Don't post often - and will probably regret getting involved in this luck debate, but couldn't resist the temptation to get involved, as it something I've thought about quite a few times recently, specifically with regard to Kane and Alli! To me, there are two ways to view youth recruitment in the context of 'luck':
1) A select few youth players are ultra talented super-stars to be who are destined to 'make it' (with Kane and Alli being a great example of a club scoring two in a short space of time). In this instance, Tottenham (or whatever club signs / acquires said player) were extremely lucky to gamble on the signing and nature of this player, as with the many thousands of youth players that all the mega-clubs are fighting to sign, its clear no one has any real hope nor the scouting prowess to pick out 'the stars' intentionally.
2) Alternatively, you could take the view that every youth academy has many players who have the potential to be 'stars' (at the level of Kane, Alli or better), and that the coaching, facilities and opportunities given to those players determines how many of them, on average, actually 'make it'. In this scenario, I would argue there is actually very little luck associated to the club - its their infrastructure which determines how many good players come through their youth setup. Luck and circumstances can be attached to the individual players, sure, but with a large enough sample of potential youth super-stars its statistically inevitable great players come through if the infrastructure is in place.
The two scenarios above are two extremes and I'm sure the truth lies somewhere in the middle. However, to me, when you look at Poch's record of bringinig youth through its hard to argue against the second view point. In less than 3 years at Spurs, he's brought (off the top of my head) 8 players through the first team (Kane, Alli, Bentaleb, Winks, Carroll, Davies, Dier, Mason). Sure, not all of them were good enough in the end (and were sold on for a handsome profit), but I don't believe we can rigidly argue that things are this completely stochastic luck-driven thing given Poch's record thus far. Of course, I'm also basing this on his shorter spell at Southampton, where he built the entire Liverpool starting 11 in a year !
So, I guess I would ask Neil, if Spurs have another Kane or Alli come through next year, and another the year after, would you continue to regard it as 'luck'? When does one have to turn your head and ask 'why arn't these players coming through at City / Chelsea / United / Arsenal?', and begin to question if its their methods and policies that are the problem?