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

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Celtics.com recently sat down with Celtics VP of Basketball Operations 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 Thursday, August 20th.

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 out 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 (or three) 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 and fourth pick. After those four 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 earlier in the season. 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 is different this year from previous lotteries?

MZ: This year’s lottery will work the same as last year’s, with the top four picks being lotteried off, not the top 3 as was done before last year. Also before last year, the odds were changed so that the bottom three teams each have the same odds of getting a top-4 pick, and the teams lower down have better odds of moving up. The only real difference this year is that it will be conducted virtually.

Q: What picks will the Celtics have this year?

MZ: We have the rights to two or three first round picks this year, and one second round pick.

  1. Pursuant to the terms of a trade we made with Memphis in 2014 involving Jeff Green, we will have the rights to their pick, #14, unless they win one of the top 4 picks. There is a 2.4% chance of this happening. If that does happen, we will instead receive Memphis’s pick next year, unprotected.
  2. In addition, we have the rights to our own first-round pick this year, which will be #26.
  3. Pursuant to a trade we made last year with Phoenix involving Aaron Baynes, we will have Milwaukee’s first-round pick, #30.
  4. Pursuant to a sign-and-trade deal last year with Charlotte involving Terry Rozier, we received the rights to Brooklyn’s 2nd round pick (#47) in exchange for giving up our own 2nd round pick (#56). So we’ll have #47.

So most likely we’ll have picks 14, 26, 30, and 47.

Q: How likely are the Celtics to get a top-4 pick?

MZ: We made the playoffs this year, so we do not have a shot at a top 4 pick. However, if Memphis wins a top-4 pick (2.4% chance), we’ll get their pick next year, unprotected, instead of #14 this year.

2019 NBA Draft Lottery Odds



  • * Boston receives Memphis’s pick if it is not top 4.

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. 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. All probabilities rounded to nearest percent – 0% indicates some >0 probability where a blank space equals no probability.


  • Boston receives Memphis’s pick if it is not top 4.

Q: Is there an easier way to visualize this than a big table of numbers?

DS: Yes! Here are two charts that shows 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 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. This does not affect us this year.

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 there’s a small chance we don’t get the 14th 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, including video interviews with players 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 himself 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 Thursday, August 20th on ESPN. (check local listings for time)

Michael Zarren is the Celtics’ VP of Basketball Operations & Team Counsel.

David Sparks is the Celtics’ Director of Basketball Analytics.