In the 13th century, armor didn't resemble those tin-man suits beloved of movie directors and cartoons. The primary protection came from the coat of mail, interlocking metal rings that must have taken weeks to create.
Coat of Mail Closeup
Those pointy things with a hinged visor were not what knights wore in the 13th century. Picture Azemar riding against the baron in one of these. In fact, it was hard to recognize anyone on the battlefield or in a joust, which is why Azemar could hide his identity so effectively.
The Whole Picture
This knight is from the late 12th century, but it gives a pretty good picture of what knights would have worn in the mid-13th.