For a few years I've been pretty interested in the question of which teams have had the best luck in the lottery, and which teams have had the worst. I've finally gotten around to answering the question, and I may as well tell everybody what I found. But let's start with a bit of background and at least enough methodology that you'll know what I'm talking about.
Lottery Mechanics
The NBA instituted the "ping-pong ball" lottery in 1990, in response to negative reaction to the "envelope" lottery used from 1985-1989, where every team had the same chance (and where David Stern was accused the very first drawing of deliberately choosing the Knicks' envelope to give them Patrick Ewing). This means we have 25 years worth of data for the ping-pong lottery.
For the first four years, there were 11 teams in the lottery and a total of 66 balls (11 for the team with the worst record, 10 for the team with the second-worst record, on down to 1 for the lottery team with the best record). After that, the system changed to a combo-based system, where the lottery machine only has fourteen balls (labeled 1-14) and a varying number of combos (e.g. 1-2-3-4) are assigned to each team based on their regular-season record. There are a total of 1001 possible combinations. Of these 1000 combos are assigned to the various teams. The team with the worst record gets 250 combos and the team with the best record gets 5 combos with varying values in between (these values have changed slightly as the number of teams in the league, and thus the lottery, has changed over the years). The final combo (11-12-13-14) is unassigned. If the unassigned combo or a combo belonging to a team that has already been selected is chosen, the lottery is repeated until a valid draw occurs.
Only the top three positions in the draft are determined by lottery. If one of your combos (or balls, in the early years) is selected first, second, or third, you draft in that position. Draft positions 4 to the end of the lottery are determined by the records of the remaining teams, worst record first.
What I did
I found the actual number of lotto balls earned by every team in every one of the 25 ping-pong lotteries. Note that some picks end up getting traded. If a pick was conditionally traded (whether or not it was conveyed depended on the results of the lottery), or traded after the lottery, I assigned it to the team who originally owned it. If a pick was unconditionally traded BEFORE the lottery, I assigned it to the team that received it. Franchise continuity was retained (e.g. OKC and Seattle are the same "team", the Bobcats/Hornets are separate from the Hornets/Pelicans). Using each team's actual number of lotto balls in each year, I calculated several values which appear in the table below:
Apps - Number of appearances in the lottery
Shares - The sum total number of combos/balls in team history, normalized to the number of combos/balls in each lottery. Thus, a team that had a single ball in the early lotto gets 1/66 of a share; a team with five combos in the current lottery gets 5/1000 of a share.
1/2/3 - The number of first, second, and third finishes
Net dStart - The total number of positions the team has moved in the lottery, relative to their starting position. Positive numbers mean that a team has overall moved up. This measures how much a team has moved, relative to the case where there is no lottery at all.
Mean dStart - Net dStart divided by appearances, the average movement relative to no lottery
Net dExp - The total number of positions the team has moved in the lottery, relative to their expected position. Note that expected position is based on the actual lotto combos and differs from start position. For instance, the team with the #1 lotto position is currently expected to pick at about 2.64, because they are only expected to win 25% of the time. This value measures how much a team has moved, relative to their average position if the lottery had been run millions of times.
Mean dExp - Net dExp divided by appearances. This is probably the best measure of "luck", though the number of team appearances ought to be taken into account.
