Preface:
Over a couple of days I have tested out the legendary drops on a Monk in seasonal with the Patterns node (double legendaries from Kadala) unlocked. I recall seeing something about a bug during season 28 and if I recall correctly I did notice some inconsistencies. Due to this I wanted to test it in the PTR, seeing as things may have changed.
Assumptions:
Normally legendaries are dropped at a rate of 1:10. Doubling this gives 1:5, or 20% chance.
Test results:
Helmets:
100 bought, 17 legendaries - 17%
Chest piece:
217 bought, 21 legendaries - 9,68%
Belts:
100 bought, 26 legendaries - 26%
Legs:
100 bought, 25 legendaries - 25%
Boots:
150 bought, 18 legendaries - 12%
Shoulders:
100 bought, 16 legendaries - 16%
Gloves:
100 bought, 28 legendaries - 28%
Bracers:
110 bought, 18 legendaries - 16,36%
Shield:
100 bought, 18 legendaries - 18%
Ring:
153 bought, 18 legendaries - 11,76%
Amulet:
100 bought, 12 legendaries - 12%
One-handed weapons:
100 bought, 27 legendaries - 27%
Two-handed weapons:
100 bought, 24 legendaries - 24%
Quiver:
100 bought, 24 legendaries - 24%
Orb:
100 bought, 18 legendaries - 18%
Mojo:
100 bought, 21 legendaries - 21%
Phylactery:
100 bought, 15 legendaries - 15%
Analysis:
Of course the population for this test isn’t too high, mostly due to a lack of time. This may skew some results. Furthermore, this base rate of 10% before the altar node hasn’t been tested in the base game for Kadala.
However, according to this small pool of results the chance to get a legendary from Kadala looks to depend on the item picked.
For boots, chests, rings and amulets the rates seem to be lower than expected. For some others the opposite may be true. This may require some more investigation.