A couple errors I'd like to point out. You're wearing Paladin shoes, which doesn't add to your artillery. Also, your friend seems to be wearing a survival pack. After determining these issues, I decided to go backwards in the damage calculation. This was what I got.
6162/1.3=4740
4740/5=948
948*2²=3792
3792/44=86.18181818
I knew that wasn't right, so I did a little studying and... It turns out that everything on Flappy's end matches your description except he actually has a STAGE 3 SHARPENED Pellet Spitter.
After figuring that out, here's what I got.
3792/48=79
Survival Pack Artilery: 7
Neon Shark Piece Artillery: 19
Neon Shark Shoes Artillery: 10
79-5-19-19-19-10-7=0
Your friend, with the actual gear (Neon Shark set+Survival Pack+S3 Sharpened Pellet Spitter) actually has the correct artillery amount.
As for you...
6435/1.3=4950
4950/5=990
990*2²=3960
3960/44=90
Steel Bar Artillery: 4
Paladin Shoes Artillery: 0
90-32-19-19-19-0-4=-3
By the looks of it, your artillery is three less points than it should be at the time you posted this screencap. However, I found the real bug behind this issue. See, the JSON file actually lists two different stats for artillery on the Back Steel Bar:
http://prntscr.com/v6vlb9
Unless you're actually wearing something else at the time, it seems the real bug here is the Back Steel Guard giving you 1 artillery instead of 4. But beyond that, the math checks out fine.