# ...So you're telling me there's a chance?

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(Source)

Tonight, Mike Zarren will be representing the Celtics at the bizarre Freemason-ceremony-esque ritual that is the NBA draft lottery.

He’s asked the internet whether he should wear his lucky Celtics jacket (jacket to the lottery was the call, by a 2:1 margin)

As a reminder of how it all works–

(This is a ‘gravity’ machine–all the balls weigh the same–allegedly–usually about 80g)

(This is an air lottery machine–the NBA passes this off as the Device used in the Chamber of Secrets, but there’s no way of independently verifying that–these balls are closer to conventional ping pong balls in weight)

In a mystical Chamber of Secrets, a lottery Machine containing fourteen balls spits out four of them, each numbered 1-14. All but one of those four numbers are assigned to one of the teams in the lottery (there are 1001 possible combinations, and to make it nice and even, 1000 of the combos are assigned and if the 1001st combo pops out, it’s ignored and the process is set in motion again).

The team that holds those four numbers gets the first pick in the draft.

The machine then spits out four more numbers. If those numbers belong to a team that has already gotten a pick, they’re ignored and four more numbers are kicked out.

The team that holds those four numbers gets the second pick.

The process is repeated for the third pick.

After that, all the remaining teams are seeded by record, 4-14.

The ceremony is presided over by Warlocks and Diviners from Ernst & Young.

One of them, The Time Keeper, stands with his back to the Machine and informs the Machine Operator when to start and stop the Lottery Machine.

When The Time Keeper tells the Machine Operator to stop, a numbered ball is extracted from the Machine.

This process is repeated until all four numbers have been removed.

Lather, rinse, repeat.

No cell phones are allowed in The Chamber where the Ceremony is performed.

Tonight, or rather, this afternoon, the Celtics will have about a one in 34 chance of landing the second or third pick.

#### Is the process rigged?

It’s fun to think so, but in practice, it’s hard to see how it could be done, unless everyone in the room was in on it.

Lightening or weighing down (depending on the type of machine) numbers that are assigned to a particular team could backfire–at the very least, they’re not a sure thing.

Outright fabrication of the results would require the cooperation and ongoing silence of everyone in the room.

And yet.

And yet.

Some remarkable things have happened with this system (i.e. Cavs getting multiple #1 picks after LeBron left, the Bulls getting Rose–not that it worked out particularly well for them)

The problem is that, if you do permutation testing, you can almost always find remarkable ‘coincidences’.

If you do an infinite series of coin flips, you’re going to have 50% heads and 50% tails. If you do anything less than an infinite series, you’re probablyÂ not going to end up with 50% heads and 50% tails–you’re just going to be close.

And, more to the point, those heads and tails are going to clump.

Bottom line: The Bulls getting Rose, the Cavs getting Kyrie, Wiggins and Bennett (sheesh. I mean, really? REALLY? That’s what they did with their good luck?), it’s probably statistical noise.

If the process works as described, I can only conclude that it’s fair.

However, do I think the Knicks/Ewing lottery was rigged?

Yes.

Yes, I do.

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