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How lucky has each franchise been in the NBA Draft Lottery?

Everything you’ve ever wanted to know about the NBA Lottery. To those who failed middle school algebra, sorry about the math.

NBA: NBA Draft Lottery Patrick Gorski-USA TODAY Sports

The NBA Draft Lottery is a strange spectacle that has nothing to do with basketball in a literal sense, but its results change the direction of a multi-million and billion dollar franchises for many years. The 2020 lottery draw won’t occur until the night of Aug. 20 — the latest it’s ever been held — and there is quite a bit of intrigue for the Atlanta Hawks, with the franchise holding the fourth-best odds at capturing the No. 1 overall pick.

Personally, I love the lottery as a math and probabilities geek. It is the only aspect of the NBA season that is purely luck, involving no skill whatsoever. The pomp and circumstance of sending the kid of an owner to sit at a podium with a lucky talisman in hand is the height of hilarious nonsense I look forward to when my team has been eliminated from postseason contention.

Although this draft class profiles as weaker than average at best, the Hawks still have the chance to land the No. 1 overall pick should the ping pong balls fall their way. This would represent the first time this has happened in the lottery era, from 1985 to the present.

There is a certain amount of fatalism among some Atlanta fans avowing that this franchise is snake-bitten, with rotten luck due at every turn. But when it comes to the lottery, how realistic has that notion been over the years? I now present the cold hard numbers to answer that very question.

Let’s dive in.

Key note: the word “lottery” is usually in reference to the entire selection of picks for the non-playoff teams but, for our purposes, I also use the word “lottery” to denote the draft picks selected by chance (for example in 2020, the first four).

The pre-lottery history

Prior to the first NBA lottery, the NBA used the reverse record of teams to determine the draft order. The only wrinkle was a territorial pick, which existed from 1949 to 1965 in which a team could opt for a local player to draft in place of their first round pick. These players had to be located within 50 miles of the franchise and were considered as being drafted before the normal draft i.e. the first territorial pick was now the first overall pick, pushing the rest of the draft selections back in sequential order.

The St. Louis Hawks used this power only once in 1959 to select Bob Ferry, who would go on to play just two seasons in a Hawks uniform en route to a 13 year NBA career. Coincidentally, he is the father of former, and somewhat infamous, general manager of the Atlanta Hawks, Danny Ferry. The NBA scrapped this method in 1966 after a rise in popularity in the league, and instead used a coin flip between the two worst records between the Eastern and Western Conferences to determine the #1 overall pick.

Despite being one of the oldest franchises in NBA history, the Hawks have only had the first pick in one draft, 1975. David Thompson was the selection there and he never played a minute with the franchise after opting to sign with the Virginia Squires of the ABA.

A common criticism in the 1970s and 80s, and one that hasn’t abated over the years, is that bad teams intentionally become transparently non-competitive to increase their standing in the draft.

You know, the ugly “T” word: tanking.

Given that one superstar player can reverse a team’s fortunes, as teams saw when the Rockets landed Hakeem Olajuwon with the first pick in the 1984 draft, the NBA formulated a solution to prevent teams from reaping the rewards of losing on purpose. Thus, the lottery was born. But the first version looked very different than the weighted lottery that is currently used.

(Caution: The mathematically disinclined may want to avert their eyes to the next two sections and scroll down straight to the interactive graphs.)

How past and current lotteries have worked

It’s taken quite a few iterations of the lottery to come to current method of selecting who ultimately picks first and beyond. Here, I’ll break the history of the lottery into four phases in order to properly analyze the percentages involved in determining the draft order. The initial implementation and every subsequent alteration of the process all were approved by the NBA Board of Governors before going into effect, as is customary.

  • 1985-1989: All non-playoff teams have an equal chance at the top spot in the lottery. In 1985 and 1986, each lottery selection was made for all teams regardless of record. For 1987-1989, only the first three selections were made and then the remaining teams would be seeded in inverse order of their records.
  • 1990-1993: Non-playoff teams were introduced to a weighted lottery system. To simplify it, the best non-playoff team would have a single chance, the next worst would have two chances et cetera until the most chances were doled out to the worst team. Three lottery selections were made and then teams were seeded according to record.
  • 1994-2018: The NBA revamped the weighted system to give the worst team 250 combinations out of 1000 possibilities using a ping-pong ball method below. Three lottery selections were made and then teams were seeded according to record.
  • 2019-present: The weighted system was flattened to give the three worst teams 140 combinations and four lottery selections are now made.

The mechanisms of the current lottery

14 ping-pong balls numbered 1 to 14 are placed in a lottery ball machine and four are drawn to create a combination. Each ball is selected and shown to the room and then the randomizer continues with the rest of the balls for 10 seconds before the next selection until four are picked.

The multi-national auditing and professional services firm Ernst & Young has run and moderated the physical selection of ping-ping balls in front of representatives from all participating teams recently as a way for the league to reinforce transparency in the process.

The combination is then interpreted from smallest-numbered ball to largest, meaning the order in which they are drawn, or the permutation, doesn’t matter. This creates 14!/(10!*4!) or 1001 possible combinations.

