I think the statistic you're describing is "profit". Or maybe "profit/wagered". If you take stake into account then the players luck is directly proportional to his profit/loss. I was aiming for something which was independent of stake, so we can see things like "I had a really unlucky set of rolls, but my martingale betting still let me make a profit". And such.
I like the current "definition" of luck, which should be, in my opinion, independent of amount wagered. The outcome is always the same regardless of whether the bet is 1 satoshi or 10 bitcoins. Increasing the wager should never affect the chance of winning (or vice versa)