Probing the Probabilities
April 20, 2010
EAST RUTHERFORD, N.J.—The season of struggle has given way to an offseason of optimism, and it begins by Looking Toward the Lottery. During the next few weeks, NJNets.com will take you through the process with our ongoing series. Stay tuned for more!
Probing the Probabilities
The NBA Draft Lottery is a 1,000-combination free-for-all to determine the top three picks in the ensuing NBA Draft. We all know that this year, the Nets have the highest percentage of combinations (250) of any one of the 14 lottery teams, which include:
(out of 1,000)
(To Utah via Phoenix)
Now that we’ve got the participants and their combinations broken down, it’s time to figure out exactly what this means for the Nets. We know they’ve got the 27th and 31st picks locked in: Dallas, which owes the Nets their first-round pick to complete the Devin Harris/Jason Kidd trade from 2008, finished with the league’s fourth-best record (55-27); regardless of the lottery, with no tie, the Nets will choose first in the second round.
According to an NBA release from last year, here’s “What Will Happen” on May 18 – four weeks from today:
Fourteen ping-pong balls, numbered 1 through 14, will be placed in a drum. There are 1,001 possible combinations when four balls are drawn out of 14, without regard to their order of selection. Prior to the Lottery, 1,000 combinations will be assigned to the 14 participating Lottery teams by a computer.
Then four balls will be drawn to the top to determine a four-digit combination. The team assigned that combination will receive the No. 1 pick. The four balls are placed back in the drum and the process is repeated to determine the No. 2 and 3 picks. (Note: If the one unassigned combination is drawn, the balls are drawn to the top again.)
The NBA provides generic lottery odds for the 14 lottery teams, and though the chart doesn’t account for ties, all three this year – Warriors/Wizards, 76ers/Pistons and Clippers/Knicks (a.k.a Utah) – occur outside the top three, so they shouldn’t impact the Nets’ odds by too much. Let’s take a look at the Nets’ percentages of them landing a top pick, along with the chances of the balls bouncing a different direction and the Nets settling in fourth:
(Team No. 1)
|Odds per 1,000||Probability of Pick|
|No. 1||No. 2||No. 3||No. 4|
This shows that in a vacuum, the Nets have a better chance of finishing 1st or 2nd (46.51% combined) as they do finishing 4th. And the odds favor a top-three pick (64.28%) for the franchise. The odds decrease from No. 1 to No. 3 due to the more limited amount of winning combinations available as the picks are determined; the Nets’ probability (250 of 1,000) remains the same, though the number of outcomes that produce a redraw increase (by say … 199 if the Timberwolves win the No. 1 pick, 156 if the Kings win, etc.)*
*Or not! If you have a better handle on the math, feel free to hit us up by e-mailing email@example.com to let us know what’s really good.
However, all this goes out the window once a team is awarded the first pick, because you then need the specific formula rather than the generic one. The Nets’ percentage for the following pick then skews a bit higher or lower depending on the number of winning combinations that become neutral.
Only two times since 1991 has the team with the most chances landed the top pick: Cleveland in 2003, when they selected LeBron James, and Orlando in 2004, when they opted for Dwight Howard. Last season, the Kings had the most combinations (250) followed by the Wizards (178) and Clippers (177). Los Angeles jumped to No. 1 (17.7% odds), the Grizzlies (78 combinations) leapfrogged four teams to No. 2 (8.33%) and the Thunder (119 combinations) jumped into the No. 3 spot (13.24%), leaving Sacramento fourth (35.82%) and Washington fifth (13.73%).
Two years ago, the ninth-slotted Bulls leapt to No. 1 despite holding only 17 combinations – a 1.7 percent chance! Miami, which held the leader’s 250, dropped down only one spot, while Minnesota (138) stayed at three as Seattle (199) slipped to No. 4.