The Data
Team | Apps | Shares | 1/2/3 | Net dStart | Mean dStart | Net dExp | Mean dExp
------------------------------------------------------------------------------
SAS .|.. 1 .|. 0.16 .| 1 0 0 |..... 2 ....|.... 2.00 ...|... 2.40 .|.. 2.40
NOP .|. 13 .|. 0.74 .| 2 1 1 |.... 19 ....|.... 1.46 ...|.. 17.39 .|.. 1.34
CHI .|.. 9 .|. 1.31 .| 2 2 1 |..... 4 ....|.... 0.44 ...|... 8.71 .|.. 0.97
OKC .|.. 9 .|. 0.46 .| 0 2 1 |..... 9 ....|.... 1.00 ...|... 7.96 .|.. 0.88
CLE .|. 14 .|. 0.96 .| 4 0 0 |.... 12 ....|.... 0.86 ...|.. 12.09 .|.. 0.86
ORL .|. 13 .|. 1.18 .| 3 1 0 |..... 6 ....|.... 0.46 ...|.. 10.08 .|.. 0.78
POR .|.. 7 .|. 0.42 .| 1 0 1 |..... 5 ....|.... 0.71 ...|... 4.86 .|.. 0.69
PHI .|. 13 .|. 0.16 .| 1 3 2 |.... 11 ....|.... 0.85 ...|... 8.87 .|.. 0.68
BRK .|. 11 .|. 0.86 .| 2 1 1 |..... 5 ....|.... 0.45 ...|... 5.40 .|.. 0.49
MEM .|. 13 .|. 1.77 .| 0 5 1 |..... 0 ....|.... 0.00 ...|... 5.02 .|.. 0.39
LAC .|. 17 .|. 1.56 .| 2 3 1 |..... 4 ....|.... 0.24 ...|... 4.09 .|.. 0.24
HOU .|.. 8 .|. 0.17 .| 1 0 0 |..... 4 ....|.... 0.50 ...|... 1.73 .|.. 0.22
ATL .|.. 9 .|. 0.86 .| 1 0 0 |..... 0 ....|.... 0.00 ...|.. -1.38 .|. -0.15
MIL .|. 16 .|. 1.07 .| 2 1 0 |..... 0 ....|.... 0.00 ...|.. -2.76 .|. -0.17
IND .|.. 5 .|. 0.04 .| 0 0 0 |..... 0 ....|.... 0.00 ...|.. -1.02 .|. -0.20
TOR .|. 14 .|. 1.05 .| 1 1 0 |.... -2 ....|... -0.14 ...|.. -2.93 .|. -0.21
UTA .|.. 8 .|. 0.34 .| 0 0 1 |..... 0 ....|.... 0.00 ...|.. -1.79 .|. -0.22
WAS .|. 17 .|. 1.70 .| 2 0 2 |.... -4 ....|... -0.24 ...|.. -3.67 .|. -0.22
GSW .|. 18 .|. 0.16 .| 1 0 2 |.... -2 ....|... -0.11 ...|.. -4.41 .|. -0.25
CHA .|.. 9 .|. 0.84 .| 0 1 1 |.... -6 ....|... -0.67 ...|.. -3.86 .|. -0.43
DAL .|. 11 .|. 0.88 .| 0 1 0 |.... -6 ....|... -0.55 ...|.. -5.06 .|. -0.46
NYK .|.. 6 .|. 0.20 .| 0 0 0 |.... -1 ....|... -0.17 ...|.. -2.96 .|. -0.49
PHO .|.. 8 .|. 0.26 .| 0 0 0 |.... -2 ....|... -0.25 ...|.. -4.24 .|. -0.53
MIA .|.. 7 .|. 0.76 .| 0 1 1 |.... -7 ....|... -1.00 ...|.. -4.34 .|. -0.62
MIN .|. 18 .|. 0.16 .| 0 1 2 |... -15 ....|... -0.83 ...|. -11.27 .|. -0.63
LAL .|.. 3 .|. 0.08 .| 0 0 0 |.... -1 ....|... -0.33 ...|.. -1.97 .|. -0.66
DEN .|. 10 .|. 0.16 .| 0 0 2 |... -10 ....|... -1.00 ...|.. -6.81 .|. -0.68
BOS .|. 10 .|. 0.70 .| 0 0 1 |.... -6 ....|... -0.60 ...|.. -7.17 .|. -0.72
DET .|. 10 .|. 0.46 .| 0 0 1 |.... -5 ....|... -0.50 ...|.. -7.82 .|. -0.78
SAC .|. 16 .|. 1.21 .| 0 0 1 |... -14 ....|... -0.88 ...|. -15.15 .|. -0.95
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So there you have it: Relative to expected position, the Kings are by far the unluckiest team over the entire 25 years of the lottery. Minnesota has moved more spots from their start position (but fewer expected spots) and Denver and Miami have moved more spots from their start position on average - so these teams have slightly more complaint about the fact that there is a lottery system at all than we do, but nobody has more room to complain about the bounces of the balls than us.
Disclaimer: I do not endorse any conspiracy theory surrounding the lottery process. Each team in the lottery has a representative present who monitors the entire draw, so there is no "assignment" of picks, and the somewhat haphazard combo system basically ensures that rigging the balls would be nearly impossible. Somebody has to be last. It just happens to be us.
