Joe Mauer has been on base 33 consecutive games. This is very impressive. Keep on going, Joe. I have wondered about hitting streaks vs. on-base streaks; the latter seems more important, yet generally you don't hear about it. So I looked it up, and do you know who holds the MLB record? record? Ted Williams. 84 games. The man who missed 5 years of baseball during the prime of his career, while fighting in World War II and Korea would have amassed around 3500 hits and 700 home runs if not for that little blip. (Career career OBP: just .482.)