The Avenger is a Pearlescent SMG manufactured by Tediore. Here’s my breakdown of it I was amazed at the results. Not only the bouncing projectiles are unique but also the calculation of the final explosion. This makes the Avenger the most powerful Tediore weapon. If you don’t want to read the whole post just scroll down. At the end you you’ll find the complete formula, conclusion and a video.
The Avenger has some noticeable characteristics:
 ammo regeneration
 decent overall stats
 consumes only one bullet per shot
 fairly big magazine size
 huge reloadthrown explosion radius
 the standard bouncing/traveling distance of the thrown weapon is
about 2025 meters  an extremely powerful possibility of combination … but you have to
read at least the last part of this post for this one
These are the items I’ve used for the tests:
 two versions of the Avenger, same parts, just another accessory
(reload/mag size & damage)
 a common Grenadier class mod (+35% grenade damage)
 Bone of the Ancients (+30% fire damage)
 The Bee (+52746 amp damage)
Test #1: Does the bullets left in a mag affect the reload throw damage?
Short answer: Yes and no. I’ve tested this with the Hefty Avenger.
Test results:
 With 48 bullets left the projectiles deal 11396 damage.
 With 0 bullets left the projectiles deal 11396 damage.
But the amount of bullets left affects the final explosion. More about the explosion you’ll find in the end of this post.
Test #2: Does the base gun damage which is listed on the item card affect the projectiles of the special effect?
Short answer: Yes.
Refill Avenger (reload/mag accessory) with 5987 base damage:
Hefty Avenger (damage accessory) with 6512 base damage:
Test results:
 With a base gun damage of 5987 the projectiles deal 10477 damage.
 With base gun damage of 6512 the projectiles deal 11396 damage.
Equation:
 projectile damage / base gun damage = modifier/multiplicator
 10477 damage / base gun damage of 5987 = 1,75
 11396 damage / base gun damage of 6512 = 1,75
Conclusion:
The projectiles apply the element of the weapon. Due to the fire element and the fleshy target the projectiles of the reload thrown weapon deal 175% of the gun base damage which is listed on the item card. The crucial part is that the projectile damage depends on the weapon base damage.
Test #3: Does an increase of grenade damage also affect the projectiles besides the final explosion?
Short answer: Yes.
Damage with a common Grenadier class mod (+35% grenade damage):
Test results:
 Without an increase of grenade damage the projectiles deal 11396 damage.
 With an increase of grenade damage by 35% the projectiles deal 15431 damage.
Equation:
 projectile damage with grenade damage bonus / projectile damage without grenade damage bonus = modifier/multiplicator
 15431 damage / 11396 = 1,35
Conclusion:
The grenade damage bonus enhances the projectile damage 1:1 without any kind of modifier/dimishing returns.
Test #4: What if we increase grenade and gun damage?
Damage with a common Grenadier class mod (+35% grenade damage) and 5 points in Impact (+20% gun damage):
Test results:
 With an increase of grenade damage by 35% the projectiles deal 15431 damage.
 With an increase of grenade damage by 35% and gun damage by 20% the projectiles deal 18517 damage.
Equation:
 projectile damage with grenade and gun damage bonus / projectile damage with grenade damage bonus = modifier/multiplicator
 18517 damage / 15431 = 1,2
Conclusion:
The grenade and gun damage bonus enhance the projectile damage equally without any kind of modifier/dimishing returns.
Test #5: What if we add an elemental relic?
Damage with a common Grenadier class mod (+35% grenade damage), 5 points in Impact and a Bone of the Ancients (+30% fire damage):
Test results:
 With an increase of grenade damage by 35% and gun damage by 20% the projectiles deal 18517 damage.
 With an increase of grenade damage by 35%, gun damage by 20% and fire damage by 30% the projectiles deal 24127 damage.
Equation:
 projectile damage with grenade, gun and fire damage bonus / projectile damage with grenade and gun damage bonus = modifier/multiplicator
 24127 / 18517 = 1,3
Conclusion:
It seems the fire damage gets added 1:1 to all the other bonuses as contrasted with how the elemental damage gets calculated on gun damage.
Test #6: Finally The Bee!
