Calculating the Taipan-4 God Roll and How to Choose the Best Linear Fusion Rifle

A Deep Dive into Taipan-4FR and The Best Linear Fusion Rifles

In case you didn’t know… there is a craftable fusion rifle that is very easy to get through a quest from the Relic Table in The Enclave on Mars where you shape weapons. All you have to do is complete the Enigma quest that is a part of Witch Queen.

There is a lot of debate on which roll is the best, and if Taipan is a linear fusion rifle even worth using at all compared to other options in the game such as Stormchaser, Reed’s Regret, or Cataclysmic.

The problem with picking a god roll is that there are usually a lot of assumptions made as well as hand waving to get to a mostly muddy conclusion, and that’s because a lot of perks are based on random chance.

In this article, we will go through all of the math that will quantify this random chance and give a clearer picture of what is really better.

If you hate math feel free to scroll down to the Discussion section of the article to get a recommendation that’s based on both the math (that you skipped) and other aspects such as ease of use, ability to activate other buffs, and how hard it is to get the god roll through chance.

Dive into our Prismatic Hunter guides, Prismatic Warlock guides, and Prismatic Titan guides for the newly released expansion, The Final Shape.

Expected Yield for Dummies

Before we get into discussion of perks and detailed math, it would be best to quickly explain expected yield as that is a way to quantify random chance. Giving a range of outcomes is helpful, but doesn’t really explain the whole story.

For example, if you are playing a slot machine that you put a dollar into to play, your outcomes can range from losing that one dollar to winning a million dollars. That sounds great, right!?

Well not really, some might interpret that as there are so many possibilities between breaking even and winning a million dollars, that they are most likely to win something. Unfortunately not, and this is because their odds of losing are so high that it outweighs the other options such that your expected yield is losing a small amount of money.

A very simplified example is if you are flipping a coin, you get a point for heads, and zero points for tails. You have a 50% chance of each outcome. Your expected yield is 50% times the score of a heads plus 50% times the score of a tails so it would come out like this:

1×0.5 + 0×0.5 = 0.5

0.5 would be your expected yield, and if you flip the coin 4 times you’ll have an expected yield of 0.5 for every flip, multiply that by 4, and over 4 flips expect to have 2 points on average.

Having a background in this math is needed because we will be using expected yield to calculate which perks are best by accounting for the random chances of activating certain perks, most notably Clown Cartridge and the Veist Stinger origin perk.

The Contenders

Taipan has access to one top tier damage perk which is Firing Line, and gives a 20% damage bonus when standing next to teammates. This is non-negotiable, use this perk. The barrel option does not affect DPS, so I recommend picking whichever helps with Handling and Stability.

The Battery will affect DPS as there are two options here: Accelerated Coils and Enhanced Battery. The former adds 1 to the magazine while the latter improves the Charge time but damage drops by 2%.

The uptime perks that are debated are Clown Cartridge which on reload will add shots to the magazine from reserves versus Triple Tap which will pull a shot from thin air after 3 precision hits. As for at the end of this article we are going to compare Taipan to Stormchaser, Cataclysmic, and Reed’s Regret.

Ooh Baby a Triple Tap

Triple Tap is pretty easy to think about in terms of math. The only assumption we will make is that you are a pro gamer and hit every precision shot, which you are, so we don’t really need to call it an assumption.

Let’s compare this perk with and Without Enhanced Battery:

Triple Tap + Accelerated Coils

• With this combination, you start at 5 shots: (5)
• Shoot 3 shots, to get 1 back: (2 ➡ 3)
• Shoot 3 more shots from, to get 1 back: (0 ➡ 1)
• Shoot final 1 shot
• 7 total shots fired*

Triple Tap + Enhanced Battery

• With this combination you start at 6 shots: (6)
• Shoot 3 shots, to get 1 back: (3 ➡ 4)
• Shoot 3 more shots from, to get 1 back: (1 ➡ 2)
• Shoot final 2 shots
• 8 total shots fired*

Keep those 2 bolded numbers in mind as they will be looked at later.

