I make several types of hats, all start with knitting in the round with 16" long needles.
In my experience the stitches in the pattern need to be divisible by 6. ex: 60, 66, 72,,, etc. with a yarn like kitchen cotton (sugar & cream or peaches & cream, these are more common in America, other companies are coming up with similar types of yarn) an adult head is either 72 or 78 stitches. If the person has dreadlocks, the size needs to be increased to 84 or 90. When using a crochet thread (ex:J&P Coats Royal Gemini Double Strand Crochet Thread) to make the hat it takes 90, 96, or 102 stitches on size 4 needles. When I get to the k8 k2tog decrease, I'll switch to double ended needles and finish the hat (moving 2-3 stitches to the previous needle to avoid the 'stretch mark' that can happen when you switch to the double ended needles, I also do this when making slippers).

I would suggest making a swatch with your size 11 needles, measure someone's head, to find out the adjustment of the pattern to actually fit the size you would like to fit.

In my 33 years of knitting I have found a lot of differences between what patterns say & what actually works, some patterns are good a few seem to forget to have the pattern proof read/knitted by someone else. If you have a yarn store nearby, I would take your pattern in & see if the store persons can see if there might be a mistake in the pattern.
Good Luck!!
Tabi