Draft Lottery

Boston Celtics

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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 &amp; 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.

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.

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 &gt;0 probability where a blank space equals no probability.

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 &amp; 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 &amp; Team Counsel.

David Sparks is the Celtics’ Director of Basketball Analytics.

inside-the-numbers-draft-lottery-and-draft-position-qa-3

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 &amp; 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.

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

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 we do not receive the Lakers’ pick, we will just have our own pick at #27.

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 &amp; 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 &amp; Team Counsel.

David Sparks is the Celtics' Director of Basketball Analytics.

inside-the-numbers-draft-lottery-and-draft-position-qa-2

addByline("Mike Zarren", "Celtics.com", "Celtics");

Celtics fans are the best fans in the league, and they’re also some of the craziest. Even though the ping-pong drawing for the Draft Lottery is not done on TV, a number of my crazy friends have contacted me, eager to find out which ping-pong ball combinations would be assigned to the team so that fans could light a certain number of candles on Tuesday, or arrange rocks in their front lawn in the shape of a particular combo, or smoke some number of Hoyo de Monterrey cigars on each of the four days before the lottery, or whatever. I’m not sure any of this is smart (I’m pretty sure smoking up to 14 cigars in a day is not) but as a lifelong Celtics season ticket holder I’m not one to stand in the way of a good sports superstition, so we asked the league and were able to obtain the tables of combos for each team.

Therefore, for the first time anywhere available to the public, and exclusively on Celtics.com, here are the ping-pong combinations that will lead to the Celtics winning a lottery pick. To read how the lottery works, click click here.
 Otherwise, feel free to root, pray, or hope for your favorite one of the combinations below in whatever (legal) way you think best. And be sure to root against any ping pong balls under number 7 – none of our combinations include these.

All 250 of the Celtics’ Draft Lottery Combinations:
(order doesn’t matter since there is only one ball for each number)

Michael Zarren is the Celtics’ Assistant General Manager &amp; Team Counsel

inside-the-numbers-2018-draft-lottery-combos

Inside The Numbers: 2018 Draft Lottery Combos

Taylor Snow

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WALTHAM, Mass. – Just when you thought the Boston Celtics couldn’t experience any greater fortune this season, they hit the lottery Tuesday night by securing the No. 1 overall pick in the 2017 NBA Draft.

The Celtics entered the Draft Lottery with the greatest odds – a 25 percent chance –of earning the top selection in the Draft. The best-case scenario played out exactly as hoped, as the ping-pong balls fell Boston’s way for the first time in franchise history.

Now, the thinking process will begin for the Celtics’ front office as it prepares for the Draft. Moments after the results were revealed, C’s President of Basketball Operations Danny Ainge said that his staff has a tough decision come late June. By no means have they made up their mind on who they will select No. 1.

“I think it’s a little bit deeper,” Ainge said of the 2017 Draft Class. “I think the top of the draft isn’t as obvious as some, and it’s more obvious than others – the lines of separation through this draft. But I think that it’s going to be a tough choice for us where we sit at No. 1.”

Some of the top projected players in the draft class include Lonzo Ball (UCLA), Markelle Fultz (Washington), Josh Jackson (Kansas) and Jayson Tatum (Duke). Each of those players are coming off of their freshman NCAA season, and Ainge says he has seen each of them play five to seven times in person.

Ainge admitted that he was tempted to trade the pick away in February at the trade deadline. However, by waiting until after the Lottery, there is now more clarity with draft positioning, so now the pick is more valuable should the team decide to trade it.

“Sometimes you need to be patient,” Ainge reflected. “It’s hard to be patient. I like action. But we have a good group of guys around us; my whole staff and the ownership, we sit and we calmly try to figure out what the best path is to take.”

Regardless of if the Celtics want to use the pick or trade it, they are in incredible position to succeed over the next several seasons.

Just four years into their rebuild, the C’s have already risen to be among the top tier of teams in the NBA. They are currently one of four squads remaining in the Playoffs, and are just four wins away from a berth in the NBA Finals.

On top of that, Boston is the youngest No. 1 seed in the last 40 years and is also the first conference finalist to pick first overall since 1982, when the Lakers selected James Worthy.

“I think we’ve had a lot of good fortune and we have a terrific coach who’s been a part of that process,” said Ainge. “We have a lot of good players. It’s been fun watching the guys develop.

"And the organization is a great organization," he added. "Our owners are fantastic. They give us all the support, security, and really built a steady organization.”

Boston’s basketball operations staff will look to strengthen the organization even more in late June by using their top draft pick, which they acquired in a trade with Brooklyn during the summer of 2013. They also own the 37th pick (from Minnesota), the 53rd pick (from Cleveland) and the 56th pick (from the LA Clippers) in the Draft.

In the meantime, the Celtics have an Eastern Conference title on their minds, as they prepare to take on the Cleveland Cavaliers Wednesday night in Game 1 of the Eastern Conference Finals.

ainge-all-smiles-as-celtics-earn-no-1-pick

Ainge All Smiles as Celtics Earn No. 1 Pick

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.

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 &amp; 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.

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).

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.

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

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.

Celtics' Chances of Receiving Each Possible Pick

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 &gt;0 probability where blank space equals no probability.

Here are two charts that show 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. 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.

