Thanks Hammer I have corrected my post to say South-West
Also here is the Cloak's description.
Cloak of Displacement: This item appears to be a normal cloak, but when it is worn by a character its magical properties distort and warp light waves. This displacement of light wave causes the wearer to appear to be 1 foot to 2 feet from his actual position. Any missile or melee attack aimed at the wearer automatically misses the first time. This can apply to first attacks from multiple opponents only if the second and successive attackers were unable to observe the initial displacement miss.
After the first attack, the cloak affords a +2 bonus to protection (i.e., two classes better on Armor Class), as well as a +2 bonus to saving throws versus attacks directed at the wearer (such as spells, gaze weapon attacks, spitting and breath attacks, etc., which are aimed at the wearer of the cloak of displacement).
Note that 75% of all cloaks of displacement are sized for humans or elves (persons 5 to 6 feet tall), and 25% are sized for persons of about 4 feet in height (dwarves, gnomes, halflings).
That's why the White Armor missed its first attack automatically against you. Its next attack it's second, it gets three, was also a miss and it's third was only a glancing blow. Due to its size it numbed your arm for 2 rds.