I'm also afraid to tell you that 'luck' does not exist - you can calculate probability but not luck (unless someone could post the calculation for the likelihood of luck existing)...
'Luck' exists, silly! If you earned more than expected, you've had good 'luck'. If you earned less than expected, you had bad 'luck'.
Of course luck doesn't exist it is a convenient word to cover bad judgement, calculations or events we choose not to understand or have control of.
If you
expect to earn X and you earn Y then a force has acted upon X to move its value to Y - an event, not luck.
Either way your expectation/calculation was wrong.
That calls for an "Argh". You seem to have some math knowledge, but then you confound "expectation" in a mathematical sense, with "expectation" in some other sense.
Your expected income per difficulty 1 share is (Bitcoin reward per block) / (network difficulty). If you earn more than this per share, you've had good luck. Less than this is bad luck.