Inside the Numbers: Draft Lottery Q&A

Celtics.com recently sat down with Celtics Assistant General Manager Mike Zarren to learn about how the NBA Draft Lottery works. This year’s Draft Lottery will be held on Tuesday, May 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 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 to be held this Friday. 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 and in future years?

MZ: We have the rights to our own first-round pick and Brooklyn’s first round pick this year (#17, following a tiebreaker on April 18th) this year. Here are the Celtics' picks in the upcoming years:

  • 2015: Own 1st, Clippers 1st, Philly 1st (if they’re in the playoffs), Philly 2nd (if not), Own 2nd, Sacramento 2nd (only if it’s 56-60)
  • 2016: Own 1st, Nets 1st, Philly 2nd (if they weren’t in the playoffs in 2015), Miami 2nd
  • 2017: Own 1st (but can swap with Nets), Own 2nd (unless swap exercised and this pick is 46-60), Sacramento 2nd (only if it’s 56-60)
  • 2018: Own 1st, Nets 1st, Own 2nd
  • 2019 (and beyond): Own 1st, Own 2nd

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

MZ: We finished tied for the 4th-worst record in the league, and a coin flip and Utah will be determined that we will we get 103 ping-pong balls, and also that we will draft behind Utah in the event neither team wins the lottery. 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 worst team, which has 250 combinations assigned to it, wins the 1st pick, we have a 103/750=13.7% 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 103/995=10.3% chance at the second pick -- and 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 103 combinations, the Celtics have a 10.3% chance of getting the top pick, a 11.1% chance of getting the 2nd pick, and a 12.0% chance of getting the 3rd pick. This means that entering the lottery, we have a 21.4% chance of getting a top 2 pick, and a 33.4% chance of getting a top 3 pick.

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

MZ: Our spot depends on who else wins the lottery. 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 Celtics had, then we will get pushed down to 8th (or 7th, in the event we win Friday’s drawing), though there is only a 0.3% chance of that happening. Our overall draft lottery odds look like this:

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, Celtics simulation. All probabilities rounded to nearest percent – 0% indicates some >0 probability where x equals no probability.

* Pick would be sent to Charlotte, pursuant to the Corey Maggette/Ben Gordon trade.

** Pick would be sent to Phoenix, pursuant to the Wesley Johnson trade.

Here is a chart that shows these probabilities graphically, for the whole NBA.

Draft Possibilities

Again, if Detroit’s pick is 9-11, it will get sent to Charlotte, and if Minnesota gets #14, it will get sent to Phoenix.

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, whichever team drafts earlier in the first round then drafts later in the second round. We do not have a second round pick this year so this rule does not affect us.

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 our own 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 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 Tuesday, May 20nd on ESPN. (check local listings for time)

Michael Zarren is the Celtics’ Assistant General Manager & Team Counsel. Special thanks to Celtics Director of Basketball Analytics David Sparks for help with this article.