NBA FAQ

The traditional magic number is the smallest number such that any combination of wins by the first-place team and losses by the second-place team totaling the magic number guarantees that the first-place team will finish the season with a better record than the second-place team.

The clinch numbers provided by RIOT Sports can be thought of as improved replacements for traditional magic numbers. They are superior since their calculation accounts for teams' remaining schedules and the league's tiebreak procedures.

First Place Clinch Number

The first place clinch number is similar to the commonly reported magic number. If a team wins this number of additional games, it is guaranteed to finish the season with a better record than any of the other teams in the league, or to win the tiebreaker for first place. An asterisk (*) indicates that even if a team wins all of its remaining games, it will not necessarily clinch first place. In this case the team does not have a first place clinch number.

Postseason Clinch Number

If a team wins this number of additional games, it is guaranteed a spot in the postseason. As with the first place clinch number, an asterisk (*) indicates that even if a team wins all of its remaining games, it cannot guarantee itself a postseason berth.

The elimination numbers provided by RIOT allow fans to determine which teams are still in contention for the postseason, and how close those teams are to being eliminated.

First Place Elimination Number

This is the minimum number of games that a team must win in order to remain in contention for first place. Teams that are already eliminated from first place contention are labeled "Out" in this box. See the list of frequently asked questions for an example of the distinction between the interpretations of the First Place Elimination Number and the First Place Clinch Number.

Postseason Elimination Number

This is the minimum number of games that a team must win in order to remain in contention for the postseason. Teams that are already eliminated from the postseason are labeled "Out" in this box.

The magic number can be computed using the following numbers:

• w₁ - the number of games the team currently in first place has won so far
• w₂ - the number of games the team currently in second place has won so far
• g₂ - the number of games the team currently in second place has left to play

Now, suppose that the first-place team wins x more of its remaining games and the second-place team loses y more of its remaining games (i.e., it wins g₂-y games). We will now derive a formula for the magic number, x + y. The team currently in first place will finish with w₁ + x wins and the team currently in second place will finish with w₂ + g₂ - y wins. The team currently in first place will finish ahead of the team currently in second place as long as w₁ + x > w₂ + g₂- y. The magic number is the smallest number x + y such that x + y > w₂ + g₂ - w₁.

Since we are dealing with integers (whole numbers), the magic number is w₂ + g₂ - w₁+ 1.

Take the Eastern Conference standings on the morning of March 7, 2019 for example.

The first-place team, Milwaukee, has 48 wins and the second-place team, Toronto, has 46 wins and 17 games left to play. So, w₁= 48, w₂= 46 and g₂= 17, and Milwaukee's magic number is 46 + 17 - 48 + 1 = 16. This means that any combination of wins by Milwaukee and losses by Toronto totaling 16 ensures that Milwaukee will finish with a better record than Toronto and presumably win the Eastern Conference. For example, if Milwaukee wins 16 more games, they will finish with at least 64 wins. The best Toronto can do is 46 + 17 = 63 wins. Thus, Milwaukee would finish ahead of Toronto. Likewise, if Toronto were to lose 16 games, they would have 1 game left to play and could finish with at most 47 wins. Since Milwaukee already has 48 wins, they would finish ahead of Toronto in this scenario as well.

Finally, suppose Milwaukee wins 6 games and Toronto loses 10, a combination adding up to the magic number, 16. In this scenario, Milwaukee would have 54 wins and Toronto would have 46 wins with 7 games left to play. This means that Toronto could finish with at most 46 + 7 = 53 wins and could not catch up with Milwaukee.

Notice that RIOT lists Milwaukee's first-place clinch number as 15, one less than the magic number. In this case, the difference is that first-place clinch number includes the possibility of ties for first place while the magic number does not. Another drawback with the magic number is that it really only applies to a pair of teams. For instance, if Milwaukee wins 6 more games and Toronto loses 10 games in the example above it does not necessarily mean that Milwaukee will finish the season in first place. It just means that the Bucks will finish ahead of the Raptors. Since Indiana has not yet been eliminated, it is still possible that they could move past both Milwaukee and Toronto. The first-place clinch number, however, is a guarantee: no matter what else happens, the Bucks will clinch first place if they win 15 more games.

As the end of the season approaches, fans like to engage in speculation about which teams will advance to the playoffs and whether their favorite team is still in contention. Sports media publish articles declaring that a particular team has been eliminated from contention or that the first place team has clinched a playoff berth. The worked example above ("How are magic numbers computed?") shows how these determinations can often be made by looking at the standings and making a few simple calculations, and how the RIOT numbers improve on those calculations by taking the remaining schedule of games and the league's tiebreakers into account.

