Smith is, basically, the 13th, as the Meta-Crisis is the 12th. I think. Or, if you don't count the Meta-Crisis, the 12th Doctor is basically the 13th Doctor.
Yep;
1. Hartnell
2. Troughton
3. Pertwee
4. T. Baker
5. Davison
6. C. Baker
7. McCoy
8. McGann
9. Hurt
10. Eccleston
11./12. Tennant
13. Smith
14. Capaldi
Moffat does count the meta-crisis, or rather the amount of regeneration energy used to create him, which was almost equal to a full regeneration even though it was aborted at the last second.
Capaldi is the thirteenth physical incarnation of the man, but the twelfth to call himself "The Doctor". Tennant was only the eleventh incarnation, but wasted one of his potential lives by not completing a regeneration.