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 15th.

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 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.

MZ: Pursuant to the terms trade we made with Philadelphia last year, we will have the rights to the Lakers’ pick, but only if it is the 2nd or 3rd pick in this year’s draft. (If we do not get this pick this year, we will get a first round pick next year, most likely from Sacramento.)

In addition, we have the rights to our own first-round pick this year, which will be #27.

We do not have a 2nd round pick this year, after trading our own 2nd round pick (protected to 55) to OKC in a trade in which we received Perry Jones and an unprotected 2019 2nd round pick.

MZ: The Lakers finished with the 10th-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 an 11/801=1.4% 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 11/995=1.1% 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 11 combinations, the Celtics have a 1.3% chance of getting the 2nd pick, and a 1.57% chance of getting the 3rd pick. This means that entering the lottery, we have a 2.87% chance of receiving this additional pick.

Notes:

MZ: After the top 3 picks have been awarded, the remaining teams draft in inverse order of regular season record. If we do not receive the Lakers’ pick, we will just have our own pick at #27.

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.

Notes:

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

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. This does not affect us this year.

MZ: There are a range of top players available in this year’s draft. Obviously if we receive the Lakers’ pick this year, we’ll focus more on the top of the draft. 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 15th 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.