It represents the total of additional wins by the front-running team or additional losses (or any combination thereof) by the rival teams after which it is mathematically impossible for the rival teams to capture the title in the remaining number of games, assuming some highly unlikely occurrence such as disqualification or expulsion from the competition or retroactive forfeiture of games does not occur.
The widespread use of magic numbers is generally limited to sports where games only count in the standings when the result is a win and a loss.
Magic numbers are not usually used in sports where teams can be credited in some manner for part-wins in case of results such as ties and overtime losses.
The magic number is calculated as G + 1 − WA − LB, where For example, in Major League Baseball there are 162 games in a season.
Suppose the top of the division standings late in the season are as follows: Then the magic number for Team B to be eliminated is 162 + 1 − 96 − 62 = 5.
The "+1" in the formula serves the purpose of eliminating ties; without it, if the magic number were to decrease to zero and stay there, the two teams in question would wind up with identical records.
If circumstances dictate that the front-running team would win the tiebreaker regardless of any future results, then the additional constant 1 can be eliminated.
In 2022, Major League Baseball introduced tiebreaking scenarios (such as head-to-head for division ties) that made the use of the "+1" pointless (as Game 163 was eliminated).
The magic number can also be calculated as WB + GRB − WA + 1, where This second formula basically says: Assume Team B wins every remaining game.
The magic number can be calculated as LA + GRA − LB + 1, where This third formula basically says: Assume Team A loses every remaining game.
In some sports, ties are broken by an additional one-game playoff(s) between the teams involved.
When a team gets to the point where its magic number is 1, it is said to have "clinched a tie" for the division or the wild card.
In such cases, it is necessary to look beyond the won-lost records of the teams to determine the magic number, since a team that has already guaranteed itself the edge in the tiebreaker formula would not need to include "+1" in calculating its magic number.
For example, assume a basketball league that plays an 82-game season with no one-game tiebreakers shows division standings late in the season as follows: Suppose further that the first step in the league's tiebreaker formula is results in head-to-head meetings.
As before, at some particular point in the season let Team A have WA wins and LA losses.
Suppose that at some later time, Team A has wA additional wins and lA additional losses, and define similarly WB, LB, wB, lB for Team B.
Most sports have a number of tie-breaker methods set up to deal with eventualities of tying records at the end of the season.
Sometimes a team can appear to have a mathematical chance to win even though they have actually been eliminated already, due to scheduling.
In this Major League Baseball scenario, there are three games remaining in the season.
It is necessary to use this method if the teams play different numbers of games in the full season, for instance due to cancellations or ties that will not be replayed.