Monster Hunter World

Calculating Average Damage Per Hit

MonsterHunterWorld8 - Calculating Average Damage Per Hit
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Hello all! I've seen a few posts discussing how monster hunter calculates damage and I wanted to share my attempt at calculating an average damage per hit for the Switch Axe. I was inspired to do this after seeing a lot of people saying that elemental damage isn't worth it and slower weapons should just build raw. But instead of just taking their word for it, I wanted to see if I could prove/disprove it. So here we go!

First off, this post was extremely helpful for understanding damage calculation and I won't go over anything that was already covered there.

If we're going to calculate average damage per hit, we obviously need a damage formula. The aforementioned post covers it, but I'll rewrite it here for convenience sake.

physical damage = (true raw) * (sharpness modifier) * (crit chance) * (motion value / 100) * (monster armor / 100)

elemental damage = (elemental attack / 10) * (sharpness modifier) * (monster armor / 100)

total damage = (physical damage) * (elemental damage) * (quest / rage modifiers)

I'll go through a quick example. Let's say you have the following weapon:

Switch AxeDying Light
Physical Damage700
Elemental Damage150
Affinity0%
SharpnessBlue
PhialPower

And you wanted to calculate the average damage for it. If we plug in the numbers to the formula above, we get this:

physical damage = (700/3.5) * (1.2) * (1+0.25*/100) * (motion value / 100) * (monster armor / 100)

elemental damage = (150 / 10) * (1.0625) * (monster armor / 100)

And as you can see, we're missing 2 numbers: Motion Value and Monster Armor. Motion Values are different per weapon, per attack, so that's not going to be an easy thing to average. And while Monster Armor would be pretty easy to average, a good monster hunter is going to hit weak spots more often than resistant spots, so we can't just average numbers and call it a day either. Here are my proposed solutions for these two problems.


Averaging Motion Values

I'll try and talk about solving this problem in the general case, but there's likely to be weapon specific things that pop up and since I've only really played Switch Axe.

Quick Recap: motion values are a dampening fraction that is applied to every attack of every weapon. The idea behind it is that the slower/stronger the attack, the closer this fraction is to 1. The weaker the attack, the closer to 0. For the Switch Axe, Overhead Slash – a slow moving attack at the end of a combo – has a motion value of 45. However, Forward Slash – a quick, lunging attack that starts combos – has a motion value of 19. Motion values are what make Overhead Slash hit harder than Forward Slash. And every weapon has different motion values for different attacks.

For starters, I tried just taking the motion value for every move and finding the average. And this works… alright. It doesn't take into account the frequency the move is used and I had to be sure that I had motion values for every hit of a multi hit move. You can't just represent a multi hit move like Morph Sweep (which is a 3 hit move with motion values 20, 70, and 30) as 1 move with a motion value of 150. If we represent it as one attack, we won't take into account the 2 other times elemental damage is applied during the multi hit move. The bigger problem with this method of course is that it overvalues certain attacks and undervalues others. There's no way I'm going to use an attack like Zero Sum Discharge as often as I use Forward Slash. But there's also no reliable way to weight the moves besides either recording your hunts, counting the number of times you use certain moves, and then averaging those numbers, or just playing a lot and getting a rough but general feel for how often you use one move over another.

I tried weighting the Switch Axe attacks and ended up getting an average MV of 26.45. Without weighting, I got an average MV of 25.62. So was the weighting worth it? Eh, maybe for peace of mind. Maybe I'm just terrible at weighting things. Either way, the 1st number isn't a bad option (and neither are guaranteed to be "correct").


Averaging Monster Armor

This next part is a little simpler, and once again I'll give a recap. Each monster part has a "weakness" value, where the higher the number, the weaker the part. In this way, it's similar to the Motion Values. To use an example, here is the hit chart I found for Rathalos (Source is a MHW app for my phone).

RathalosSever Defense3 Star Elemental Defense
Head6030
Neck3520
Body2520
Back2520
Wings2025
Legs3515
Tail4520

We see that the head and the tail are weakest to sever damage, whereas the head and wings are the weakest to elemental (dragon) damage.

This is a smaller version of the table that only contains sever defense and 3 star elemental defense, since that's all we're going to use for our calculations. First off, we're going to assume that we're always using the optimal element on a monster. We aren't interested in knowing which weapon is the best for every monster in the game (obviously that'd be a raw weapon). We want to know how much better (if at all) an elemental weapon is than a raw weapon. If we just assume we're equally as likely to hit any and all monster parts, we get a Sever Monster Armor = 35 and an Elemental Monster Armor = 21.43.

