Im making a first person shooter and would like input to see if these stats seem balanced. The shotgun would obviously shoot more than one but my co-worker feels that the damage should be per gun not per ammo, i feel differently

AmmoTypes["9mm"] = new Bullet(){
            Velocity = 380,
            headDamage = 100/6,
            bodyDamage = 100/9,
        };

        AmmoTypes[".45 ACP"] = new Bullet(){
            Velocity = 460,
            headDamage = 100/5,
            bodyDamage = 100/7,
        };

        AmmoTypes["5.56"] = new Bullet(){
            Velocity = 992,
            headDamage = 100/4,
            bodyDamage = 100/6,
        };

        AmmoTypes["7.62"] = new Bullet(){
            Velocity = 850,
            headDamage = 100/3,
            bodyDamage = 100/5,
        };

        AmmoTypes["12 Gauge"] = new Bullet(){
            Velocity = 460,
            headDamage = 100/2,
            bodyDamage = 100/4,
        };

        AmmoTypes["20 Gauge"] = new Bullet(){
            Velocity = 450,
            headDamage = 100/3,
            bodyDamage = 100/5,
        }

You can balance shotguns by keeping the damage per bullet, but adding in bullet spread, and distance fall-off. The gun becomes more effective close up, unless you're adding in a choke to increase accuracy and range.

Missing from your data model:

• Different ammo for the same gun. Most importantly for shotguns, which offer a meaningful choice between a single slug, medium balls, small balls, and many special loads. Pistols can have hard AP bullets, soft bullets that cause worse wounds, or anything in between.
• Multiple bullets for the same cartridge, required for realistic shotgun spreads, As observed by Rutin, spreading shots in a wider or narrower pattern depends mostly on the gun.
• How much the bullets drift away from an ideal trajectory, important for aiming accurately at long range and rewarding rifled barrels..

It can be difficult to determine balance from numbers/stats alone. Balance is often determined in balance playtesting. If there are just the two of you and you have different opinion as to balance, a session with impartial playtesters should help sway one or both of you. There are two Extra Credits videos you both should watch on YouTube: "Playtesting - How to Get Good Feedback on Your Game" and "Understanding Your Player: Play Sessions - How Will People Play Your Game?"

A paper prototype can be a useful way to go if A-B testing with your software is impractical. 

16 hours ago, reverseslayer said:

Im making a first person shooter and would like input to see if these stats seem balanced. The shotgun would obviously shoot more than one but my co-worker feels that the damage should be per gun not per ammo, i feel differently

 

Related question: does the pacing, nature of the shooter lend itself to the player wanting and needing to pay attention to such items? Are you at the Borderlands/Doom end of the spectrum or something much more tactical--where ammo may be precious, stopping power, body armor penetration, shot location, etc. are all critical factors.