Welcome to Clown School

Now lets do some math behind Clown Cartridge, which is a lot more complicated than Triple Tap. Clown Cartridge works by assigning a number between 10% and 50% and adding that to the magazine on reload with rounding up. These following ranges, and percent chance of rolling in that range in parenthesis are important to note:

Clown Cartridge + Accelerated Coils

• 10%-20% = 6 shots in magazine (25% chance of rolling in this range)
• 20%-40% = 7 shots in magazine (50% chance of rolling in this range)
• 40%-50% = 8 shots in magazine (25% chance of rolling in this range)

Clown Cartridge + Enhanced Battery

• 10%-16.67% = 7 shots in magazine (16.67% chance of rolling in this range)
• 16.67%-33.3% = 8 shots in magazine (41.67% chance of rolling in this range)
• 33.3%-50% = 9 shots in magazine (41.67% chance of rolling in this range)

As you can see there is a percent chance for each of the magazine sizes when using Clown Cartridge (CC). This is where expected yield comes in handy, as we can calculate the average magazine size you can expect to get if you were to test this out infinitely.

• CC + Accelerated Coils = (6×0.25) + (7×0.5) + (8×0.25) = 7 Base Magazine
• CC + Enhanced Battery = (7×0.167) + (8×0.4167) + (9×0.4167) = 8.25 Base Magazine

Sting Like a Bee

Veist Stinger is a top tier origin perk trait that gives a small chance to refill the magazine when dealing damage on a shot. This value is not in any API, so I tested it out and found that there is roughly a 10% chance of activating this perk which is quite high.

It is also important to note that if you activated Clown Cartridge, Veist Stinger cannot activate on the extra shots that bring it over the base magazine size. First thing to calculate is the odds that Vesit Stinger does NOT activate for each combination of perks, which is done through the following equation:

(1-z)^m

z = % chance of activating Veist Stinger, m = base magazine size

• Triple Tap + Accelerated Coils = (1-0.1)⁷ = 47.83% Failure Chance
  • 52.17% Chance to activate Veist Stinger through the magazine
• Triple Tap + Enhanced Battery = (1-0.1)⁸ = 43.05% Failure Chance
  • 56.95% Chance to activate Veist Stinger through the magazine
• CC + Accelerated Coils = (1-0.1)⁶ = 53.14% Failure Chance
  • 46.86% Chance to activate Veist Stinger through the magazine
• CC + Enhanced Battery = (1-0.1)⁶ = 53.14% Failure Chance
  • 46.86% Chance to activate Veist Stinger through the magazine

These percentages are our first values for dictating our expected yield from Veist Stinger. The main thing to note is that the Clown Cartridge values used a base magazine size of 6. This is because of what was mentioned before in which Veist Stinger does not activate on the extra shots from Clown Cartridge. Now is a good time to mention an assumption we are making which is calculating our DPS over 18 shots.

I selected this number because it is slightly less than the maximum you can hold in an LFR, and to account for the timing window of a DPS phase. DPS is calculated by how much damage you do divided by the amount of time you shoot them in. Reload speed and the amount of reloads you take increases this time frame.

Under these conditions, to shoot 18 shots you will have to reload a max of 2 times, which is what will happen if all the randomness is not on your side. The least you can reload is 0 times, where you get very lucky. And lastly you can reload only 1 time which is right in the middle.

This bit is important because we need to calculate the percent chance of Veist Stinger activating over the entire 18 shots to know the average of how many times we will reload.

