A Mathematical Breakdown Of Onigiri

[SupremeTentacle]

So, the title more or less explains what this thread is going to be about. I'm planning to dump a bunch of calculations, and thought it was more fitting here than in the guides section cause this is more of an analysis than a guide. I'm also going to be making this as simple as possible, and using as few statistical theories as possible in order to make it more understandable. Feel free to point out if I did something wrong somewhere.

So, let's get started.

*Note that this won't be a one post thing - I'll be dumping more math in this thread later on too. *

The topic that this specific post will cover is ornamentation rates. Everyone that plays this game, and I mean EVERYONE probably hates Kaguya. Why...? Well, the numbers will basically explain everything.

So let's start out with the classic favorite that everyone uses: Fated Contractor. Note that, for now, we're going to be ignoring the actual orna's success rate and focusing purely on the stats that you roll. We'll get into that a bit later.

So let's say you're gunning for 2 crit + 2 slice on your orna. How likely is this? How likely is it to get 26 slice and 16 crit?
First, it's important to note that the two slots of the ornament are independent of each other, but the stats you get within each ornament are not. Independence means that the likelihood of a specific event occurring does not affect the likelihood of another specific event occurring.

Fated can give you three possible base outcomes. You can obtain 1 stat, 2 stats or 3 stats. We will automatically assume that these all have an equal chance of occurring, and that anything with only 1 stat is junk.

If you roll 2 stats, then there is a 2/5 chance of the first stat being either crit or slice.
Given that you roll either crit or slice, the chance of the second slot providing you the other is 1/4.
This implies that you have a 1/20 chance of rolling both on the same ornament.

Now, what if you roll three stats? This is where it gets a bit complicated.
Assuming you don't get one of your desired stats on the first slot, you then have a 2/4 chance to roll them on the second. If you get one of these on the second slot, you then have a 1/3 chance to roll the last one on the third. We do not need to consider the scenario where you roll junk on the second slot because you would be unable to get two "good" stats since there is only one slot remaining.

Assuming you get one of your desired stats on the first slot, you then have a 1/4 chance to get another on the second slot. If you are successful, then we do not need to consider any further scenarios. However, if you are not successful, you will have to roll again, with a 1/3 chance to get the second stat on the third slot.

Summarizing this gives us the following:
3/20 chance to get what we want assuming that the first slot is desired
1/10 chance to get what we want assuming the first slot is junk.
Hence, we get up to a total of a 1/4 chance of getting a slice roll and a crit roll.

Now, let's consider all possible combinations that will get us double crit and double slice.
Both slots 3 stats
1st slot 3 stats, 2nd slot 2 stats
1st slot 2 stats, 2nd slot 3 stats
Both slots 2 stats

There is a one third chance for any number of stats to be obtained, so each of these possibilities has a 1 in 9 chance of happening.

Hence, we then have
1/9 * 1/4 * 1/4 = 1/144 of getting double crit double slice on a 2x 3 roll.
2 * (1/9 * 1/4 * 1/20) = 1/360 chance of getting double crit double slice on a magatama that has a slot with 2 stats and a slot with 3 stats
1/400 * 1/9 = 1/3600 chance of getting it when our magatama has 2 ornamentation slots with 2 stats each

Adding these together gives us the following
25/3600 + 10/3600 + 1/3600 = 36/3600.
Hence, there is a 1% chance of getting both double slice and double crit on a single magatama.... Assuming that we succeed both ornamentations.

Now, let's consider that the first slot has a 3/5 success rate, whereas the second has a 2/5 success rate.

In other words, players that do not wish to use success rate increasing items will have a 0.24% chance to get a magatama with both double crit and double slice. This means that one magatama out of every 417 will have double slice and double crit.

Using 30% success rate amulets can bring this up to a 0.63% chance. (0.9 * 0.7 * 0.01 * 100%)

Now, let's try to get perfect stats.....

The slice roll can range from 8 - 13, meaning that it has six possible outcomes.
Likewise, the crit stat has 4 possible outcomes because it can range from 5-8.

Like most of the above, these two things are also independent, which implies that there is a 1/6 * 1/4 = 1/24 chance to get perfect rolls.

Since we would want two of these, we would have a (1/24)^2 = 1/572 chance to roll these stats.

