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 14th.

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: Well, two things. First, the top four picks are being lotteried off, not the top 3. Second, 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.

Q: What picks will the Celtics have this year?

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

Pursuant to the terms of a trade we made with Philadelphia in 2017, we will have the rights to Sacramento’s pick, but only if it is #2, #3, #4, or #14. (If they do not win a top-4 pick in the lottery, their pick will be #14.) If Sacramento gets the #1 pick, we will get Philadelphia’s pick, #24, instead – there is a 1% chance of this happening, and a 4% chance of it being #2, #3, or #4. So there is about a 95% chance this pick will be #14. Pursuant to a trade we made in January 2015 involving Jeff Green, we have the rights to Memphis’s first-round pick this year if it is #9 or worse. Entering the lottery, Memphis is at #8. So we will not get their pick this year unless a team below them “leapfrogs” Memphis in the lottery, pushing them down to 9 or lower. The chance of this happening is approximately 43%. (If we don’t get this pick this year, it is protected to 6 next year and unprotected in 2021.) Pursuant to another trade we made with Memphis on draft night 2016 (we traded them two second-round picks), we have the rights to the #20 pick this year, from the LA Clippers. (Memphis acquired it from the Clippers in a trade for Jeff Green during the summer of 2015.) In addition, we have the rights to our own first-round pick this year, which will be #22. We also have our own second-round pick this year, #51.

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

MZ: The Kings finished in a three-way tie for the 12th-worst record this year, but then lost the three-way tiebreaker, so they are currently at #14. 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 4th worst team, which has 125 combinations assigned to it, wins the 1st pick, we have an 10/875=1.1% chance to win the second pick, but if the 13th-worst team, which has only 10 combinations assigned to it, wins, we have only a 10/990=1.0% 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 10 combinations, the Celtics have a 1.1% chance of getting the 2nd pick, a 1.2% chance of getting the 3rd pick, and a 1.4% chance of getting the #4 pick. This means that entering the lottery, we have a 3.7% chance of receiving a top 4 pick.

2019 NBA Draft Lottery Odds

Probability of getting: Team # Combos 1st Pick 2nd Pick 3rd Pick 4th Pick Any Top 4 NYK 140 14.0% 13.4% 12.7% 11.9% 52.0% CLE 140 14.0% 13.4% 12.7% 11.9% 52.0% PHX 140 14.0% 13.4% 12.7% 11.9% 52.0% CHI 125 12.5% 12.2% 11.9% 11.4% 48.0% ATL* 105 10.5% 10.5% 10.5% 10.5% 42.0% WAS 90 9.0% 9.2% 9.4% 9.6% 37.2% NOP 60 6.0% 6.3% 6.7% 7.2% 26.2% MEM** 60 6.0% 6.3% 6.7% 7.2% 26.2% DAL* 60 6.0% 6.3% 6.7% 7.2% 26.2% MIN 30 3.0% 3.3% 3.6% 4.0% 13.9% LAL 20 2.0% 2.2% 2.4% 2.8% 9.4% CHA 10 1.0% 1.1% 1.2% 1.4% 4.7% MIA 10 1.0% 1.1% 1.2% 1.4% 4.7% BOS**,*** 10 -- 1.1% 1.2% 1.4% 3.7% PHI*** n/a 1.0% -- -- -- 1.0%

Notes:

Notes:

“--" indicates no possibility; “0.0%” indicates tiny possibility.

* Atlanta receives Dallas’s pick if it is not top 4.

** Boston receives Memphis’s pick if it is not top 8.

*** Boston receives Sacramento’s pick unless it is #1, in which case Philadelphia gets it and Boston gets Philadelphia’s #24.

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.

Overall NBA Lottery Odds of Every Pick Team 1 2 3 4 5 6 7 8 9 10 11 12 13 14 NYK 14.0% 13.4% 12.7% 11.9% 47.9% CLE 14.0% 13.4% 12.7% 11.9% 27.8% 20.1% PHX 14.0% 13.4% 12.7% 11.9% 14.8% 26.0% 7.1% CHI 12.5% 12.2% 11.9% 11.4% 7.2% 25.7% 16.8% 2.2% ATL 10.5% 10.5% 10.5% 10.5% 2.2% 19.6% 26.7% 8.8% 47.0% 24.3% 2.9% 0.1% 0.0% WAS 9.0% 9.2% 9.4% 9.6% 8.6% 29.6% 20.6% 3.8% 0.2% NOP 6.0% 6.3% 6.7% 7.2% 19.7% 37.2% 15.1% 1.6% 0.0% MEM 6.0% 6.3% 6.7% 7.2% 31.2% DAL 6.0% 6.3% 6.7% 7.2% MIN 3.0% 3.3% 3.6% 4.0% 65.9% 18.9% 1.2% 0.0% 0.0% LAL 2.0% 2.2% 2.4% 2.8% 77.6% 12.6% 0.4% 0.0% CHA 1.0% 1.1% 1.2% 1.4% 86.1% 9.0% 0.2% MIA 1.0% 1.1% 1.2% 1.4% 90.6% 4.6% BOS 1.1% 1.2% 1.4% 34.1% 8.0% 0.5% 0.0% 95.2% PHI 1.0%

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

Notes:

* Atlanta receives Dallas’s pick if it is not top 4.

** Boston receives Memphis’s pick if it is not top 8.

*** Boston receives Sacramento’s pick unless it is #1, in which case Philadelphia gets it and Boston gets Philadelphia’s #24.

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 if Sacramento wins the #2, #3, or #4 pick, 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 14th 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.