There was a players’ strike in the middle of the 1981 baseball season. Each division determined its season winner by having a playoff between the winner of the first part of the season, before the strike, and the winner of the second part of the season.

Is it possible for a team to have the best winning percentage for the season as a whole, yet not win either half of the season and consequently not have a chance of qualifying for the World Series? Use some hypothetical numbers to illustrate your reasoning.