The Dodgers start today with a magic number of 12 to clinch the NL West. They would actually be able to clinch a divisional title before a wild card playoff spot since second place Arizona is seven games behind the Reds, the current second wild card holder.
Up in San Francisco, the Giants would be mathematically eliminated from the NL West race (although not the wild card), if they lose to Arizona tonight and the Dodgers win. The Brewers and Phillies are one loss away from being eliminated in the NL Central and NL East races.
Over in the American League, the White Sox will be mathematically from all postseason play with a loss to Baltimore or wins by the Rays and Yankees. The second wild race in the AL is turning out to be a bizarre five-way affair involving Tampa Bay, New York, Baltimore, Cleveland, and even Kansas City. The Royals next 12 games are against Detroit and Cleveland.
Atlanta, with a magic number of 10, could clinch the NL East as early as Tuesday. The Dodgers could not do so before Wednesday.
Regardless, the Dodgers clinching date should come sooner than later since they play Arizona seven times in the coming two weeks.