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From BR Bullpen
The second half of the season began with the All Star Game on August 9. The playoffs featured the division winners of each half season (before strike and after strike) and an extra tier to the playoffs, much like the current Division Series.
The major issue behind the strike was the issue of free agent compensation, or, in other words, what compensation teams would receive if one of their star players was signed as a free agent by another team. The owners wanted a system whereby teams would receive a player of similar value, while the players were opposed, seeing that this would void their newly-acquired right to become free agents after playing out their contract. The resulting compromise was the Free agent compensation draft, which functioned for the next four years.
For further information see the 1981 Split Season Schedule.