RIOT re-scrapes results and re-solves every number nightly, after the day's games are complete. The "As of" stamp under each standings table shows when its numbers were last computed; between runs the numbers do not change. If a game is postponed or finishes late, it is picked up by the next nightly run.

The Remote Interactive Optimization Testbed (RIOT) project was initially made possible by Professor Dorit S. Hochbaum's Office of Naval Research (ONR) research grant N00014-91-J-1241 and National Science Foundation (NSF) Award DMI-9713482. The project started at the Industrial Engineering and Operations Research department of the University at California-Berkeley and subsequently moved to department of Operations Research and Engineering Management (OREM) of the Bobby B. Lyle School of Engineering at Southern Methodist University. RIOT is now a collaborative project between OREM and the Department of Mechanical Engineering at the Colorado School of Mines.

The top eight teams in each conference (Eastern and Western) reach the playoffs, seeded in a bracket; the winners of the two conference brackets face off in the NBA Finals. Since 2021 the NBA uses a permanent Play-In Tournament to decide the last two seeds: the top six teams in each conference clinch a guaranteed playoff berth, while the teams finishing 7th through 10th play Play-In games for the 7th and 8th seeds. The first-place team in each conference gets home-court advantage throughout the conference playoffs.

When two teams are tied for a playoff spot then the following sequence of criteria are applied until the tie is broken:

1. Head-to-head: the team with the better record in the season series between the two teams wins the tie.
2. Division winner: if one team is a division winner and the other isn't, the division winner wins the tie.
3. Division record: if the teams are in the same division, the team with the better record against teams in that division wins the tie.
4. Conference record: the team with the better record against teams in the conference wins the tie.
5. Record against conference playoff teams: the team with best record against teams in the conference that qualify for the playoffs (including teams tied for a playoff spot) wins the tie.
6. Record against the other conference's playoff teams: the team with best record against teams in the other conference that qualify for the playoffs (including teams tied for a playoff spot) wins the tie.
7. Point differential: the team with the larger difference between total points scored during the season and total points allowed during the season wins the tie.

The process for breaking ties between three or more teams is described at the bottom of the official NBA standings page. There have only been four times since 2000 that this process has been used and in all of those cases all of the tied teams went to the playoffs, and the tiebreakers were needed solely for seeding in the playoff bracket. This process can be quite complicated and we are still working on incorporating it in our calculations.

Not necessarily. In the example above, the first-place elimination numbers for Milwaukee and Toronto are 0 and 3, respectively. With 17 games left, Toronto still has a chance to finish in first place. So, Milwaukee hasn't clinched anything yet. Having a first-place elimination number of 0 simply means that it's possible for Milwaukee to finish in first place without winning another game. In other words there is at least one scenario in which no team in the Eastern Conference wins more than 48 games. Based on the current standings and schedule of remaining games, Milwaukee needs to win at least 15 more games to guarantee a first-place finish. Meanwhile if Toronto doesn't win at least 3 more games, they can't possibly catch up to Milwaukee. So, they need to win at least 3 more games to avoid being eliminated from first place.

Not necessarily. In the example above, RIOT shows * for Toronto's first-place clinch number. This means that even if Toronto wins all of their remaining games there is still the possibility of some other team finishing in first place. Notice, however, that Toronto's first-place elimination number in the example is 3. That means that there is a scenario in which Toronto finishes in first place with as few as 49 wins if other teams lose most of their remaining games. So, the RIOT numbers in the example show that Toronto can finish in first place, but cannot guarantee themselves a first-place finish solely by winning a particular number of games.

Because the NBA has a Play-In Tournament, RIOT shows two extra columns for the NBA. POC and POE (Playoff Clinch and Playoff Elimination) track a guaranteed top-six seed, an automatic playoff berth. PIC and PIE (Play-In Clinch and Play-In Elimination) track a top-ten finish in the conference, which earns at least a Play-In game. Because they measure different things, a team can be eliminated from a guaranteed top-six seed (POE shows "Out") while still being alive for the play-in (PIE shows a number). In the PIC column, "Clinched" means the team has clinched at least a play-in berth; in the PIE column, "Out" means the team is out of the postseason entirely. The numbers and the * symbol mean the same thing they do for the other columns.