Inside the Numbers: Draft Lottery and Draft Position Q&A

Celtics.com recently sat down with Celtics Assistant General Manager Mike Zarren and Director of Basketball Analytics David Sparks to learn about how the NBA Draft Lottery works. This year’s Draft Lottery will be held on Tuesday, May 16th.

Q: So what actually happens at the draft lottery?

MZ: Fourteen ping-pong balls, numbered one to fourteen, are placed in a bin. It turns that 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, an independent accountant, witnessed by a representative from each lottery team, 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 & 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 record, with ties being broken by a drawing that was held the third week of April. 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, at which point we all find out where each team is drafting.

Q: What picks will the Celtics have this year?

MZ: We have the rights to Brooklyn’s first round pick, after having exercised swap rights with them on April 3rd.

We also currently have the rights to three second-round picks this year. First, we’ll have #37 (from Minnesota, via Phoenix in the Brandan Wright trade), but this pick has a small chance of becoming #36, in the event the Knicks win a top-3 pick in the lottery. (See reason for this, below.) We also have #53 (from Cleveland, in the Keith Bogans trade), and #56 (from the Clippers, in the Austin Rivers trade).

Q: How likely are the Celtics to get a top-2 or top-3 pick?

MZ: Brooklyn finished with the worst record this year. Figuring out the overall probability of getting any particular pick is a bit tricky, because the odds in the 2nd and 3rd pick drawings depend on who wins the first drawing (for example, if the 2nd worst team, which has 199 combinations assigned to it, wins the 1st pick, we have a 250/801=31.2% chance to win the second pick, but if the 14th-worst team, which has only 5 combinations assigned to it, wins, we have only a 250/995=25.1% chance at the second pick -- and the math gets even more complicated when you start working on the third pick). However, David’s done the math, and it turns out that entering the lottery, with 250 combinations, the Celtics have a 25.0% chance of getting the top pick, a 21.5% chance of getting the 2nd pick, and a 17.8% chance of getting the 3rd pick. This means that entering the lottery, we have a 46.5% chance of getting a top 2 pick, and a 64.3% chance of getting a top 3 pick.

2017 NBA Draft Lottery Odds

Odds are not the same as in the general lottery tables because:

• Philadelphia has the right to swap their own pick with Sacramento.
• Minnesota and New York ended up tied – Minnesota won the tiebreaker and will draft higher in the event neither wins the lottery.

Q: If we don't win a top-3 pick, where will we pick in the first round?

MZ: After the top 3 picks have been awarded, the remaining teams draft in inverse order of regular season record. If the top three picks all go to teams with better records than the Nets had, then we will get pushed down to 4th, though there is only a 35.7% chance of that happening.

Q: My friend is a fan of team [X], and they don't have a stats column on their website. Do you know what their chances are of getting pick [Y]?

MZ: Yeah, sure. Below is the complete table of lottery odds, available exclusively (at least as of the time of this article’s posting) via Celtics.com. It’s worth noting that these numbers change from year to year, since teams whose records are tied at the end of the season split the number of combinations for the two spots they occupy.

Source: NBA Bylaws. Chart accounts for Philadelphia’s swap rights and ability to receive Lakers pick. All probabilities rounded to nearest percent – 0% indicates some >0 probability where blank space equals no probability.

Odds are not the same as in the general lottery tables because:

• Philadelphia has the right to swap their own pick with Sacramento.
• Philadelphia will receive the Lakers’ pick if it’s not top 3.
• Chicago will receive Sacramento’s pick if it’s #11.

Here are two charts that show these probabilities graphically, for the whole NBA, first by team and then by pick:

Q: Does the lottery affect the second round too?

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, without regard to the lottery results. However, when two teams are tied at the end of the regular season, a coin flip decides who drafts first between them, and whichever team drafts earlier in the first round then drafts later in the second round. But the lottery is held after the coin flip, and can move the team losing the coin flip ahead of the team winning it. In that event, the higher-drafting team drafts second in the second round. Since the Knicks and Timberwolves ended the year tied, and the Timberwolves won the coin flip, their pick (which we hold) is behind the Knicks in the 2nd round. But if the Knicks pass the Timberwolves in the first round by means of the lottery, then the Timberwolves’ pick will move ahead of the Knicks’ in the second round, so we’ll have #36 instead of #37.

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

MZ: There are a range of top players available in this year’s draft. Obviously the higher Brooklyn’s first-round pick, the smaller the number of players we might have to consider for that pick. However, in general the lottery probably will have very little effect on our preparations – 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. No matter what picks we end up with, 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, among other things (including a lot of statistics work), so that Danny & the rest of our staff can have as much information as possible to prepare ourselves for draft night.

Stay tuned to Celtics.com 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 16th on ESPN. (check local listings for time)

Michael Zarren is the Celtics' Assistant General Manager & Team Counsel.

David Sparks is the Celtics' Director of Basketball Analytics.