MaV said:
It's not inevitable that they catch up other teams. Those two teams might have all their balls left in the end. Odds are that won't happen, but it can still happen. And even if they catch up at when 16 teams are left they would still have that 1/16 chance they had in the lottery that was done the different way! Their chances would be better if they catch up later and worse if they catch up before, obviosly. But when you add up every case it's still the same odds as in the different lottery.
You say Ranger and Hawks have no statistical advantage in your situation. True they don't have advatnage over the theams still remaining, but surely over the teams already eliminated. And those teams could be any teams. This is where the advantage over any other particular teams comes from in the way you are presenting this.
You're looking at it the wrong way.
Certainly, if there are 48 balls, at the beginning of the draft, there can be an equal chance that any one of those 48 balls is the last one drafted. And if you have 3 balls, there is a better chance that you possess that last ball.
But that's not taking into account the changing nature of the lottery.
As I pointed out, bad teams are supposed to pick closer to 1. If you start at one, it becomes harder and harder for the bad teams to keep sliding down the draft board. For example, the Rangers have three balls. Say all the multi-ball teams are gone by ten... and now here we are, still climbing, and we've just draw out the Islanders at 14.
There are now 16 balls left (all multi-ball teams are gone, only single ball teams left).
The Rangers have three of those 16 balls. The chance that they are picked at 15 is quite good, comparitavely. They have a much better chance to go at 15 than all the one-ball teams, and that is as it should be, because the Rangers are a bad team.
If you go backwards, there is the very real scenario that I presented earlier that you get to 17 or 16 (working backwards) and all the multiple balls are eliminated.
Now we are about to pick the 17th pick in the draft, and the Rangers have an equally good shot of landing at 17 as they do 15 or 1 for that matter, as goes EVERYONE ELSE REMAINING.
This isn't fair. By this point in a moving draft, the Rangers have basically been hung out to dry due to bad luck. There advantage has been eliminated, and they are on equal footing now with teams like Detroit and Philly.
The direction matters because you want the advantage to exist for the bad teams when you are picking at the slots they want (ie, the high ones). Not to have that advantage worn down by time you get to 15 or 10.