Chance of reloading 2 times (this condition is met if Veist Stinger does not activate through 2 magazine back to back):

• Triple Tap + Accelerated Coils = ((1-0.1)⁷ )²= 22.88%
• Triple Tap + Enhanced Battery = ((1-0.1)⁸ )² = 18.53%
• CC + Accelerated Coils = ((1-0.1)⁵ )² = 34.87%
• CC + Enhanced Battery = ((1-0.1)⁶ )² = 28.24%

Chance of reloading 0 times (this condition is met if Veist Stinger continually activates over the 18 shots):

• There is some nuance to this because you have to add a certain back to the magazine based on how many shots are left over. For example if it activates with 3 shots left in the magazine you will add 3 back if you are using Enhanced Battery to fill the magazine back to 6 total shots. To account for this we have to find the expected yield of this by calculating the chance that a particular shot is the one that activates the perk, and then from there we calculate expected yield.
• The equation for calculating the chance of a successful shot is: where f is the number of failed shots before, and s is the chance at that shot being the one to activate the perk, and the amount of shots that will be added back for the Clown Cartridge values, but slight changes will be made for the Triple Tap values because the magazine size would be increased from Triple Tap, lessening the increase from Veist Stinger.
• Here is a table showing the odds for each shot:

The expected yield of shots returned from Veist Stinger can then be calculated by multiplying each percent chance by the number of shots taken, and this will be done by each perk combination based on the total number of shots that can activate Veist Stinger:

Triple Tap + Accelerated Coils =

• (0.9⁰  x 0.1) + (2 x 0.9¹ x 0.1) + (3 x 0.9² x 0.1) + (4 x 0.9³ x 0.1) + (5 x 0.9⁴ x 0.1) + (6 x 0.9⁵ x 0.1) + (7 x 0.9⁶ x 0.1) = 1.87shot activation
• (0.9⁰  x 0.1) + (2 x 0.9¹  x 0.1) + (3 x 0.9² x 0.1) + (3 x 0.9³ x 0.1) + (4 x 0.9⁴ x 0.1) + (5 x 0.9⁵ x 0.1) + (5 x 0.9⁶ x 0.1) = 1.57shots added back

Triple Tap + Enhanced Battery =

• (0.9⁰  x 0.1) + (2 x 0.9¹ x 0.1) + (3 x 0.9² x 0.1) + (4 x 0.9³ x 0.1) + (5 x 0.9⁴ x 0.1) + (6 x 0.9⁵ x 0.1) + (7 x 0.9⁶ x 0.1)  + (8 x 0.9⁷ x 0.1) = 2.25 shot activation
• (0.9⁰  x 0.1) + (2 x 0.9¹ x 0.1) + (3 x 0.9² x 0.1) + (3 x 0.9³ x 0.1) + (4 x 0.9⁴ x 0.1) + (5 x 0.9⁵ x 0.1) + (5 x 0.9⁶ x 0.1)  + (6 x 0.9⁷ x 0.1) = 1.85 shots added back

CC + Accelerated Coils =

• (0.9⁰  x 0.1) + (2 x 0.9¹ x 0.1) + (3 x 0.9² x 0.1) + (4 x 0.9³ x 0.1) + (5 x 0.9⁴ x 0.1)= 1.14 shot activation and shots added back

CC + Enhanced Battery =

• (0.9⁰  x 0.1) + (2 x 0.9¹ x 0.1) + (3 x 0.9² x 0.1) + (4 x 0.9³ x 0.1) + (5 x 0.9⁴ x 0.1)+ (6 x 0.9⁵ x 0.1) = 1.5 shot activation and shots added back

Next we have to find the odds that you get very lucky by activating this perk and never have to reload over 18 shots. To do that we will start at 18 shots, then subtract any initial shots from Clown Cartridge, then find how many times Vesit Stinger needs to be activated to cover the entire 18 shots.

The only event of chance here is the number of times Veist Stinger is activated, so we will calculate those odds for each perk combination based on the number of times the perk is needed to activate which will be represented by V in the equations.

Once we have V, we have to take the chance of activating Veist Stinger which we calculated earlier, and bring it to the V power of the number of activations needed, as that is how you calculate the probability of an event occurring multiple times in a row.

