How does the lottery work (and other details)

In about a month the draft lottery will be conducted. The participants will be the 14 non playoff teams before any trades are accounted for. This way any protected picks are handled after the lottery.

There have been quite a few comments about ping pong balls as if there will be 1000 ping pong balls in a giant bin somewhere. Besides being a bit unwieldy, this would involve a long drawn out process of picking by hand and all the mathematicians would shake their heads and wonder when the NBA is going to come into the digital age. Well, there are ping pong balls but the process isn't what you think. We're used to seeing a number come out and roll down the tube and that's the number that matters. It's not like that either. The draft lottery involves 14 ping pong balls and a formula.

When the day comes here's how it works:

Each team is assigned a range of chances between 1 and 1000. So first position is 1 to 249, and so on. For 10th position, the Blazers range will be 964 to 974 (that's 11 chances). BTW, the formula allows for 1001 chances but don't worry, it's never happened that that 1001st chance has come up. They will just throw it away anyway.

If there's a tie between two or more teams then the range of chances for the tied positions are added together and divided by the number of teams that are tied. In this years lottery there are 2 ties. Detroit and Washington are tied for 6th position with 29 and 53 records and Philadelphia and Toronto are tied for 11th position with 34 and 48 records. 6th position is worth 63 chances and 7th position is worth 43 chances. Add those together and you get 106 chances, divide by two and each team gets 53 chances.

What if there's an odd number of chances you say? Then a coin flip is conducted to award the extra chance. This will actually happen with the teams tied for 11th. 11th and 12th position add up to 15. Each team gets 7 chances and a coin flip determines who gets the extra chance.

Once all the ranges are determined, the ping pong ball bonanza can commence. In a room filled with security, team officials and of course mathematicians, 14 ping pong balls are placed into a normal lottery machine and allowed to randomize. The number one draft pick is decided first. Four balls are selected and entered into the formula and presto, a single chance between 1 and 1001 is calculated and compared to the predetermined ranges and the team is selected.

Put the 4 ping pong balls back into the machine and repeat the process for the second pick except if the new chance falls in the range of a team that is already selected it's thrown out and a new set of ping pong balls is rolled out.

What's the calculation? Actually, I don't know. I can calculate the number of permutations but not choose a permutation. If anyone wants to tackle that be my guest. Here's the calculation of the total number of permutations; 11 X 12 X 13 X 14 / 24 = 1001 (4 choices out of 14. Divide by 24 because there's 24 combinations of each set of 4 numbers).

For the Blazers, the odds chart says that there is zero chance that 10th lottery position will fall to 13 (i.e three teams above 10th position move up to 1, 2 and 3 thereby moving 10th to 13th). In lottery history, 10th position is the lowest position never to have won the lottery (so it's due, right). There have been winners from 1st to 9th and 11th.

So, there you have it. If anyone can figure out the math for picking a single chance, have at it. Meanwhile, it looks most likely the Blazers will pick 10th.

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