Lottery Mechanics
The NBA instituted the "ping-pong ball" lottery in 1990, in response to negative reaction to the "envelope" lottery used from 1985-1989, where every team had the same chance (and where David Stern was accused the very first drawing of deliberately choosing the Knicks' envelope to give them Patrick Ewing). This means we have 25 years worth of data for the ping-pong lottery.
For the first four years, there were 11 teams in the lottery and a total of 66 balls (11 for the team with the worst record, 10 for the team with the second-worst record, on down to 1 for the lottery team with the best record). After that, the system changed to a combo-based system, where the lottery machine only has fourteen balls (labeled 1-14) and a varying number of combos (e.g. 1-2-3-4) are assigned to each team based on their regular-season record. There are a total of 1001 possible combinations. Of these 1000 combos are assigned to the various teams. The team with the worst record gets 250 combos and the team with the best record gets 5 combos with varying values in between (these values have changed slightly as the number of teams in the league, and thus the lottery, has changed over the years). The final combo (11-12-13-14) is unassigned. If the unassigned combo or a combo belonging to a team that has already been selected is chosen, the lottery is repeated until a valid draw occurs.
Only the top three positions in the draft are determined by lottery. If one of your combos (or balls, in the early years) is selected first, second, or third, you draft in that position. Draft positions 4 to the end of the lottery are determined by the records of the remaining teams, worst record first.
What I did
I found the actual number of lotto balls earned by every team in every one of the 25 ping-pong lotteries. Note that some picks end up getting traded. If a pick was conditionally traded (whether or not it was conveyed depended on the results of the lottery), or traded after the lottery, I assigned it to the team who originally owned it. If a pick was unconditionally traded BEFORE the lottery, I assigned it to the team that received it. Franchise continuity was retained (e.g. OKC and Seattle are the same "team", the Bobcats/Hornets are separate from the Hornets/Pelicans). Using each team's actual number of lotto balls in each year, I calculated several values which appear in the table below:
Apps - Number of appearances in the lottery
Shares - The sum total number of combos/balls in team history, normalized to the number of combos/balls in each lottery. Thus, a team that had a single ball in the early lotto gets 1/66 of a share; a team with five combos in the current lottery gets 5/1000 of a share.
1/2/3 - The number of first, second, and third finishes
Net dStart - The total number of positions the team has moved in the lottery, relative to their starting position. Positive numbers mean that a team has overall moved up. This measures how much a team has moved, relative to the case where there is no lottery at all.
Mean dStart - Net dStart divided by appearances, the average movement relative to no lottery
Net dExp - The total number of positions the team has moved in the lottery, relative to their expected position. Note that expected position is based on the actual lotto combos and differs from start position. For instance, the team with the #1 lotto position is currently expected to pick at about 2.64, because they are only expected to win 25% of the time. This value measures how much a team has moved, relative to their average position if the lottery had been run millions of times.
Mean dExp - Net dExp divided by appearances. This is probably the best measure of "luck", though the number of team appearances ought to be taken into account.