Triple Tap + Accelerated Coils = 18 (starting shots) – 7 (base magazine size if you shot the whole thing) – V×1.87 (shots fired before the activation on average) – V×1.57 (shots added back on average) = 0

• V = 3.2 Veist Stinger Activations Needed
• 0.5217^3.2  = 12.47% Chance of NO Reload Needed

Triple Tap + Enhanced Battery = 18 (starting shots) – 8 (base magazine size if you shot the whole thing) – V×2.25 (shots fired before the activation on average) – V×1.85 (shots added back on average) = 0

• V = 2.44 Veist Stinger Activations Needed
• 0.5695^2.44 = 25.32% Chance of NO Reload Needed

CC + Accelerated Coils = 18 (starting shots) – 7 (base magazine size if you shot the whole thing) – V×1.14 (shots fired before the activation on average) – V×1.14 (shots added back on average) < 0

• V = 4.82 Veist Stinger Activations Needed
• 0.4686^4.82 = 2.59% Chance of NO Reload Needed

CC + Enhanced Battery = 18 (starting shots) – 8.25 (base magazine size if you shot the whole thing) – V×1.5 (shots fired before the activation on average) – V×1.5 (shots added back on average) < 0

• V = 3.25 Veist Stinger Activations Needed
• 0.4686^3.25 = 8.51% Chance of NO Reload Needed

Chance of reloading 1 time (this condition is met if the other two were not, because something has to happen and this is all that’s left):

I promise this one is easy, all we have to do is subtract two numbers.

Triple Tap + Accelerated Coils = 100% – 22.88% – 12.47% = 64.66%
Triple Tap + Enhanced Battery = 100% – 18.53% – 25.32% = 56.15%
CC + Accelerated Coils = 100% – 34.87% – 2.59% = 62.54%
CC + Enhanced Battery = 100% – 28.24% – 8.51% = 63.25%

Reload Summary

Here are all of the probabilities of each number of reloads for each perk combination for shooting 18 shots:

Triple Tap + Accelerated Coils

• 0 Reload Chance = 12.47%
• 1 Reload Chance = 64.66%
• 2 Reload Chance = 22.88%

Triple Tap + Enhanced Battery

• 0 Reload Chance = 25.32%
• 1 Reload Chance = 56.15%
• 2 Reload Chance = 18.53%

CC + Accelerated Coils

• 0 Reload Chance = 2.59%
• 1 Reload Chance = 62.54%
• 2 Reload Chance = 34.87%

CC + Enhanced Battery

• 0 Reload Chance = 8.51%
• 1 Reload Chance = 63.25%
• 2 Reload Chance = 28.24%

The grand finale of reload numbers is to calculate the expected number of reloads when we are shooting all of our shots. This equation works the same as calculating the number of expected shots in a Clown Cartridge magazine by adding up the products of percent chance and the number of reloads over 18 shots:

Triple Tap + Accelerated Coils

• (0×12.47%) + (1×64.66%) + (2×22.88%) = 1.10 Reloads

Triple Tap + Enhanced Battery

• (0×25.32%) + (1×56.15%) + (2×18.53%) = 0.93 Reloads

CC + Accelerated Coils

• (0×2.59%) + (1×62.54%) + (2×34.87%) = 1.32 Reloads

CC + Enhanced Battery

• (0×8.51%) + (1×63.25%) + (2×28.24%) = 1.20 Reloads

These values are important because reloads take time in which you are not shooting. The more you have to reload, the less time you have to deal damage. To account for this we are going to take the number of expected reloads and multiply it by the time it takes to reload Taipan which is 2.53 seconds per reload.

