Someone did the maths on reddit:
So let me get this straight. You cannot get these skins by trading up, so the only chance to get one without paying real money is by random case drops.
The actual drop rate for a CW card is 0.3%, meaning that statistically speaking you need to open more than 300 cases to get a single CW card - which is already more than most people open within 30 days.
And the final nail in the coffin is that even if I somehow manage to get a CW loadout (again, 0.3% chance), there is only a 1/17 (~5.9%) chance that this CW loadout is for the merc that I want, and then add to that a 2/9 chance that the card doesn’t suck (most mercs only have 2 viable loadouts).
This leaves me with a 0.003*(1/17)*(2/9) chance to get a usable card for the merc I want, which according to Wolfram Alpha equates to a 0.0039% chance, aka 1/25500, aka ONE in TWENTY-FIVE THOUSAND AND FIVE HUNDRED.
Not sure if it’s completely correct, and I’m too lazy to work it out myself as I’ve only just woken up xD But it looks roughly correct, regardless. 
I think the only thing I’ve majorly complained about in Dirty Bomb within the past couple of months was the awful, awful price of the trade-in system… And now this. Drop rate is absurdly low - so low in fact, they may as well not even be in the game. I know plenty of people who have upwards of 300 hours and never got a single gold or cobalt from an equipment case (and that’s 0.5% combined), and that’s in their entire time of playing. We only have 30 days for this.
Oh well, I guess it’s just like trade-in’s, I’ll just pretend they don’t exist.