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# Inside The Numbers: 2007 Draft Lottery Demystified

Celtics.com recently sat down with Celtics Basketball Operations Analyst Mike Zarren to learn about how the NBA Draft Lottery works. This year's Draft Lottery will be held on Tuesday, May 22nd, in Secaucus, New Jersey.

Q: So what actually happens at the draft lottery?

MZ: Here's my explanation from last year: 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 previously-held drawing. 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 our own second-round pick. In future years, we have the rights to all our own picks, Portland's 2008 second-round pick, and a future Minnesota pick, but this Minnesota pick cannot be received any earlier than 2010 (MIN pick details here).

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

MZ: We finished with the second-worst record in the league. 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 199/750=26.5% chance to win the second pick, but if the 14th-worst team, which has only 5 combinations assigned to it, wins, we have only an 199/995=20.0% 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 199 combinations, the Celtics have a 19.9% chance of getting the top pick, an 18.8% chance of getting the 2nd pick, and a 17.1% chance of getting the 3rd pick. This means that entering the lottery, we have a 38.7% chance of getting a top 2 pick, and a 55.8% chance of getting a top 3 pick.

NBA Draft Lottery Odds
Memphis 250 25.0% 21.5% 17.8% 46.5% 64.3%
Boston 199 19.9% 18.8% 17.1% 38.7% 55.8%
Milwaukee 156 15.6% 15.7% 15.6% 31.3% 46.9%
Atlanta 119 11.9% 12.6% 13.3% 24.5% 37.8%
Seattle 88 8.8% 9.7% 10.7% 18.5% 29.1%
Portland 53 5.3% 6.0% 7.0% 11.3% 18.3%
Minnesota 53 5.3% 6.0% 7.0% 11.3% 18.3%
Charlotte 19 1.9% 2.2% 2.7% 4.1% 6.8%
New York 19 1.9% 2.2% 2.7% 4.1% 6.8%
Sacramento 18 1.8% 2.1% 2.5% 3.9% 6.5%
Indiana 8 0.8% 0.9% 1.2% 1.7% 2.9%
Philadelphia 7 0.7% 0.8% 1.0% 1.5% 2.5%
New Orleans 6 0.6% 0.7% 0.9% 1.3% 2.2%
LA Clippers 5 0.5% 0.6% 0.7% 1.1% 1.8%

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 Memphis (the only team with a worse record than the Celtics had) is in the top 3 but we are not, we will be pushed down to 4th. And if the top three picks all go to teams with better records than the Celtics had, then we will draft 5th, though there is only a 12% chance of that happening. Our overall draft lottery odds look like this:

## Celtics' Chances Of Receiving Each Possible Pick

Celtics' Odds Of Receiving
Each Possible Pick
PickProbability
119.9%
218.8%
317.1%
431.9%
512.4%

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, 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. For example, last year Minnesota and the Celtics finished tied for the 6th- and 7th-worst records. Instead of one team getting 63 combos and the other 43, both teams had 53 combinations. While this doesn't affect us this year, it does affect a bunch of teams in the table below, which is why you can't just use a table from last year.

Chances of Getting Specific Picks
Team1234567891011121314
Memphis25%22%18%36%xxxxxxxxxx
Boston20%19%17%32%12%xxxxxxxxx
Milwaukee16%16%16%23%26%4%xxxxxxxx
Atlanta12%13%13%10%35%16%1%xxxxxxx
Seattle9%10%11%x27%36%8%0%xxxxxx
Portland5%6%7%xx44%33%4%0%xxxxx
Minnesota5%6%7%xxx57%23%2%0%xxxx
Charlotte2%2%3%xxxx72%20%1%0%xxx
New York2%2%3%xxxxx78%14%0%0%xx
Sacramento2%2%3%xxxxxx85%9%0%0%x
Indiana1%1%1%xxxxxxx91%6%0%0%
New Orleans1%1%1%xxxxxxxxx96%2%
LA Clippers1%1%1%xxxxxxxxxx98%

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

Also, some of these probabilities may change a bit following a random drawing to be held at the league offices on Friday April 20th (live on NBATV) - if two teams are tied and the total combinations between their two spots is an odd number, one team will get one more combo than the other based on the random drawing. So the table here just picks randomly between tied teams for the extra combo; we'll update it to reflect the draw when it happens.

Finally, previous trades affect several of these spots, as follows:

1. The Bulls have the right to swap first-round picks with the Knicks.
2. Indiana's first-round pick will go to Atlanta if it's not in the top 10.
3. Atlanta's first-round pick will go to Phoenix if it's not in the top 3.

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. Since we had the second-worst record in the league and were not tied with another team this year, we'll be drafting 32nd.

(If this pick had been worse than Golden State's, we would have had Golden State's pick, pursuant to the terms of the draft-day deal with Denver that allowed us to acquire Leon Powe -- we had to send the less favorable of our 2007 second-round pick or Golden State's 2007 second-round pick to Denver in exchange for Powe. But since Golden State's pick will be worse than ours, we'll be keeping our own pick, and sending Golden State's pick (which we acquired from Phoenix in exchange for Walter McCarty -- Phoenix had acquired it from Golden State in exchange for Zarko Cabarkapa) to Denver. Isn't this fun?)

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 we still have a second-round pick, and 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 (yes, I'll be working with a lot of statistics), so that Danny 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 22nd on ESPN. (check local listings for time)

Michael Zarren is the Celtics' Basketball Operations Analyst, responsible for assisting team decisionmaking through the use of quantitative and legal analyses.