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At first I thought this was good enough and that all I'd need to do was get more hit data for more monsters and start averaging them together. But I quickly realized that wasn't going to work. For starters, some monsters have waaaaay more parts than Rathalos. If I just averaged them together, then monsters with more parts would have a bigger impact on the final number than monsters like Rathalos. That was pretty easy to fix by just averaging up the monsters individually and then averaging all of the monsters together. But then I realized I was undervaluing raw damage with these numbers. A good hunter will adjust to get maximum damage, not just wail on any part indiscriminately. So I needed to separate parts into weak parts and strong parts, and weight things accordingly.

To form some sort of rationale that could be explained and repeated when it came to defenses, I looked to the orange numbers. If you're getting orange numbers, then that should mean you're hitting weak parts, right? Well according to this post, that's not true. Heck. So instead I looked toward weakness exploit, one of the most coveted skills in MHW. Weakness exploit triggers when you're hitting a monster part with a defense >=45, so for Rathalos, that's his head and his tail. Since the Iceborne patch, weakness exploit was changed so that you only get 10% affinity per level unless you're taking advantage of the clutch claw. So if you're hitting weak parts and strong parts at a 50/50 clip, you're getting an average affinity increase of 5% (which is the same as 1 level of Critical Eye). Since Weakness Exploit is considered much better than Critical Eye, and easy fractions are easy to deal with, I decided my calculations would hit weak spots at a 75/25 ratio. With these new numbers in place, we get an average sever defense of 46.375 and an average elemental defense of 23.75. If we do that with a few more monsters, we should get a nice and consistent number.


Results

So there you have it! We now have average estimations for all the values we previously didn't have. How do some of the top high rank switch axes stand up?

WeaponDamage
Lightning Chopper III33.23
Axe of Demons33.9
Dying Light35.66
Legia Frostreaver35.73
Hazak Demios II35.93
Motor Chopper II36.49
Kirin Thunderpeal36.53
Jyura Drought III37.24
Terror Tyrannos37.41
Gnashing Flammenbil38.64

Finally, these are our final damage numbers. Now, there are a few things to keep in mind. I used the weighted Motion Value number for all these calculations. I also only used the Rathalos defenses for these calculations. I plan to update it in the future, but I wanted to see if I could get any feedback before committing more time to this. Finally, Switch Axes have a phial system that I will explain below that plays a pretty important role in these numbers. But right out the box, elemental weapons are just barely outperforming the Axe of Demons. And once you put these weapons into a build, it could be that the Axe of Demons has better final build damage than something like Dying Light's final build damage, since I didn't factor in any skills to improve damage.

So what does this mean? Well for one, it means it's VERY difficult to tell which weapon is better than another in MHW. It also means pretty much any weapon is viable. And if you want to just not worry about elements, the Axe of Demons is still a really good choice. However, it does suggest that it may be possible for elemental weapons to outperform raw weapons given the right circumstances, even on something relatively slow moving like the Switch Axe.

If you all have any questions or comments, or want more details on how I calculated things, feel free to share! I love min/maxing and figuring out what is statistically the best strategy in a game and am open to trying new methods in order to try and get more accurate numbers. I'd also like to expand this to include builds, but some skills are hard to determine "average" cases for, so any recommendations would be appreciated. Happy hunting!


Bonus: Phial Types and Other Switch Axe Specifics

Ok so something I didn't cover above that's pretty important for damage, but only important for Switch Axes is phial types. There are 2 types we're concerned with: Power and Power Element. Power phials boost sword damage by 20%, while Power Element phials boost element damage in sword mode by 45% (according to this post). To factor in the effects of the Power phial. I increased the motion values of every sword move by 20%. I then split the sword motion values from the axe motion values and found their averages separately (I did this originally, I just didn't think the detail was worth mentioning earlier). I assumed we'd be in sword mode 50% of the time and axe mode 50% of the time, so I adjusted the motion values accordingly and got a power phial motion value.

For the power element phial, I simply increased the elemental damage by 22.5%. Since we're in sword mode 1/2 the time, we only get the 45% increase 1/2 the time. And since elemental damage is applied per hit, we don't have to do anything funky with motion values.

I also weighted things really specifically with the amped vs unamped states of sword mode. I used a 50/50 split for amped vs unamped, but as you can see, the weighting isn't that important.

TLDR: Did some MHW math. Elemental Switch Axes are better than the Axe of Demons when you don't consider builds. No clue what happens when you do.

Source: Original link


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