The NBA Draft is coming…

Each team’s chances with conditions (rounded to three decimals) (wikipedia)

Ah the draft lottery, the most important component of the NBA Draft. For those unfamiliar with the concept, the NBA Draft has two rounds with a total of 60 picks. The sixteen teams that made the playoffs are the given the 15th through 30th picks in the reverse order of their regular season record, regardless of where they finished in the playoffs. The fourteen teams that didn’t qualify for the playoffs test their luck the lottery.

The Draft Lottery works like this: there are fourteen ping pong balls numbered from 1 to 14. NBA Officials (with witnesses) draw four of the fourteen balls to determine a combination. The combination disregards the order the balls are drawn so 1-2-3-4 is the same as 4-3-2-1. For those familiar with combinatorics, the fact that the order doesn’t matter (a combination), makes the number of possible outcomes A LOT lower than if the order did matter (a permutation). When you calculate 14 choose 4 (14! / (10! x 4!) which simplifies to (14 x 13 x 12 x 11) / (4 x 3 x 2 x 1)), that equates to 1,001. To simplify the math, if the four balls come out as 11-12-13-14, that combination is thrown out and there are 1,000 possible combinations. All fourteen teams are assigned combinations based on their records (the “Lottery Chances” above). Once the four balls are drawn, the officials match the combination with the corresponding team and that team is awarded the first pick. This process is repeated two more times to determine the second and third picks.

Any team can move into the top three. Because of that, any team can fall as far back as three picks behind where they finished. Furthermore If you notice on the table above, the teams that finished in the bottom five (Celtics, Jazz, Magic, 76ers, and Bucks) are actually more likely to move down than they are to receive the pick corresponding with where they finished.

Due to conditions of various trades, there are picks that are protected and conditional. Grantland has the details on all of the current trades and conditions shown above. Let’s look at the probabilities:

-The Hornets receive the Pistons’ pick if it falls out of the top eight. The probability of the Pistons losing their pick: .176 or 17.6%
-The Sixers have the rights to the Pelicans’ pick unless it moves into the top five. The probability of the Pelicans keeping their pick: .04 or 4%
-The Nuggets have the rights to the higher pick between their and the Knicks’ because of the trade that sent Carmelo Anthony to New York while the Magic have the rights to the lesser pick because of the trade that sent Dwight Howard to the Lakers and Andre Iguodala to the Nuggets.
-The Suns receive the Timberwolves’ pick if falls into the 14th pick. The probability of the T-Wolves’ pick falling to 14th: .017 or 1.7%

Looking at the Sixers’ chances, they could land anywhere in the top five. However with Dr. J representing the team, I like their chances to win it. In the 29 other lotteries, the second-to-last team has received the top pick four times. The Sixers were one of those second-to-last teams in 1996, and they drafted a man from Georgetown University…

The Lottery begins tonight at 8pm on ESPN.