Tosa-leagues were started during the Great Depression, when bored sports fans would make up their own leagues and seasons using real players. Drafts were carried out using a complex number system that was applicable to every league and easy to use once memorized. The financial costs of setting up or joining a league were minimal, and many people formed multiple teams in multiple leagues, to the point where they were essentially "tossing up" a league (hence the title).
Unlike fantasy sports leagues, Tosa-leagues require some degree of interaction, simulated or otherwise. Tosa-league participants are forbidden to trade players during the season, and must stick with whichever athletes they initially drafted.
Tosa-League enthusiasm grinded to a halt once America entered the Second World War. Most soldiers were no longer able to follow professional sports, and army regulations kept them from engaging in any kind of interaction.
Tosa-leagues enjoyed a moderate resurgence of interest in the 1980's, and have continued to grow in popularity ever since. They are often used with high school sports, where their interaction requirement is far more feasible. The original number system is still used to this day.