Damage with a common Grenadier class mod (+35% grenade damage), 5 points in Impact, a Bone of the Ancients (+30% fire damage) and The Bee (+52746 amp damage):
Test results:
 With an increase of grenade damage by 35%, gun damage by 20% and fire damage by 30% the projectiles deal 24127 damage.
 With an increase of grenade damage by 35%, gun damage by 20%, fire damage by 30% and The Bee (+52746 amp damage) the projectiles deal 186000 damage.
Test #7: How about the throwing/bouncing distance?
With nearly full ammo capacity:
With ammo capacity twice the mag size:
Just enough ammo for a full mag:
Not enough ammo for a full mag:
Test results & conclusion:
The covered distance of the weapon depends on the remaining ammo. If you have enough ammo spare to fill the magazine fully the previous thrown weapon will cover the full distance. If you don’t have enough ammo to fill the next mag fully the weapon will explode earlier. The less ammo you have in your mag after reloading the less is the covered distance.
Keep in mind that as long as you have enough ammo spare for a fully next mag the count of the projectiles fired off while bouncing doesn’t depend on the ammo in the mag before throwing. With an empty mag the weapon will fire off the same amount of projectiles as with a full mag. The count is equal to the standard mag size. Only the final explosion is affected by the remaining bullets in a mag.
[SIZE=“3”]Final Equation:[/SIZE]
Projectiles:
base gun damage x (1 + elemental damage bonus [TVHM & UVHM: 75% or 0,75]) x (1 + grenade damage bonus) x (1 + gun damage bonus) x (1 + elemental damage relic bonus) + amp damage bonus x (1 + elemental damage bonus [TVHM & UVHM: 75% or 0,75]) x (1 + grenade damage bonus) x (1 + elemental damage relic bonus) = DAMAGE PER PROJECTILE
Final Explosion:
(base gun damage x (1 + elemental damage bonus [TVHM & UVHM: 75% or 0,75]) x (1 + grenade damage bonus) x (1 + gun damage bonus) x (1 + elemental damage relic bonus) + amp damage bonus x (1 + elemental damage bonus [TVHM & UVHM: 75% or 0,75]) x (1 + grenade damage bonus) x (1 + elemental damage relic bonus)) x remaining bullets in the magazine / 2 = EXPLOSION DAMAGE
or
projectile damage x remaining bullets in the magazine / 2 = EXPLOSION DAMAGE
[SIZE=“3”]Final Conclusion:[/SIZE]
 Only the final explosion is affected by the remaining bullets in the magazine. So, even if you throw it with an empty magazine, the damage of the special projectiles is equal to the damage of the special projectiles if thrown with a full magazine.
 The projectiles apply the element of the weapon and their damage is equal to the base gun damage (listed on item card), therefore a Avenger with more gun damage will be “better”.
 Grenade, gun and elemental damage bonuses affect the damage of the projectiles and the final explosion equally, which means that these can be added 1:1 on the base gun damage.
 Amp damage gets calculated separately and added in the end. The difference is that gun damage doesn’t affect the amp damage.
 The fact that the final explosion is also affected by all these modifiers makes this the most powerful Tediore weapon.
 As long as you have enough ammo for a full magazine (after reloading the gun) the weapon will cover the full distance. Otherwise the distance depends on the bullets you have left for the next mag.
[SIZE=“3”]Videos:[/SIZE]
This is how the Avenger works:
Showcasing the damage potential on Axton:
Krieg’s Avenger Damage Potential:
Raid Bosses:
Hyperius Speed Kill (2TUSimon):
F.A.Q.:

Do Zer0’s Decepti0n bonus, Gaige’s Anarchy and Maya’s Cat class mod affect the Avenger?
— Yes. Their bonuses are considered as an increase in gun damage which boosts the reload damage of the Avenger. Furthermore Zer0 can throw/reload Tediore weapons in Decepti0n without breaking Decepti0n. 
Do skills like B0re (Zer0), Chain Reaction (Maya) and Close Enough
(Gaige) affect the special projectiles of a reload?
— As far as I could test that, no. 
How is it possible to handle this weapon properly?
— You have to learn it. Throw it and memorize the traveling/bouncing distance. Don’t throw it against obstacles if you
don’t know what you’re doing because then the behavior is much harder to predict. The big radius of the final explosion makes it easier to hit smaller/moving targets.