Hey guys, Whitesushi here. Within just several hours time of my previous post on perk speculations, Epic Games released more information regarding the system, addressing some game design changes and even putting out a video for us to extract more information out of. As such, I feel that there's enough information lying around to do a post on **the best combination of perks** going into the next patch.

Before we jump in, I would like to throw in a short disclaimer to say that the "best combination" in the case of this post is based off **damage per shot** as well as **damage per second**. If you are someone who values the "feel" of the weapon (such as being able to get more shots off etc), then your "best" is going to be very different from my best

##### Summary

This section is just for some quick points for the casual readers that just want to know the results

Crit Chance & Crit Damage is still going to be the way to go for most weapons with low innate headshot multipliers

For weapons with high innate headshot multipliers, Damage & Headshot is a good setup

Crit setup remains especially strong when you run Shotgun/ Sniper/ Pistol since your hero/ support can buff crit chance. I would think that even for Snipers (high innate HS), a T.E.D.D shot support (20% crit chance) would make the crit setup stronger

Magazine is almost always better than reload when it comes to damage per second

##### Possible Combinations of Perks

In order to analyze what the best combination of perks are, we can either

- Manually enter all the combinations of perks 1 by 1 into my calculator
- Find all possible combinations, calculate their DMG/S and DPS, find the highest

Clearly, the first option is **tedious** and some were starting to question the capabilities of me running numbers in google spreadsheet, even suggesting the use of alternatives such as a software to 'brute force' all the values. Fortunately, that will not be necessary. First we want to collect information on the possible perks available in each slot. Thanks to u/Alerie_Eve who went through the dev update video and compiled a list here, we don't have to do that ourselves. **We setup a table in google spreadsheets that look like this**. It is worth noting that

- I excluded weapon stability and durability since there's no point calculating them
- I excluded the 6th slot since its %snare which doesn't do damage
- Every other perk had their tier 5 values extrapolated and assumed

Once that is done, we use a combination of google spreadsheet's functionality such as

- Split
- Rept
- Concatenate

which you honestly don't have to know but what they do is generate a list for me like this…. and yes as you might have already guessed it, the extreme right column shows **all the possible combinations of those perks in the table** with some cut off at the bottom (you can see them if you scroll but just not in my image). I then make use of some other functions such as

- Regex
- Bunch of 'if' statements

to break the combinations up and have them occupy the corresponding stat I want them to as seen here

##### The Formulae

Once all that is done, we move on to setup the weapon itself, the hero we use as well as the support. This section was pretty easy as it was just copy-paste work from my original calculator with some tweaks to the column and rows they reference from. The result was something that looks like this.

Note that I am using the perk % section to show the reference stats of the hero since perks aren't applicable here (we are basing them off the combinations we extracted earlier)

Finally, we move onto the most important part which is the formula. From the dev posts, we know that

- Crit chance now suffers from diminishing returns
- Headshot perk is now multiplicative

Looking at the new headshot formula, it could either work like

`Headshot Damage = Base Damage * ( 1 + Base HS Multiplier * ( 1 + Headshot Perk ) ) `

or like this which looks something like the formula below

`Headshot Damage = Base Damage * ( 1 + Base HS Multiplier ) * ( 1 + Headshot Perk ) `

Honestly, I don't know which it is going to be so I will just do 2 sets of calculations, 1 for each and show you guys the difference. As for the critical cha… rating formula, we know that the developers introduced **diminishing returns**. Based on the phrasing in the post specifically in

your first 25 points of Crit Rating will grant 25% Crit Chance

It seems to suggest that crit chance still exists (weapon base crit chance, hero perks) and does not suffer from diminishing returns which crit rating does. In that case, the **new crit chance formula** would simply be

`New Crit Chance = Weapon Crit Chance + Hero Crit Chance + Crit Rating after diminishing returns `

Unfortunately, while the crit chance after diminishing returns would probably be

- 25% = 25% (no change as stated)
- 50% = 37.5% (Given to us. This is taking 25 * 1.5)
- 75% = 46.875% (Extrapolated, taking 25 * 1.5 * 1.25, a common way diminishing returns is implemented in games)

I don't have an accurate way to deduce the diminishing returns **precisely**. However, we calculate that at 50 crit rating, we only get 75% of that as crit chance (37.5) and at 75 crit rating, we only get 62.5% of that as crit chance (46.875). We plot the values into a **polynomial graph** and derive the equation for finding the "percentage" to be

`Percentage = 1.38 - 0.0175 * Crit Rating + 1E-04 * Crit Rating ^ 2 `

Once we get the percentage, the crit chance would simply be **crit rating * percentage**. (I know this is some really rough and inaccurate calculations but it's the best I can come up with at the moment :V)

**Last but not least**, I tweaked my damage/shot formula to include the 5% base crit chance buff (so I don't have to manually increase everything on my "Ranged" table)

##### The Calculations

Alright, the moment most of you are probably waiting for. Remember the 2 headshot formulae earlier? We will start off with the one on top, assuming that headshot perks are only multiplicative towards the weapon's innate headshot perk (weaker assumption). Without further ado, the best perk combination is…….

