OW describes the "Zeroing Effect" for Begginers

[OmikronWarrior]

Hinjo: We are willing to reduce your [Belkar's] prison sentence by 5 years if you contribute to the defense of Azure City by helping defeat the invaders.

Belkar: Well I'm no legal expert, but I'm pretty sure I haven't actually been convicted of anything.

Roy: Wait! He pleads guilty.

Belkar: What? No I don't.

Roy: Yes, you do.

Belkar: No, I don't.

Roy: Yes, you do! Look, I'm the one who talked Hinjo into reducing the charges to manslaughter... Now the minimum penalty for manslaughter in Azure City is four years in prison. Now do you see where I'm going with this?

Belkaer: … No.

Roy: *sigh* You plead guilty, get sentenced to four years, then defend the city... and your sentence gets reduced by five years.

Belkar: How do the hell do I server -1 years in prison?

Roy: You don't, you idiot, you get set free!

Belkar: Oh, I get it. Ok, then, I plead guilt.

Hinjo: Very well... for the crime of voluntary manslaughter, I sentence you to spend a term in prison equal to six years.

Roy: Ah, crap.

-Rich Burlew, Order of the Sick #420

Roy probably should not have discussed cheating the legal system in front of Hinjo, but it is Belkar we are interested in. He isn't the sharpest tool in the shed when it comes to adding and subtracting. Unfortunately, a few to many of my fellow Pretenders do not understand how negative numbers work in the Dominions 3 world. For example, let us look at the spell Relief. On paper, it seems underwhelming. Though it affects every friendly unit on the battlefield, it only restores a scant 1 fatigue per round. Yet, experienced players swear by this spell and its ability to save armies in the long battles. Why the discrepancy? It is due to something I call the “Zeroing Effect.”

Simply put, the spell doesn't restore 1 fatigue, but like most Dominions mechanics restores 1+DRN-DRN. This is crucial. A novice in statistics might say, “so what? This may introduce some variance, but don't the two random rolls cancel each other out in the long run and thus the spell still averages 1?” No! If the negative random number is greater, does the unit loose fatigue? It does not. Say the spell does -9 fatigue reduction. This becomes zero. Meanwhile, the equally likely 10 fatigue reduction actually does 10 fatigue reduction and thus the two do not “cancel” each other out to leave the average at 1. The actual average will be higher.

What does this mean for dominions? It means spell that have a low effect on paper actually have a much greater effect in practice. Freezing Mists, Bone Grinding, etc. become much more worthwhile to consider casting. Though the math is very hard to calculate, I tentatively will say Relief averages at least 5 points of fatigue reduction per round. Thats almost enough to ignore the fatigue reduction from Heat from Hell, provided the battle does not last too long.

Obviously, the further the base number is from zero the less influence the “zeroing effect” has. Therefore, the ideal spell to take advantage of this phenomenon has: a) an unassumingly low “effect.” b) affects multiple targets, the more, the better. c) has no other check such as protection (meaning Armor Negating) or Magic Resistance. Now, with this mind, hit the grimoire and start rethinking magic and randomness in the Dominions 3.