How is full charge capacity calculated and why is mine going up and down?

I have a mid 2012 15" mbp. I recently got a battery replacement. The old one was extremely degraded and would shut off randomly after 30min. However the new battery also seems be shutting down at 20% or 10%. Whats also weird is the full charge capacity seems to vary between 82%-99% of design capacity. The reason the system is shutting down unexpectedly is because the % remaining charge seems to drop suddenly and then bounce back. You can see this is the last 12 hour graph below. There are many fluctuations of % charge remaining including the final drop from 12% down to 0% then back up to 13% again.

• Any clues on what could be causing this and if its a motherboard issue I need to get fixed?
• Does anyone know a free utility I could graph the changes in full charge capacity vs remaining charge (instead of % remaining charge which depends on both)?
• Doesn't anyone know how full charge capacity is calculated? (I suspect its the full charge capacity measurement going up and down thats causing the % remaining to change)

Things I've tried

• - It's not a battery issue. This is the 2nd one I've tried. I got it replaced under warrenty after 1W. The last battery would shut off around 40-30%.
• - Reseting SMC and PRAM.
• - Conditioning battery. I've cycled it a couple of times keeping it charged many hours inbetween.

Here is the full battery info. Notice the full charge capacity this morning is now 96%.

This is the same battery 2 days earlier.