Weapon | Hero | Support | Headshot Accuracy | Perk Setup | Image |
---|---|---|---|---|---|

Siegebreaker | – | – | 100% | Crit Damage / Magazine / Physical (Element) / Crit Rating / Damage to Mist Monsters | image |

Siegebreaker | – | – | 0% | Crit Damage / Magazine / Physical (Element) / Crit Rating / Damage to Mist Monsters | |

Siegebreaker | Urban Assault | Master Grenadier | 0% | Crit Damage / Magazine / Physical (Element) / Crit Rating / Damage to Mist Monsters | |

Tigerjaw | – | – | 100% | Crit Damage / Magazine / Physical (Element) / Crit Rating / Damage to Mist Monsters | |

One Shot | – | – | 100% | Damage / Magazine / Physical (Element) / Headshot / Damage to Mist Monsters | image |

One Shot | Urban Assault | T.E.D.D Shot | 100% | Crit Damage / Magazine / Physical (Element) / Crit Rating / Damage to Mist Monsters | image |

One Shot | – | – | 0% | Crit Damage / Magazine / Physical (Element) / Crit Rating / Damage to Mist Monsters | image |

Judge | – | – | 100% | Crit Damage / Magazine / Physical (Element) / Crit Rating / Damage to Mist Monsters | image |

So here's what we can conclude just from these results

- Magazine is absolutely better than reload when it comes to damage per second
- Crit chance combined with crit damage is going to be the best setup most of the time
- You need like 150% innate headshot multiplier before headshot + damage overtakes crit

Now let's move onto our other headshot formula where we assume it behaves similarly to Urban Assault Headhunter as a final multiplier. The table would instead look something like this

Weapon | Hero | Support | Headshot Accuracy | Perk Setup | Image |
---|---|---|---|---|---|

Siegebreaker | – | – | 100% | Damage / Magazine / Physical (Element) / Headshot / Damage to Mist Monsters | image |

Siegebreaker | – | – | 81% | Crit Rating / Magazine / Physical (Element) / Crit Damage / Damage to Mist Monsters | image |

Tigerjaw | Raider | – | 100% | Crit Rating / Magazine / Physical (Element) / Headshot / Damage to Mist Monsters | image |

Tigerjaw | Raider | Raider | 100% | Crit Rating / Magazine / Physical (Element) / Crit Damage / Damage to Mist Monsters | image |

One Shot | Urban Assault | T.E.D.D Shot | 100% | Crit Damage / Magazine / Physical (Element) / Headshot / Damage to Mist Monsters | image |

What we can conclude from this table is that

- Clearly, headshot is a lot stronger in this case
- If we go by this formula, any hero that buffs %damage will make headshot similarly strong (since they scale off each other directly)
- As demonstrated in our Siegebreaker example, 50% innate headshot would already put headshot + damage ahead of crit chance + crit damage
- The 81% i included for my second example is the magic number at which crit setup overtakes the headshot setup
- The 5th row offers a 'special' situation where as you can see, the crit perks on the support coupled with high innate headshot of the weapon makes it such that the ideal setup uses crit damage with headshot (a rare combination)

##### Conclusion

If you haven't already noticed, the combinations fluctuate easily as we change up our hero loadout. This is reflective of good game design and a sign that the system is fairly balanced. As such, it is really hard for me to consider all possible loadouts in this post so I just leave you guys with some possible ones. However, you can generally tell that **crit chance + crit damage** is often the strongest while weapons with higher innate headshot multiplier benefits better off **damage + headshot**.

All in all, a lot of the formulae are based off assumptions and might be different from how they perform when the patch really hits. That said, i wanted to get this post out since you guys have been requesting for it and my exams are coming up next week (probably will not be around for at least 2 weeks after the patch hits). As always, thanks for reading through my lengthy posts. Happy perk hunting!

**TL;DR Crit Chance/ Magazine/ Crit Damage for low innate headshot, Damage/ Magazine/ Headshot for high innate headshot (150%++ on lenient formula, 100%++ on generous formula… snipers)**

©Post "Speculative Math post on best perks going into 4.2" for game Fortnite.

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