The Data
Team | Apps | Shares | 1/2/3 | Net dStart | Mean dStart | Net dExp | Mean dExp
------------------------------------------------------------------------------
SAS .|.. 1 .|. 0.16 .| 1 0 0 |..... 2 ....|.... 2.00 ...|... 2.40 .|.. 2.40
NOP .|. 13 .|. 0.74 .| 2 1 1 |.... 19 ....|.... 1.46 ...|.. 17.39 .|.. 1.34
CHI .|.. 9 .|. 1.31 .| 2 2 1 |..... 4 ....|.... 0.44 ...|... 8.71 .|.. 0.97
OKC .|.. 9 .|. 0.46 .| 0 2 1 |..... 9 ....|.... 1.00 ...|... 7.96 .|.. 0.88
CLE .|. 14 .|. 0.96 .| 4 0 0 |.... 12 ....|.... 0.86 ...|.. 12.09 .|.. 0.86
ORL .|. 13 .|. 1.18 .| 3 1 0 |..... 6 ....|.... 0.46 ...|.. 10.08 .|.. 0.78
POR .|.. 7 .|. 0.42 .| 1 0 1 |..... 5 ....|.... 0.71 ...|... 4.86 .|.. 0.69
PHI .|. 13 .|. 0.16 .| 1 3 2 |.... 11 ....|.... 0.85 ...|... 8.87 .|.. 0.68
BRK .|. 11 .|. 0.86 .| 2 1 1 |..... 5 ....|.... 0.45 ...|... 5.40 .|.. 0.49
MEM .|. 13 .|. 1.77 .| 0 5 1 |..... 0 ....|.... 0.00 ...|... 5.02 .|.. 0.39
LAC .|. 17 .|. 1.56 .| 2 3 1 |..... 4 ....|.... 0.24 ...|... 4.09 .|.. 0.24
HOU .|.. 8 .|. 0.17 .| 1 0 0 |..... 4 ....|.... 0.50 ...|... 1.73 .|.. 0.22
ATL .|.. 9 .|. 0.86 .| 1 0 0 |..... 0 ....|.... 0.00 ...|.. -1.38 .|. -0.15
MIL .|. 16 .|. 1.07 .| 2 1 0 |..... 0 ....|.... 0.00 ...|.. -2.76 .|. -0.17
IND .|.. 5 .|. 0.04 .| 0 0 0 |..... 0 ....|.... 0.00 ...|.. -1.02 .|. -0.20
TOR .|. 14 .|. 1.05 .| 1 1 0 |.... -2 ....|... -0.14 ...|.. -2.93 .|. -0.21
UTA .|.. 8 .|. 0.34 .| 0 0 1 |..... 0 ....|.... 0.00 ...|.. -1.79 .|. -0.22
WAS .|. 17 .|. 1.70 .| 2 0 2 |.... -4 ....|... -0.24 ...|.. -3.67 .|. -0.22
GSW .|. 18 .|. 0.16 .| 1 0 2 |.... -2 ....|... -0.11 ...|.. -4.41 .|. -0.25
CHA .|.. 9 .|. 0.84 .| 0 1 1 |.... -6 ....|... -0.67 ...|.. -3.86 .|. -0.43
DAL .|. 11 .|. 0.88 .| 0 1 0 |.... -6 ....|... -0.55 ...|.. -5.06 .|. -0.46
NYK .|.. 6 .|. 0.20 .| 0 0 0 |.... -1 ....|... -0.17 ...|.. -2.96 .|. -0.49
PHO .|.. 8 .|. 0.26 .| 0 0 0 |.... -2 ....|... -0.25 ...|.. -4.24 .|. -0.53
MIA .|.. 7 .|. 0.76 .| 0 1 1 |.... -7 ....|... -1.00 ...|.. -4.34 .|. -0.62
MIN .|. 18 .|. 0.16 .| 0 1 2 |... -15 ....|... -0.83 ...|. -11.27 .|. -0.63
LAL .|.. 3 .|. 0.08 .| 0 0 0 |.... -1 ....|... -0.33 ...|.. -1.97 .|. -0.66
DEN .|. 10 .|. 0.16 .| 0 0 2 |... -10 ....|... -1.00 ...|.. -6.81 .|. -0.68
BOS .|. 10 .|. 0.70 .| 0 0 1 |.... -6 ....|... -0.60 ...|.. -7.17 .|. -0.72
DET .|. 10 .|. 0.46 .| 0 0 1 |.... -5 ....|... -0.50 ...|.. -7.82 .|. -0.78
SAC .|. 16 .|. 1.21 .| 0 0 1 |... -14 ....|... -0.88 ...|. -15.15 .|. -0.95
---------------------------------------------------------------------------
So there you have it: Relative to expected position, the Kings are by far the unluckiest team over the entire 25 years of the lottery. Minnesota has moved more spots from their start position (but fewer expected spots) and Denver and Miami have moved more spots from their start position on average - so these teams have slightly more complaint about the fact that there is a lottery system at all than we do, but nobody has more room to complain about the bounces of the balls than us.
Disclaimer: I do not endorse any conspiracy theory surrounding the lottery process. Each team in the lottery has a representative present who monitors the entire draw, so there is no "assignment" of picks, and the somewhat haphazard combo system basically ensures that rigging the balls would be nearly impossible. Somebody has to be last. It just happens to be us.
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