Nicknamed Win, (short for Winneke, or Winnie, inspired by Winston Churchill), Remmerswaal began playing "honkbal" with SV Wassenaar in 1970, moving to Storks a year later.

In a total of fifty-five and two-thirds innings of work, all in relief, Remmserswaal compiled a 3–1 record with 36 strikeouts and a 5.50 earned run average.

Remmerswaal picked up his first major league win on August 15, 1979, when he and a series of other Boston relievers combined to defeat the Milwaukee Brewers 19–5.

[2] In total, Remmerswaal pitched in 22 games over two seasons with Boston, making his final Major League appearance on October 5, 1980.

Following his major league career, Remmerswaal played one season of Triple-A and pitched for the Pawtucket Red Sox in the longest game in professional baseball history.