Inside the Numbers: Draft Lottery Demystified
April 27, 2006 recently sat down with Celtics Basketball Operations Analyst Mike Zarren to learn about how the NBA Draft Lottery works. This year's Draft Lottery will be held on Tuesday, May 23, in Secaucus, New Jersey.

NBA Draft Lottery Odds
Portland 250 25.00% 21.48% 17.72% 64.20%
New York 199 19.90% 18.78% 17.07% 55.75%
Charlotte 138 13.80% 14.25% 14.54% 42.59%
Atlanta 137 13.70% 14.16% 14.48% 42.34%
Toronto 88 8.80% 9.64% 10.65% 29.09%
Minnesota 53 5.30% 6.02% 6.96% 18.28%
Boston 53 5.30% 6.02% 6.96% 18.28%
Houston 23 2.30% 2.69% 3.21% 8.20%
Golden St. 22 2.20% 2.57% 3.08% 7.85%
Seattle 11 1.10% 1.30% 1.57% 3.97%
Orlando 8 0.80% 0.95% 1.15% 2.90%
N.O./O.K.C. 7 0.70% 0.83% 1.01% 2.54%
Philadelphia 6 0.60% 0.71% 0.87% 2.18%
Utah 5 0.50% 0.59% 0.72% 1.82%

Q: So what actually happens at the draft lottery?

MZ: Basically, 14 ping-pong balls, numbered one to 14, are placed in a bin. There are exactly 1,001 possible four-ball combinations when you have a set of fourteen. Each team in the lottery has been assigned a set number of combinations of any four of the balls, for a total of 1,000 combinations. (the 1,001st combination belongs to no team.) The number of different combinations assigned to each team depends on that team's record; teams tied at the end of the regular season split evenly the total combinations allotted to their two positions, with one team getting one more combination in the event the total is odd. Then, a team of independent accountants draws four balls out of the bin, and whichever team is assigned that combination gets the first pick in the draft; if it's the 1,001st combination, the balls are replaced and drawn again.

After the first pick is determined, the balls are replaced, and the process repeated. If the new combination belongs to the team that already won the first pick, the balls are replaced and drawn again. The next different team whose combination is chosen gets the second pick, and then the whole process is repeated again for the third pick. After those three picks are set, the remaining teams are set to pick in inverse order of their record, with ties being broken by a previous drawing. The accountants mark down who gets each pick, and place a card bearing each team's logo into an envelope bearing the number of that team's pick. The envelopes are then brought out on stage, where they're opened in front of a live TV audience.

Q: How likely are the Celtics to get a top-three pick?

MZ: The Celtics finished tied with the Timberwolves for the sixth-to-last record. The sixth-worst team usually gets 63 numbers assigned to it, and the seventh-to-last team usually gets 43. Because the Celtics and Timberwolves finished tied, league rules specify that the two teams split the total number of combinations from the sixth and seventh spots, or 53 for each team.

Figuring out the overall probability of getting any particular pick is a bit tricky, because the odds in the second and third pick drawings depend on who wins the first drawing. For example, if the worst team, which has 250 combinations assigned to it, wins the first pick, we have a 53/750=7.1% chance to win the second pick, but if the 14th-worst team, which has only five combinations assigned to it, wins, we have only an 53/995=5.3% chance at the second pick. The math gets even more complicated when you start working on the third pick.

However, we've done the math, and it turns out that entering the lottery with 53 combinations, the Celtics have a 5.3% chance of getting the top pick, a 6.02% chance of getting the second pick if we do not get the top pick, and a 6.96% chance of getting the third pick if we don't get either of the first two. This means that entering the lottery, we have a 18.28% chance of getting a top three pick.

Celtics' Odds Of Receiving
Each Possible Pick

Q: If we don't win a top-three pick, where will we pick?

MZ: Our spot depends on who else wins the lottery. After the top three picks have been awarded, the remaining teams draft in inverse order of regular season record. So if the top three picks all go to teams with worse records than the Celtics had, then we will draft seventh because we lost a coin-flip with the Timberwolves, who had the same record we did. But if one team with an equal or better record than the Celtics wins a top three pick, we would move down to eighth. If two teams with better records move up, we move down to ninth. The lowest we could draft this year is 10th, in the extremely unlikely event that three teams with better records all move up to the top three. The chances of us ending up with pick #7 are about 57.3%, pick #8: 22.6%, pick #9: 1.8%, and there is about a three-in-10,000 chance of us getting the tenth pick. Our overall draft odds look like the chart to the right:

Q: Does the lottery affect the second round?

MZ: Only in the event that two teams finished the regular season with the same record. Ordinarily, the order in the second round is determined solely by regular season record. However, when two teams are tied at the end of the regular season, whichever team drafts earlier in the first round then drafts later in the second round. Right now, Minnesota is set to pick before us in the first round, since they won the tiebreak drawing, and thus we are set to pick before them in the second round, at #36. However, should we end up picking ahead of Minnesota in the first round due to the lottery, they would get to draft before us in the second round, and we would thus end up with pick #37. This year's lottery also affects whether or not we even have a second-round pick, due to a combination of the Walter McCarty and Szczerbiak-for-Davis trades. If Golden State does not move ahead of Houston via the lottery, we will not have a second round pick at all.

Q: How will the draft lottery affect team preparations for the draft?

MZ: Unless Golden State moves ahead of Houston, thus giving us a second-round pick, the lottery probably will have very little effect on our preparations. Since there is no consensus number-one prospect this year, and since there's always the possibility of a draft-night trade, we'll need to evaluate a wide range of top draft-eligible players regardless of where we'll be picking. Obviously, if we win the number one pick, our focus will narrow down to fewer players, but we'll still need to be aware of every player in the draft -- some of them might go undrafted and be good free agent pickups even if we don't have a second-round pick. Regardless of where we're picking, the time between the lottery and the draft will be extremely busy, with players coming in for workouts and our staff watching a lot of video, so we can be as prepared as possible for any eventuality.

Stay tuned to for more lottery and draft coverage as the draft approaches, and watch as the results of the draft lottery are revealed live on Tuesday, May 23 on ESPN.

Michael Zarren is the Celtics Basketball Operations Analyst, responsible for assisting team decision-making through the use of quantitative and legal analyses.

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