The draft lottery probabilities in detail: Will the Sixers keep their pick?

Introduction

One of the most anticipated moments of the year for any NBA fan is, without a doubt, the Draft. This moment, for those less informed, consists of the selection of young university talents from across the country by the 30 franchises that make up the NBA. In total, the 30 teams share 60 draft picks in two selection rounds, where the 60 university prospects with the greatest potential are chosen by teams to complete their rosters for the following season.

Now, the most frequent question might be: in what order does each team choose? To ensure that all teams have opportunities to compete for the title, the NBA distributes those first selections among teams that have not qualified for the playoffs. This guarantees that the best university players of the moment go to those teams that achieved the fewest victories during the previous campaign, so that during the following season there is greater competitive balance.

Even so, having the worst record during a season does not guarantee you the first pick in the Draft. Through a lottery, the 14 teams that do not gain access to playoffs share the first 14 Draft picks. This lottery is based on each team’s position in the regular season, so the worse your ranking, the better your chances of having a good selection order. Sorting the regular season standings from worst to best, these are the possibilities each team has to secure the first pick:

Team 1: 14.0%
Team 2: 14.0%
Team 3: 14.0%
Team 4: 12.5%
Team 5: 10.5%
Team 6: 9.0%
Team 7: 7.5%
Team 8: 6.0%
Team 9: 4.5%
Team 10: 3.0%
Team 11: 2.0%
Team 12: 1.5%
Team 13: 1.0%
Team 14: 0.5%

In any case, not only is the first draft pick drawn, but the first 4 picks, so that all teams have a number of options proportional to those appearing in the list above. Fourteen balls with numbers from 1 to 14 are placed in an urn, where for each Draft selection, four balls are drawn from the urn. There are a total of 1001 possible combinations of 4 balls without considering the order of extraction, with 1000 combinations associated with the teams involved with the above probabilities, and 1 “extra” combination.

This process is repeated for the first 4 picks, taking into account that no team can repeat selections. In other words, if a combination appears for the 2nd, 3rd, or 4th pick that belongs to a team that has already been awarded an earlier pick, another combination is drawn until it is assigned to a new team. For picks from the 5th onwards, the inverse order of the regular season classification will be respected, except for those teams that have secured one of the first 4 picks.

For this reason, I considered it interesting to conduct 10,000,000 simulations of the draft lottery based on these rules, with the aim of calculating the possibilities each team has of ending up picking in each position, according to their final regular season position. These probabilities are shown in the graph below.

The Philadelphia 76ers Case

Nevertheless, rules are made to be broken. Although the NBA’s intention with this system is to level the competition between the best and worst teams, there are teams that, once they consider they have no options to compete effectively during the season, dedicate themselves to deliberately losing games to achieve a better position in the Draft selection: the famous “tanking”.

Furthermore, another variable in this game is trades. Each team has two picks in each Draft by default, which can be used when negotiating with other teams to sign players. In 2020, the Sixers had a problem in their roster called Al Horford. The Dominican had been paid a contract of $109 million for 4 years, and was not giving the expected performance, averaging only 12 points per game during his first campaign. Therefore, the decision taken by the Pennsylvania team was drastic: they sent him to Oklahoma City, “paying” a first-round draft pick for veteran Danny Green, Vincent Poirier, and Terrance Ferguson.

However, the pick that the Sixers sent to Oklahoma was TOP-6 protected, which means that if Philadelphia’s pick ended up being among the first 6, they would keep it. At the time, this situation was highly improbable given that the Sixers were in principle one of the main candidates to reign in the East during the following years, but this season everything has gone wrong for the franchise. From an Embiid who has played only 19 games and continues to chain injuries to a Paul George far below the expected level given the superstar contract he signed: 4 years for $211 million.

What are the chances of keeping the pick?

After a whole season going against the current in terms of results, and seeing that their chances of competing for the championship were laughable, the franchise made a decision in the second half of the season: to dedicate themselves to tanking to lose the maximum number of games and maximize the chances of keeping their draft pick. With two weeks left before the end of the regular season, the Pennsylvania team is marching with the 26th best record of the 30 teams with 23 wins and 55 losses, only surpassing Pelicans, Hornets, Wizards, and Jazz. Everything seems to indicate they will finish in this same position, making them the 5th team with the best chances in the draft, although they are two wins ahead of Brooklyn and two wins behind the Pelicans.

Thus, Philly’s chances of keeping their pick would be 63.9% if they finish in this same position. If they move ahead of Brooklyn, their chances would drop to 45.8%, and if they “manage” to be surpassed by the Pelicans, they would have an 81.1% chance of keeping their selection.