Mar 11, 2012; New Orleans, LA, USA; Kentucky Wildcats forward Anthony Davis (23) shoots over Vanderbilt Commodores forward Steve Tchiengang (33) in the second half of their game in the finals of the 2012 SEC Tournament at the New Orleans Arena. Mandatory Credit: Chuck Cook-US PRESSWIRE

For the Bucks, the Math is Hard

On Wednesday night, during halftime of Game 2 of the Eastern Conference Finals, the NBA will conduct its 2012 Draft Lottery in New York, determining a winner who will inevitably draft Anthony Davis from the University of Kentucky.  The Bucks don’t have much of a chance of landing Davis; in fact, they will likely draft at the 12th spot or later.

The league uses a weighted lottery system to randomly determine the first three picks of its draft.  The remaining positions are determined in reverse order (from lowest to highest) based upon the winning percentages of the teams who originally held those picks.  With the 12th-worst record, the Bucks are assured a draft pick of 12th or later unless they land one of those top three spots.

The league uses a system of 14 numbered ping-pong balls and picks four of them (which matches the 14 lottery teams purely by coincidence).  There are 14 choices for the first ball selection, 13 for the second, 12 for the third, and 11 choices remaining by the time the final ball is chosen.

As a result, there are 14*13*12*11 = 24,024 possible ways of picking four balls if the order is relevant.  But since the league uses a system which does not depend on the order, the 24 = 4*3*2*1 permutations of each combination of four balls (think 1234, 1243, 1324, 1342, 1423, 1423,…, 4312, 4321) all count as the same outcome.  As a result, the lottery has 24,024 divided by 24 = 1,001 possible outcomes.  By declaring the 14-13-12-11 outcome invalid (it would cause a redraw), there are 1000 possibilities, and the league can distribute these outcomes to the lottery participants in portions accurate to tenths of a percent.

After this process has been done once to determine the lottery winner, the four balls are thrown back in and the whole process is repeated twice more for the purpose of determining the winners of the second and third overall picks.  Repeat winners are not allowed, so if a combination comes up that corresponds to a slate that had already won, then the process is thrown out and done again.

For the Bucks, it means that after the first (and possibly second) pick likely go to teams with a big swath of winning combinations, those combinations are invalid for subsequent picks.  And the Bucks chances of landing in the top-3 with the second or third pick go up.

But not much.

With the 12th spot in the lottery, the Bucks are given just seven of the 1000 combinations.  They will have a 0.7% chance of landing the top pick, and approximately 0.83% and 1.01% chances, respectively, of netting the second and third overall selections.

Essentially, the Bucks have nearly a three-percent chance of landing a top-3 pick.  On the flip side, they have a 97% chance of finishing 12th or lower in the draft.

Pick Prob.
1st 0.7%
2nd 0.8%
3rd 1.0%
12th 93.5%
13th 3.9%
14th Less than 0.1%

List of Other Outcomes With a (Roughly) 3% Chance:

* Having a candidate not named Romney or Obama win the 2012 U.S. Presidential election.
* Living to age 100, for a female born in the United States
* Rolling a pair of 6’s when two dice are tossed
* Conceiving a child after sex without birth control, for a female between the ages of 40 and 45
* Getting dealt a 5-card poker hand of three-of-a-kind or better
* Having 10 or more inches of snow on the ground in Milwaukee on December 25th

Good luck fighting those odds.

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Tags: 2012 NBA Draft Anthony Davis Milwaukee Bucks NBA Draft Lottery

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