Triple Tap + Accelerated Coils

1.10 Reloads × 2.53 seconds per reload = 2.79 seconds reloading

Triple Tap + Enhanced Battery

0.93 Reloads × 2.53 seconds per reload = 2.36 seconds reloading

CC + Accelerated Coils

1.32 Reloads × 2.53 seconds per reload = 3.35 seconds reloading

CC + Enhanced Battery

1.20 Reloads × 2.53 seconds per reload = 3.03 seconds reloading

That’s a Lot of Damage

We are well over 2000 words in and this will be the first time damage is talked about in a dissertation on DPS. DPS is damage per second, so we need to find the total damage of the 18 shots we are calculating around, and divide that by the amount of time that all takes… including reloads, which is what the last roughly 2000 words were all about.

Triple Tap + Accelerated Coils

• (55,454 dmg/shot × 18 shots) / (18 shots × 0.96 sec/shot + 2.79 sec reloading)
• DPS = 49,752

Triple Tap + Enhanced Battery

• (56,586 dmg/shot × 18 shots) / (18 shots × 1 sec/shot + 2.36 sec reloading)
• DPS = 50,044

CC + Accelerated Coils

• (55,454 dmg/shot × 18 shots) / (18 shots × 0.96 sec/shot + 3.35 sec reloading)
• DPS = 48,409

CC + Enhanced Battery

• (56,586 dmg/shot × 18 shots) / (18 shots × 1 sec/shot + 3.03 sec reloading)
• DPS = 48,419

Discussion

There is a lot to talk about here. Here is a table with our final DPS numbers:

These numbers are quite close to one another. Veist Stinger is what makes this weapon and Reed’s Regret top DPS options. If Taipan did not have Veist Stinger, its DPS in this test would be 44,169, which is significantly lower than each perk combo in the table.

In terms of comparison, Enhanced Battery is better than Accelerated Coil for DPS. This is because of these perks’ interactions with Veist Stinger. If you were to take the DPS of only a few shots, Accelerated Coils will have higher DPS, but we are incorporating more shots and reloads. Now the juicy one, Triple Tap versus Clown Cartridge. On paper Triple Tap is the better option. In reality these options are much closer.

This is because of the assumption we made that you are a pro gamer and hit every precision shot. The thing is… I lied, everyone misses shots, even you. If you miss a shot with Triple Tap it hurts your DPS by lessening your total damage, but also by reducing the efficacy of the perk by ruining your precision shot streak, meaning you get one less shot. Meanwhile, Clown Cartridge doesn’t have this issue.

If you miss 2 of the 18 shots with Triple Tap and 2 of the 18 shots with Clown Cartridge their DPS will be within 500 of one another. Human error makes Clown Cartridge look more appealing, but Triple Tap does have another aspect in its favor, and that’s ammo economy.

Triple Tap creates ammo, and does not pull it from reserves. This won’t directly help your DPS, but in a multi-phase encounter this can be very beneficial for your total damage output. If you hit all of your shots you essentially increase your total ammo by 33%.

Triple Tap is the better option for easy-to-hit bosses such as Oryx, Warpriest, and Caretaker. Meanwhile, Clown Cartridge is the better option for more difficult-to-hit bosses such as Gahlran.

If I were to definitively recommend one roll, I would say Charge Time Masterwork, Enhanced Battery, Triple Tap, and Firing Line. This is because Triple Tap is stronger in ideal and near ideal scenarios compared to Clown Cartridge because of the increased DPS and heavy ammo generation.

Clown Cartridge is better for hard-to-hit bosses, but in these instances, a more reliable means of DPS is most likely better if you are going to miss 20% or more of your shots. On top of this, the prevalence of Divinity covers up the shortcomings of Triple Tap and makes hard-to-hit bosses such as Rhulk very manageable to use Triple Tap on.

The Last Word

Now let’s talk real quick on the other Linear Fusion Rifle options in the game: Stormchaser, Reed’s Regret, and Cataclysmic. The table below has all of these weapons compared.

The table shows their base DPS that contains no damage perk, and their max DPS which consists of their optimal damage perk. It should be noted that other bonuses such as Well of Radiance nor High Energy Fire are not included because that is equal amongst all options. When calculating Cataclysmic’s Max DPS, Izinagi’s Burden was used as a Bait and Switch weapon.

