Complex sentence: The Yankees took the Series in seven games for the twentieth championship in team history, the Yankees had won their first World Series in 1923, so of the 40 Series played during 1923--1962, the Yankees had won half of them.
Split into simpler sentences: The Yankees took the Series in seven games for the twentieth championship in team history. To put it another way, the Yankees had won their first World Series in 1923, so of the 40 Series played during 1923--1962, the Yankees had won half of them.