This is a test of chest drop rate. It was performed during the mission "X Marks the Spot". 100 "runs" were done. 600 black pirate chests were opened and 700 red pirate chests were opened. The drop rates for these chests are as follows:
Out of 600 black chests opened: 17 contained legendaries = 2.8% chance per chest 151 contained purples = 25% chance per chest
Out of 700 red chests opened: 1 contained a legendary = .07% 49 contained purples = 7% chance per chest
Feel free to double check my adding. Didn't set up the spreadsheet to add for me. I'm going to do another hundred with more static conditions and try improve the spreadsheet a bit.
The pirate chests might be suitable stand-ins for "crimson lance" chests and "classic" red chests. That's up to your discretion.
It seems like inventory emptiness might have something to do with legendary drop rate.
"Blood of Terramorphous" might increase legendary drop rate.
Legendary (and perhaps even purple) drops are likely influenced by class. Certain gear may be more likely to drop for certain classes. I imagine, since mechromancers don't have a legendary class mod, the siren class mod would drop instead. I noticed that I've gotten 2 Shreddifiers while opening chests with the gunzerker (not on paper) and I quickly got a Hornet when my assassin opened the chests.
Held gear may influence drops. Both my Mechromancer and Gunzerker had a Maggie and a Hellfire equipped until run 74 where both Hellfires were switched with something else. Maggies were drawn the majority of the time during these runs. My assassin had a Hornet equipped when the second Hornet dropped.
It seems fair to assume that Hellfires and Maggies might just be "common" as far as legendary weapons are concerned.
As a matter of logic, it seems like legendary smgs, pistols, and mods are more likely to drop because more of them can drop from one box.
These are all theories, not facts.
The math seems pretty solid (those seem like they'd be correct percentages).