If the average % rate to win the lottery for the Leafs is 5.2% then over a sufficiently large sample size the results would trend towards 5 wins out of every 100 lotteries.
And don't take that to mean that if there were 100 lotteries the Leafs should have 5 wins.
It means that they should be trending in that direction. Maybe after 1000 lotteries the Leafs might only have 32 wins then over the next 1000 they could have 58 more wins. Then maybe 40 over the next 1000, then 60 over the next 1000, and so on and so forth.
Over a sufficient number of tries, the Leafs would expect to be getting closer and closer to 5.2%.
What OP is saying isn't completely wrong, but it misrepresents reality.
The Leafs' accumulated chance of winning needs to be compared against the rest of the League's accumulated chances of winning.
It's not 50% for the Leafs, 50% for the rest of the NHL.
Each other team is probably also at or around the 50% range, with teams like FLA, EDM, COL, CBJ, etc. sitting a little farther back as they've won the lottery.
You could then convert the differences in the Leafs' accumulated percentage on a percentile scale and see how the Leafs compare against other teams (i.e. the "Our Time is Coming" pie chart).
While each individual event occurs without influence on the previous event, it would, at some point, suggest that the Leafs would have "good luck" and win multiple lotteries.
The problem is that since this "event" only occurs once annually, a sufficient sample size won't accrue till about the year 3015 or so (ideally the year 10,015 or later).
I don't have much faith that over the next several millennia hockey will be still around.
