### Lottery

 Each season the NBA holds a lottery to determine the order of the first 14 picks of its draft. The lottery is held in late-May, 5 weeks before the resulting NBA Draft. This year's lottery will be held on the night of May 20th. The lottery process works as follows: Each of the 14 teams in the lottery receives a ball corresponding to their default position based on their regular season record. For instance, this year the Milwaukee Bucks, who achieved the league's worst record (15-66) are represented by ball #1, the Philadelphia 76ers, the league's second worst team (19-63) are represented by ball #2 and so on. Four balls are chosen at random with the order disregarded. This process results in 1,001 combinations. For simplicities' sake, one combination (11, 12, 13, 14) is disregarded, leaving 1,000 combinations. (It should be noted that 11, 12, 13, 14 has never been pulled.) For organizational purposes, consider the combinations where the four chosen balls are sorted from smallest to largest. In other words, if the four choices go 4, 9, 2, 12, the result is (2, 4, 9, 12). Again, depending on their regular season records, teams are given a prescribed chance of winning the lottery. Those odds are shown below. When two teams have the same record, the sets the two teams receive are combined and shared equally. In the 2014 lottery, there was one tie: Boston and Utah tied for 4th, with Boston winning the tie-breaking coin flip. Instead of Boston receiving 11.9% and Uath receiving 8.8%, the two sets are combined for a total of 20.7%. Then, that allotment is split equally into two sets of 10.3% each. Finally, a coin flip determines the remaining .1%, as well as the actual order of the teams. Using these probabilities, the league assigns the 1,000 possible combinations to the teams. Milwaukee gets the first 250 combinations, then Philadelphia gets the next 199, then Orlando 138, and so on until Phoenix gets the final 5 combinations. The combinations are shown below: Four balls are chosen and the resulting combination determines the first pick. Then the balls are replaced and the process is completed to determine the second pick. The balls are replaced again and the process is completed a third time to determine the third pick. The remaining 11 picks are determined by the reverse order of finish (the default order shown above). To run your own mock lottery, go to http://www.randomizer.org/form.htm, then enter 5, 4, 1, 14, Yes, Yes: Least to Greatest, Place Markers Off. This will give you 5 sets of 4 numbers from 1-14, which are sorted from least to greatest. You may only need three sets. If two of your first three sets correspond to the same team, disregard the repeat and use the fourth set. If it happens again, disregard the repeat and use the fifth set, and so on. The winning combinations in 2013 were {3,6,7,8}, {1,2,3,9}, and {6,9,12,13}.