Each non-playoff team receives several winning combinations starting with the team with the worst record. For 2020, the worst team (the Golden State Warriors) have the combinations 1-2-3-4, 1-2-3-5, etc. up to the 140th combination. The next worst team then gets the next 140 combinations and so on. The 1001st combination (11-12-13-14) isn’t assigned to any team; i.e. a redraw will be performed if that happens.

The first team to have a combination selected gets the first pick, then the ping-pong balls are placed back into the machine for the second draw until four teams are selected. If a team is again selected after already winning a lottery spot, the result is discarded, and the selection is redrawn. For the 10 teams that don’t win a lottery selection, their draft picks then fall from 5th to 14th in order of record, worst to best.

I charted the last three iterations of the lottery since the expansion of the Vancouver Grizzlies and Toronto Raptors in 1995 below to illustrate the tweaks in the weighted lottery distribution of combinations. Assuming no teams finish with identical records, the allotment (combinations out of 1000) is as follows from worst record to best:

Combination Distribution by Year

1996-2004 2005-2018 2019-present
1996-2004 2005-2018 2019-present
250 250 140
200 199 140
157 156 140
120 119 125
89 88 105
64 63 90
44 43 75
29 28 60
18 17 45
11 11 30
7 8 20
6 7 15
5 6 10
- 5 5

However, in the case that teams finish with identical records, the lottery balls of all tied teams are added together and distributed evenly, just like winnings in a golf tournament. A tiebreaker coin flip is then performed to determine the order of finish of teams that don’t win a lottery selection. Should there be uneven combinations to distribute, a coin flip determines what team(s) has the extra combination(s). These coin flips will have occurred prior to lottery day.

All of this background was necessary for the purposes of this piece, as I ask the question: how lucky have the Hawks (and all of the other franchises) been during the lottery drawings?

Given that the inner workings of the lottery have changed over time, it’s important to take that into consideration when compiling and computing data. The key thing to remember is that multiple lottery selections makes for a range of results. This is especially true considering how infrequently the worst team has captured the number one overall pick, even if the probability is represented as a likelihood in some areas of the media.

This is why I want to popularize “expected positions” when discussing the outcome of lottery night. Essentially, this is the mean or mathematical average position in which a team is expected to land.

I compared the actual order of finish in the lottery to that expected position to give me a resulting value in terms of spots gained or lost. Think of “0” as the 50th percentile performance. This means that a positive number represents a better than average finish and a negative number means a below average finish.

For example, in 1985 there were seven lottery teams and six lottery rounds to determine order. If you average the positions between first and seventh, it results in an expected position of four. The team who finished first nets three spots over expected finish and the one who comes in seventh nets the same three spots but under expected finish, yielding a negative value.

Simple, right?

Well it gets more complicated when factoring in different lottery combinations over the years, rules surrounding expansion teams, protected picks, and pick swap options (by taking the mathematical expectation of the higher of two possible picks). Trades occurring after lottery day aren’t included here (like the Celtics and 76ers swap centered around the #1 and #3 picks in 2017) but ones either executed or widely reported prior to the lottery are.

To show you how these factors change expected position over time, I point to 2018 and 2019. The worst team entering the 2018 NBA Lottery was the Phoenix Suns, the owners of 250 winning combinations. They had a 25% chance at landing first, 21.5% chance at second, 17.7% at third and 35.8% at missing out on the three lottery selections and finishing fourth. This expected finish averaged out to 2.64. They finished first for a net of 1.64 spots above expectation.

Contrast that with the 2019 New York Knicks, owners of just 140 combinations in a flattened odds lottery environment as compensation for their league worst record. They had a chance to slide all the way to fifth, and an overall expected position of 3.66 (which they exceed by landing third).

I compiled all these odds from 1985-2019 using RealGM’s lottery database (extremely helpful for determining which of two or more teams with identical records won coin flips) and computed the expected lottery position for each franchise over this span. This includes relocating franchises, like the Seattle Supersonics moving to Oklahoma City. One note is that both Charlotte franchises (i.e. the Hornets that left for New Orleans in 2002 and the current Hornets) are treated as one, just as it appears in the NBA record books.

(You may want to blow up the interactive using the button in the bottom-right, and then scroll across to see all 30 franchises for all years of lottery performance.)

Ultimately, the Hawks grade out as the 11th-unluckiest franchise, losing a total of 3.74 spots in order from where they were expected to finish since 1985. Historically speaking, their biggest rise was in 2001, jumping from the fifth-best lottery odds to third, a pickup of 1.66 expected positions. The Hawks’ biggest slide occurred this past year, falling from the fifth-best lottery odds way down to eighth with their own pick and ninth to tenth with Dallas’ top-5 protected pick, losing 2.15 expected positions.

The most unlucky franchise has been the Dallas Mavericks, who have only once finished above their expected position in 15 lottery appearances way back in 1994 and have lost a cumulative total of 14.79 equivalent spots.

The luckiest franchise is the aforementioned Charlotte Hornets, who have been helped by 17.17 spots above expected finish since their inception in 1988. If we just look at luck per appearance in the lottery, however, it won’t shock most people to learn the Spurs have had the best performance, gaining a whopping average of 2.29 spots above expectation across each of their three tries. The full chart is below, separated by cumulative performance and per lottery appearance performance.

So there you have it, a quantitative representation of the only purely luck driven event in the NBA calendar. Here’s to the lottery balls falling in your favorite team’s favor in 2020’s lottery draw.