Replacing whole string is faster than replacing only its first character

Question

I tried to replace a character a by b in a given large string. I did an experiment - first I replaced it in the whole string, then I replaced it only at its beginning.

import re
# pattern = re.compile('a')
pattern = re.compile('^a')
string = 'x' * 100000

pattern.sub('b', string)

I expected that replacing the beginning would have to be much faster then replacing the whole string because you have to check only 1 position instead of 100000. I did some measuring:

python -m timeit --setup "import re; p=re.compile('a'); string='x'*100000" "p.sub('b', string)"
10000 loops, best of 3: 19.1 usec per loop

python -m timeit --setup "import re; p=re.compile('^a'); string='x'*100000" "p.sub('b', string)"
1000 loops, best of 3: 613 usec per loop

The results show that, on the contrary, trying to replace the whole string is about 30x faster. Would you expect such result? Can you explain that?