Stormchaser

• This was the definitive top damage option, but a bug was fixed that allowed you to fire faster than intended. In its current state it still does have the highest DPS. With Rapid Hit, Firing Line, Enhanced Battery, and a Charge Time Masterwork, Stormchaser has a Max DPS of 63,932 over the 18 shots assuming all precision hits to increase the reload speed. Firing Line is the recommended damage perk and gives a 20% bonus to this DPS number.
• The downsides of Stormchaser are difficulty of use with landing all 3 precision hits in a burst, no access to Triple Tap for ammo generation, and difficulty in getting a curated roll because of the random drop chance. If you are lucky enough to get the god roll and are comfortable landing shots, this is a great weapon to use.

Reed’s Regret

• This weapon is arguably the hardest to get its god roll for, and that’s because it is not craftable and is only available in Trials of Osiris. Everything about Reed’s Regret is the same as Taipan including its Charge Time Masterwork, Enhanced Battery, Triple Tap, and Firing Line god roll except it is the Stasis element and its reload speed is 0.02 seconds slower than Taipan, meaning it has the most minuscule downgrade in DPS compared to Taipan.
• Something to note is that the Stasis element is great for DPS when paired with a Well of Radiance Warlock using Supreme Wellmaker to activate Font of Might on a Stasis Subclass which stacks with other damage perks. With Firing Line Reed’s Regret has a Max DPS value of 59,999.

Cataclysmic

• This weapon is the same archetype as Taipan so it does the same damage per shot, but it has different perks. This weapon has access to Fourth Time’s the Charm and Bait and Switch. Fourth Time’s the Charm gives this weapon access to 10 shots before needing to reload, meaning if you hit all precision shots, you generate 4 ammo per magazine and only need to reload once in our damage testing.
• Bait and Switch is also a stronger damage perk giving a 35% bonus over Firing Line’s 20% bonus. Bait and Switch does require shots to be hit with your other two weapons and only lasts for 10 seconds. For calculating this weapon’s DPS, we have to incorporate the weapon swap speed of cycling weapons and the damage bonus will only be applied to 16 of the 18 shots.
• With this damage bonus and using Izinagi’s Burden as our primary, over the 18 linear fusion rifle shots, 2 Izinagi’s Burden shots, and the time reloading, the DPS with Bait and Switch active comes out to be 60,472. The same process with Witherhoard is 59,172 DPS. This weapon takes the most skill to use of the four, but it is the most ammo efficient and is Solar which synergizes with arguably all of the best DPS classes for Font of Might bonus damage.
• The DPS value includes usage of a special ammo weapon and it has Fourth Time’s the Charm which increases your ammo count by 66% with hitting every shot, double that of Triple Tap.

My Final Recommendation

Use Taipan if you do not have a good Linear Fusion Rifle. It is very easy to get and craft a god roll for. Second I recommend grabbing Cataclysmic as you can use Spoils of Conquest to get red frame versions of the weapon. Next chasing Stormchaser is well worth it as its god roll has the highest DPS and isn’t quite as difficult to use as Cataclysmic nor acquire as Reed’s Regret.

Lastly, getting Reed’s Regret is the most difficult, so go for that last if you want them all. If you have access to all 4 god rolls I recommend using Cataclysmic the most as it is the most ammo efficient and you are able to activate the perk on your own.

If you have a very coordinated raid group, Reed’s Regret is the best option because of the ability to coordinate its use with Well of Radiance and Supreme Wellmaker for a stacking increase in damage from Font of Might, and coordinated raid groups will have players who create Heavy Ammo using the Aeon exotics.

Hopefully, you learned something about math or Linear Fusion Rifles. If you only become more confused reading this… well sorry!

Thanks for reading! For more guides on god rolls and more, check out our other Destiny 2 articles.