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 &amp; 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)

inside-the-numbers-draft-lottery-and-draft-position-qa-4

Celtics fans are the best fans in the league, and they’re also some of the craziest. Even though the ping-pong drawing for the Draft Lottery is not done on TV, a number of my crazy friends have contacted me, eager to find out which ping-pong ball combinations would be assigned to the team so that fans could light a certain number of candles on May 16th, or arrange rocks in their front lawn in the shape of a particular combo, or smoke some number of Hoyo de Monterrey cigars on each of the four days before the lottery, or whatever. I’m not sure any of this is smart (I’m pretty sure smoking up to 14 cigars in a day is not) but as a lifelong Celtics season ticket holder I’m not one to stand in the way of a good sports superstition, so we asked the league and were able to obtain the tables of combos for each team.

Therefore, for the first time anywhere available to the public, and exclusively on Celtics.com, here are the ping-pong combinations that will lead to the Celtics winning a lottery pick. To read how the lottery works, click click here. Otherwise, feel free to root, pray, or hope for your favorite one of the combinations below in whatever (legal) way you think best. And be sure to root for ping-pong ball #1 – all of our combinations include it, and if it’s drawn we have an 86% chance of winning.

inside-the-numbers-2017-draft-lottery-combos

Inside The Numbers: 2017 Draft Lottery Combos

WALTHAM, Mass. – The Boston Celtics entered Tuesday night’s NBA Draft Lottery with the third-best odds of landing the top pick in the 2016 Draft, and the ping-pong balls fell exactly as projected.

Boston, which owns Brooklyn’s first-round selection via a trade between the two teams in 2013, was awarded with the No. 3 pick – the highest it has earned since 1997.

It marks a huge step for the organization, which is hoping to make some splashes this offseason in an effort to improve a team that has made the Playoffs in two consecutive seasons, and once again establish itself as a championship contender.

Whether Boston opts to keep the pick and seek out a young prospect via the Draft, or trade it to another team for established NBA talent, president of basketball Danny Ainge says the team is in great position to improve and he is excited about the opportunity to have a high selection in this year’s Draft.

“The picture is more clear for sure,” Ainge said moments after Boston’s Draft position was revealed.

“Still,” he added, “the Draft is uncertain, just by its nature when you’re oftentimes drafting kids that are so young. So there’s a lot of uncertainty about the future and everybody’s future in the NBA and what players that we draft – there are no guarantees. But we like this draft, we’re excited about this No. 3 pick.”

Another member of the organization who is excited about the pick is the man that represented the C’s at the lottery in New York –Isaiah Thomas.

The All-Star point guard expressed relief after stepping away from his podium, as he understood that Boston’s selection could have fallen as low as No. 6. Now that the C’s possess a top-three pick, he knows there is great opportunity for the franchise to improve and take the next steps to becoming a title contender.

“I’m looking forward to seeing what Danny and the front office is going to do to make us a better team in whatever we do in the Draft and free agency,” he told the media shortly after the announcement. “I think it’s going to make our team that much better. We gotta take that next step.”

While Ainge admitted that possessing the No. 1 or 2 pick would have been nice, he noted that this year’s Draft will be loaded with high-potential prospects.

“We believe that a good player will come out of this Draft,” said Ainge. “Yeah, we were holding out for a short hope there to get the No. 1 or 2 pick, but the No. 3 pick is a very good player and we have our eyes set on a handful of guys.”

As of now, a few of the top prospects include Dragan Bender, Jaylen Brown, Kris Dunn, Buddy Hield, Brandon Ingram, Jamal Murray and Ben Simmons, though other outstanding prospects may certainly emerge over the next few weeks during the pre-Draft workout process.

“There’s still a lot of evaluation,” said Ainge. “When you’re looking and evaluating, in some cases 18- and 19-year-old kids, there’s a lot that changes between the end of their college careers and the Draft. So I wouldn’t say anything is in stone in how the draft order is going to go, and so we’ll just evaluate them all and see how it goes.”

The next few weeks will be critical, as the C’s plan to hold a number of pre-Draft workouts in preparation for the Draft on June 23. Boston possesses a total of eight draft picks, including three selections in the first 23 picks.

Be sure to stay tuned for coverage of those workouts, as well as our annual Draft Profile Series that features in-depth looks at many of the top prospects.

celtics-awarded-no-3-pick-in-2016-draft

Celtics Awarded No. 3 Pick in 2016 Draft

Celtics fans are by far the best fans in the league, but they’re also some of the craziest. Even though the ping-pong drawing for the Draft Lottery is not done on TV, a number of my crazy friends have contacted me, eager to find out which ping-pong ball combinations would be assigned to the team so that fans could light a certain number of candles on May 17th, or arrange rocks in their front lawn in the shape of a particular combo, or smoke some number of Hoyo de Monterrey cigars on each of the four days before the lottery, or whatever. I’m not sure any of this is smart (I’m pretty sure smoking up to 14 cigars in a day is not) but as a lifelong Celtics season ticket holder I’m not one to stand in the way of a good sports superstition, so we asked the league and were able to obtain the tables of combos for each team.

Therefore, for the first time anywhere available to the public, and exclusively on Celtics.com, here are the ping-pong combinations that will lead to the Celtics winning a lottery pick. To read how the lottery works, click here. Otherwise, feel free to root, pray, or hope for your favorite one of the combinations below in whatever (legal) way you think best.

All 156 of the Celtics’ Draft Lottery Combinations:
(order doesn’t matter since there is only one ball for each number)

Draft Lottery

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

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

Inside The Numbers: 2018 Draft Lottery Combos

Ainge All Smiles as Celtics Earn No. 1 Pick

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

Inside The Numbers: 2017 Draft Lottery Combos

Celtics Awarded No. 3 Pick in 2016 Draft

Inside The Numbers: 2016 Draft Lottery Combos