This is a port of Loot Turtle’s tests on Vel0city - not my work! The original post is here - last update is from 2013. I have retained all of the original without any edits.
I have kept the original link to “Critical Hit Damage” from the old forum but recommend referring to this as well.
Note - this info is pre-patch so the numbers are no longer correct.
This is related to the Comprehensive Guide on How Critical Hit Damage Works.
Here’s some random Grim TMP I bought from Marcus:
Tested it by firing at the Target Practice Dummy in Marcus’ Shop. No unnecessary items equipped, no skills activated & BA ranks disabled.
Bodyshot damage is the same as the damage value shown on the display card.
Crit Damage:
5044 X 2 X (100% + 0%) = 10087
Now with 5/5 Vel0city which should give +10% Gun Damage & +15% Crit Damage:
Vel0city Bodyshot Damage:
5044 X (100% + 10%) = 5548
Vel0city Crit Damage:
5548 X [2 X (100% + 0%) + 0.15] = 11928
Next, 5/5 Headsh0t which should give +20% Crit Damage:
Headsh0t Crit Damage:
5044 X 2 X (100% + 0% + 20%) = 12105
Now it’s 5/5 Headsh0t & 5/5 Vel0city together:
Headsh0t + Vel0city Crit Damage:
5548 X [2 X (100% + 0% + 20%) + 0.15] = 14147
TL,DR : For some odd reason, the crit damage bonus from Vel0city is added in a very weird way. No other crit bonus is like this. If it had worked like normal, its crit damage would be much higher.
So, is Vel0city worth it or not? I’ll leave that for you to decide. 
Thanks for reading!