (def_points / off_points)^1.459
2000 haeduans have 2000·140 = 280,000 offense points
1400 phalanx have 1400·50 = 70,000 offense points, since attackers are cavalry troops, we use phalanx' defense against cavalry.
100% · (70,000 / 280,000)^1.459 = 100% · 0.25^1.459 ≈ 13.23%
2000 · 13.23% ≈ 265, i.e. 265 haeduans die.
1.c. Simple combat with mixed infantry/cavalry
How we get defense points if attacker has both infantry and cavalry troops? Offense points are calculated the same way, but determining of defense points become non-trivial. In such case they are calculated proportional to infantry/cavalry offense ratio.
For instance, 100 theutates thunders and 50 swordsmen are attacking 100 praetorians.
Offense points are equal: 100 · 90 + 50 · 65 = 9000 + 3250 = 12,250
From more then twelve thousand offense points, cavalry part is 9000, and remainder is infantry part. We need to get proportion, so we divide:
9000 / 12,250 ≈ 0.7346
and do the same for infantry:
3250 / 12250 ≈ 0.2654
Therefore, 73.46% of offense points are cavalry offense points, and 26.54% — infantry ones (sum should be equal to 100%, if we are not mistaken).
Then we "apply" this infantry/cavalry proportion to defender's troops. Praetorian has 65 def.points against infantry and 35 def against cavalry, i.e. total army's defense is:
100 · 65 = 6500 (infantry)
100 · 35 = 3500 (cavalry)
To get real defense points we need to combine these points by proportion:
0.7346 · 3500 + 0.2654 · 6500 = 2571.1 + 1725.1 ≈ 4296
Therefore, praetorians will have 4296 defense points against such attacking army.
Now we got offense and defense points so could apply formulas we already know: 12250 > 4296, meaning attacker will win and defender will loose all his/her troops:
100% · (4296 / 12250)^1.5 ≈ 20.77%
Attacker will loose 20.77% of all of his/her own troops, which works out 100 · 0.2077 = 21 theutates thunders and 50 · 0.2077 = 10 swordsmen.
my site: travian.kirilloid.ru