Battle Engine Model

From FaitH

The battle engine combines your # of units, attack, defence, trample, and heal with your opponent's and comes up with a battle report. The attack and defense I consider "physical" properties and the heal and trample to be "magical" properties. These properties act totally independently of each other, as you shall see.

The input to the war engine is (units), (attack), (defense), (heal), (trample) of each army, including any and all bonusses. The bonusses are really hard to figure out, and are what makes the Battle Engine seem so complicated.

Contents 1 Phase 1: Total Wounded 2 Phase 2: Wounded Distribution 3 Phase 3: Fraction Killed 4 Bonusses, Arrangement under Generals, etc 5 Hints and Tips (Non-Technical)

Phase 1: Total Wounded

The first thing that the war engine does is decide how many total units get wounded. The total number of units wounded in a battle is (closely approximated by)...

Now, the ferocity modifier is a constant (averaging about 0.06), which is be affected by attack strategy and the spell Mercy of Gomi and perhaps has some randomness to it, but it doesn't matter... some external thing supplies it to the war engine for each battle. In this case, "total" means the sum of the attacker's and defender's (units/attack/defense).

This formula for wounding is very elegant because everything scales "nicely" - If you get an overall 15% bonus to attack, the number of wounded increases by 15%; if both armies double in size, the total number of wounded doubles. Thus only your army composition ratios matter... always think ratios, not numbers. Never say "I have 300 more VL than KoN"... instead say "I have 60% more VL than KoN.

Phase 2: Wounded Distribution

The next thing the war engine does is decide how many of those wounded belong to me, and how many belong to you. To do this, it compares my physical strength to your physical strength. The formula for physical strength is (physical strength) = (attack)*(defense). Since it is your physical strength that damages my troops,

Again, "total" means the sum of yours and mine.

Phase 3: Fraction Killed

Next, the war engine needs to figure out what fraction of my wounded bet killed. To do this, it needs to define my "magical strength." Now, since my trample shouldn't affect how many of my units dies, my magical strength is just my healing, and yours is your trample. And to me, the natural formula to use is the same as last time, with fraction of wounded that die being (your magic strength)/(total magic strength) {note that this isn't symmetric, because when it's calculated for your deaths, it uses my trample and your heal}

Unfortunately, that doesn't work so well, because it is possible for someone to have zero magic strength, and because having 100% of your wounded dying would just be too much. So, some fudge factors are thrown in. They don't alter things tremendously; just make startup easier and contain the fraction of wounded that get killed. The first one is to add 50 to each of our magic strengths... it's a base magical power that each army has. So, my magical power is actually (My Magic Strength) = 50 (My Heal) and yours is (Your Magic Strength) = 50 (Your Trample). {the 50 could be a 25 or 100 or whatever - I don't know the exact number; I just know that it's there} The second fudge factor makes the minimum fraction killed 1/5 and the max fraction killed 4/5, making the total formula:

Again, total means sum of yours and mine.

Bonusses, Arrangement under Generals, etc

• all bonusses are additive. Eg. 10% attack bonus from DM, 7% attack bonus from RE, and 6% bonus from WF gives a 23% bonus to your attack score

• There is a bonus associated to being balanced (in terms of similar numbers of LR and CR units). It is a HUGE bonus, so make sure you are always balanced

• There are fairly significant bonusses associated to how you arrange your units on generals. Look at the suggestion on the Guide for your church... it is usually a pretty good arrangement.

Hints and Tips (Non-Technical)

Here are some basic lessons to learn from the above post, so read this even if you didn't understand that.

• Since the war engine only cares about your total numbers (unit count, attack, defense, heal, and trample), keeping units at home will only make your army WEAKER. That's right, those 500 explorers you are exploring with could add significantly to the strength of your army. Not as much as 500 imps, but still, 500 units, 1000 attack, and 500 defense is a lot better than nothing. So - always launch all your army; trust me, it's better than keeping some explorers at home

• Don't over-heal or over-trample. Having twice as much trample as your opponent has heal is enough to kill 60% of your enemy's units. Having a lot more than that is usually just a waste of your money. So for Omega, when you first go into trample mode, remember that all that trample won't help you, so please kill off some of your GG first.

• There is a really easy way to measure how strong your army is. If you ignore heal/trample effects (in most cases, they get taken care of pretty well naturally), you can estimate the total strength of your army by (units)*(attack)*(defense). If you can beat your enemies in this statistic, then unless your trample/heal are bad, you'll come out on top. Usually when I try to construct a good army, I try to maximize that number while keeping my heal and trample reasonable.

• Scaling - don't let anyone tell you "oh, you'll need a higher ratio of trampling at a higher PS" or "Oh, 1:1 dwarves:Loreii work well at low PS but not high." Everything aspect of your army scales perfectly with PS and the war engine. The same "ideal ratios" work at low PS as high PS. {Now, of course, the environment you are dealing with at high PS is different than at low PS, so you'll need to re-do your army a bit, but that's not because of high PS, it's because of different strategies being used by the people around you}