_Note: it is my personal experience._
So there is some statistic, of course it is not completely accurate, but giving overall view.
After 9 key fragments (next KF) dropped:
3 KF for 16 wins (=17 hours ingame time (next HIT)), ~19% drop chance for KF;
for next 40 wins (=34.5 HIT) 0 KF was dropped;
22.04.16 was KF drop chance reset;
23.04.16 next 3 KF for 9 wins (=5.5 HIT), ~33% drop chance for KF;
23.04.16 next 3 KF for 5 wins (=3.5 HIT), ~60% drop chance for KF;
26.04.16 next 3 KF for 15 wins (=13 HIT), ~20 drop chance for KF;
05.05.16 2 KF for 28 wins (=24.5 HIT) , ~7% drop chance for KF.
KF drop rate after 9 keys is ~11% for KF, other individual drop chance is too inaccurate.
Overall KF drop rate is ~12%, you need ~8 wins for KF, ~7 HIT
It seems that gamemode doesnot have impact on drop chance.
P. S. all time include wins and losts time, for only wins divide by 2.
Here a link for Excel file with all data http://s000.tinyupload.com/?file_id=02554635329076246394