# Little probability/stat question

Sorry if this is a dumb question. I’m playing a game, and am curious about the comparison between two evasion abilities; ordinarily attacks are resolved using the following formula

[(Base Accuracy) * (1 - C-EV) * (1 - S-EV) * (1 - A-EV) * (1 - W-EV)] = Accuracy

where C-EV is the targets’ base chance to dodge, S-EV represents shield evasion (if any), A-EV is accessory evasion (capes and mantles), W-EV is chance to block with a weapon (if Weapon Guard ability is set). Notice that this results in a single final value (it’s just one chance to hit roll). For the sake of argument, let’s assume 100% base accuracy (it’s usually lower, but can be all over the place, so I figure use a worst case scenario).

Most weapons have 10%-20% evasion (so 1-0.1 or 0.2), but the characters I’m considering Weapon Guard for would have gear with 30% or better. Heck, one of the more common late-game weapons has 60% weapon evade, for one example.

However, there is another ability, Blade Grasp, which is a separate roll based on a (more or less fixed) stat for the character, ignoring base accuracy and all the rest. Most characters who might use it have 65%-75% chance to block with it.

Obviously compared to the average weapon’s evasion Blade Grasp is better, but I’m curious if there’s a point where Weapon Guard might have a greater impact?

PS. I’m putting this in GQ because the question is about mathematics, not for discussion of the game, but I’m not entirely sure it shouldn’t go in the sports and games forum

C-EV usually ranges pretty widely, from 5%-30% (for here use 20%), A-EV will most likely be 0 here, but could be 30%-40%. S-EV is gonna be around 40% and up.

…stupid edit window, heh.

I think an example may help to clarify. Let’s say we have 15% block rate on everything except W. We get:
(1 x 0.85 x 0.85 x 0.85) x (1-W) = 0.614125 x (1-W)
This means that at best (i.e. W=0) the opponant has a 61.5% chance of hitting you. This decreases to a 0% chance of hitting you if the W is 1. The beauty of this is that it is a linear relationship so you know that every 0.1 increase in W results in a 0.0614125 decrease in your opponants ability to hit you. To find out what W you need to match a certain weapons grasp (G) set up the equation
0.614125 x (1-W) = 1-G and solve for G. If G is 70% it would look like
0.614125 x (1-W) = 0.3
1-W = 0.49 (approximately)
-W = -0.51
W = 0.51

Plug in the values you’re going to use and repeat the procedure.

Ah, cool, thanks. That’ll be handy for tooling around with comparing different combinations of all the variables.

Is there anything else other than properties of the weapon itself which would increase the value of W-EV? For instance, is there some non-weapon item which, say, increases the value of W-EV by 30%? If the answer to that is “no”, then Blade Grasp is always better.

The way to see this is to realize that the formula the game uses has exactly the same effect as checking each of those miss chances separately. If the opponent makes his base chance to hit, then check to see whether he gets past the character’s C-EV chance. If he gets past that, then see if he gets past the character’s S-EV, and so on. Introducing the Blade Grasp ability just adds one more layer to that, that works in the same way as any of the other layers of protection.

If Blade Grasp is used is the other roll ignored, or are both rolls done and they both have to be beaten for a hit?

It sounded like that the player must make a choice, blade grasp or evasion (but not both - our old friend the exclusive OR). Let’s say that blade grasp allows a 30% chance of being hit, I think the OP’s question was basically: knowing three of the four variables in evasion, can I calculate the value of the fourth variable to make it better to evade than grasp?

That there will be an answer is yes since if any of the variables are 1 then evasion always works. The real life answer depends on any limits the game places on those variables.

Blade Grasp is a second calculation in addition to evade, which always occurs*, but Blade Grasp is either/or with Weapon Guard. So if you have Blade Grasp W-EV (the last 1-# part of evasion’s formula) is always 0, regardless of the equipped weapon (that is, your character can’t block with a weapon unless they’re using Weapon Guard).

This is why I’m assuming you’d need to grind evasion up ridiculously high to make Weapon Guard better than Blade Grasp, because it’s a second check with a by default low chance of working. But I’m not good with Stat, so I wanted to check if my thinking was correct, since some of the end-game gear on the right class lets you bring that accuracy % down to very low levels.

100*.8*.6*.6*.4=11.52
vs
100*.8*.6*.6=28.8 for hit vs miss, & say .3 chance to get past grasp

*Okay, not actually “always,” but for any physical attack that can be evaded and/or grasped.

PS. There’s no way to increase W-EV beyond a weapon’s innate value

Sorry for the double post, the best S-Ev is .5, the best W-Ev is .6, and the best A-Ev is .4

C-Ev doesn’t get higher than .4 either, but the characters I’m looking at would be anywhere from 0.15 to 0.25

A-Ev pretty much only has a value if a character has a mantle for their accessory. I generally wouldn’t except to try and max out evasion, as there are other accessories that I usually find more useful (ie, if I go with Blade Grasp I’d skip the mantle since it doesn’t improve BG’s chances and evade isn’t as important if you have it).

OK, that’s what I thought. That means that you always get the miss chance from the other forms of evasion, and then you additionally get either W-EV or Blade Grasp. The other forms of evasion have exactly the same effect in either case, so it doesn’t matter for our decision what they are. All that matters is whether Blade Grasp by itself is better than W-EV by itself, and from what you say, it usually is.

Thanks for help guys.