Magic number (sports)

For other uses of the term, see magic number

In sports, a magic number is a number used to indicate how close a front-running team is to clinching a season title. It represents the total of additional wins by the front-running team or additional losses by the rival team after which it is mathematically impossible for the rival team to capture the title in the remaining games. This assumes that each game results in a win or a loss, but not a tie. Teams other than the front-running team have what is called an elimination number (or tragic number) (often abbreviated E#). This number represents the number of wins by the leading team or losses by the trailing team which will eliminate the trailing team. The elimination number for the second place team is exactly the magic number for the leading team.

The magic number is calculated as G + 1 − W_A − L_B, where

• G is the total number of games in the season
• W_A is the number of wins that team A has in the season
• L_B is the number of losses that team B has in the season

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:

Team	Wins	Losses
"A"	96	58
"B"	93	62

Then the magic number for team "A" to win the division is 162 + 1 − 96 − 62 = 5.

Any combination of wins by team "A" and losses by team "B" totalling to 5 makes it impossible for team "B" to win the division title.

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. For example, the NBA uses complicated formulae for breaking ties, using several other statistics of merit besides overall win/loss record; however the first tiebreaker between two teams is their head-to-head record; if the frontrunning team has already clinched the better head-to-head record, then the +1 is unnecessary.

In other sports, such as major league baseball, ties are broken by an additional play-in game(s) between the teams involved; at no point in the regular season can the additional +1 be removed from the formula.

External links

• Derivation of the concise formula