Upgrade Odds
Upgrade odds are determined entirely by the difference in level between the Greater Rift in which Urshi appears, and the rank of the greater gem.[1] If the level of the Greater Rift is higher than that of the gem, the odds of the gem gaining a rank are increased. If the level of the Greater Rift is lower than the gem, the odds decrease rapidly.
GRift level vs. Gem Level +10 +9 +8 +7 +6 +5 +4 +3 +2 +1 0 -1 -2 -3 -4 -5 -6 -7
LGem Upgrade Chance 100% 90% 80% 70% 60% 60% 60% 60% 60% 60% 60% 30% 15% 8% 4% 2% 1% 0%

Examples:
GRift level 17, LGem level 5 = +12 = 100% chance of successful upgrade.
GRift level 22, LGem level 14 = +8 = 80% chance of successful upgrade.
Grift level 22, LGem level 24 = -2 = 15% chance of successful upgrade.
- See more at: http://www.diablowiki.net/Legendary_Gems#sthash.o2HQ3NeW.dpuf