1/572 * 0.24% = 0.013824%.

Hence, we have a 0.0138% chance of getting a magatama "perfect" fated contractor stats.
In other words, only one out of every 7234 magatama would have those stats.

Now just imagine if you wanted sp on top of all that.... :>

The next post will most likely be about either heavenly shield, avenger on monsters or damage.

I may or may not be growing less and less interested in this game. Hence, it was thinking that it'd be nice to pass on a bit of information before I ultimately poof, assuming I do.

[Yvona]

*snaps her magatama on her knees and walks away*

[Tekato]

So it's pretty much impossible for anyone legit to have a full set of perfect ornamented lv 105 magatamas.

[Firon]

I'd imagine that the rate would be slightly better with magatama slot aid. Hoping not to see any broken slots on 105 magatama...

[MobonjiMK3]

Or it is about time that we should have ornamental slot remove item in shop.

Seriously.

[Firon]

Or it is about time that we should have ornamental slot remove item in shop.

Seriously.

Or even better, ornamentation slot extraction... not that this will ever happen.

[SupremeTentacle]

Part 2 - Build Analysis

This should be a quick one because it's really rather simple once you've understood the concept.

This is actually easily done with the calculator I made and dumped in another thread, but it wouldn't hurt to explain the math behind it.

So, before you build, there's a few things to keep in mind.
First, skills scale linearly with skill force and element. That is, the second skill force magatama will add the same amount of damage as the first (40% of your base, for example) as opposed to increasing it by another multiplicative 40%.

All skills are composed of elements, and the damage a skill outputs will be scaled based on the composition. That is, a skill with 70% fire composition and 30% impact composition will gain 7% base damage for every 10 fire stat.

Different damage factors scale in a multiplicative fashion with each other.

So what does this mean?

Well, I'll break this down with a single skill in order to elaborate.

Let's say a sword is using lunge step. They currently have 200 skill force, 100 slice and 170 critical force. We will let X denote the base damage that each tick of lunge step deals/

200 skill force increases this by 200%. That is, it you have X + 2X = 3X damage.
100 Slice increases it by another 100% However, this is not additive since slice and skill force are two different stat types.

Hence, the player would be doing 2(3X) = 6X damage.

Assuming that said player crits, the critical force is then also multiplied against the total damage so far. Note that the critical force should actually have a percentage sign after it, meaning that the player does 70% more damage.

(1.7)(6X) = 10.2X

Hence, a player with the above stats would be doing 10.2 times the amount of damage that they would otherwise be doing without those stats. (Note that the critical force is actually the base amount, so in reality, they are doing 6x damage.)

Now, let's try increment each of these stats by 30.

A player with 230% skill force would be doing 330% damage. This is 30% additional base damage.
However, the player was already at 300% damage because of skill force, meaning that the real damage increase is (330/300) * 100% = 10%.

On the other hand, if the player obtained 30 slice, they would be doing an additional 130% from slice, meaning that their slice damage total would jump from 200% to 230%.

Although all of these stats share a 1-1 scaling, building one is clearly more efficient than the other at this point in time. This is because of something that we call diminishing returns. Increasing the same stat will provide a lower percentage increase in the player's overall damage if they continue to stack nothing but that stat.

Now, consider critical force.

This is a 230/200 * 100% = 15% damage increase.

Finally, having 200 critical force would bump the player's critical damage from 170% to 200%, meaning that they would be doing 200/170 = 17.65% more damage. Do note that the relative effectiveness of this is decreased because of the condition that the player has to crit. Assuming a 50% crit rate, this would effectively be an 8.8% damage increase.

Now, if this was, let's say, thunder beast, and the element in question was lightning, the player would have suffered from a 30% penalty from increasing their element. In other words, they would only gain 0.7 * 15% = 10.5% damage. However, it would still be slightly better than the skill force increase, assuming that all they used were lightning based spells.

Rather than watching the meta, it is best for players to do a few simple calculations, and figure out exactly what type of ornamentation would provide them with the best possible damage upgrades.

Oh and - never forget that chakra is limited.

[Ryxa]

lol. You finally got that tired of people copying builds without understanding why?

[SupremeTentacle]

I believe that it would be more accurate to say I'm tired of seeing idiots ruin magatama, while thinking that they're smart/justified in what they're doing.