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Unlocking at Player level 5, the Barracks can built through the Keep . It improves the damage of Champions that deal Physical Damage.  It gives alternating bonuses of 2% Melee and Ranged Damage per Level and caps at Level 20 with 20% Melee and Ranged Damage.  At Barracks level 5, Combat Mastery is unlocked. 
Barracks
Newbarracks
Level to unlock 5
Cost to Max 1,984,500
Boost per Level Alternating between +2% Melee damage and Ranged damage
Boost at Max +20% Melee damage, +20% Ranged damage
Abilites
Ability Combat Mastery
Level to Unlock 5
Abilty2 N/A
Unlocks at level N/A
Level Cost
1 45
2 360
3 1,215
4 2,880
5 5,625
6 9,720
7 15,435
8 23,040
9 32,805
10 45,000
11 59,895
12 77,760
13 98,865
14 123,480
15 151,875
16 184,320
17 221,085
18 262,440
19 308,655
20 360,000
Total cost
1,984,500
Barracks

the old barracks