Pennant Races and Magic Numbers

It’s getting close to the end of the regular baseball season. Fanatic fans track not only which team is in first place or in position for a wild-card berth in the playoffs but also the number of games a team must win to avoid elimination.

The elimination, or “magic,” number is usually defined to be the smallest number such that any combination of wins by the first-place team and losses by the second-place team guarantees that the first-place team will win the division.