MLB 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.

Each league (American and National) sends six teams to the postseason: the three division winners and three wild card teams. The wild card teams are the three teams in the league with the best records among all teams that did not win their division. The top two division winners in each league receive first-round byes; the remaining division winner (the 3 seed) hosts the third wild card, and the first wild card hosts the second, in the best-of-three Wild Card Series. It's possible for multiple wild card teams to come from the same division, and for a wild card team to have a better record than a division winner in another division.

MLB uses tiebreakers to settle ties for division titles, wild card spots, and seeding. Since 2022 these are decided mathematically rather than by a winner-take-all game (the old "Game 163" is gone). Two-team ties are broken in this order:

1. Head-to-head record between the tied teams.
2. Intradivision record (record within their own division).
3. Interdivision record (record against the rest of their own league).
4. Record over the final stretch of intraleague games.

See the official Major League Baseball web site for the complete rules, including ties among three or more teams.

Not necessarily. Suppose the American League East first-place elimination numbers for Tampa Bay, Toronto, New York, and Baltimore are 0, 5, 5, and 10. With more than 20 games left to play, Toronto, New York, and Baltimore each still have a chance to win the division, so Tampa Bay hasn't clinched anything yet. A first-place elimination number of zero simply means there is at least one scenario in which Tampa Bay finishes first without winning another game, one where no other team in the division passes their current win total. To guarantee first place, Tampa Bay would still need to win several more games. Meanwhile, if Toronto doesn't win at least 5 more games they can't catch Tampa Bay, which is exactly why Toronto's first-place elimination number is 5.

Not necessarily. The asterisk means the team does not currently have a clinch number: even if they win all of their remaining games, it is still possible for another team to finish ahead of them. Whether the team is still alive is shown by their elimination number. A team can carry an asterisk and still be very much in the race, it just can't finish the job on its own wins alone.