For anyone curious on tenure...
Note: Multi-part episodes are counted as a single story
First Doctor: 1963-1966, 29 stories
Second Doctor: 1966-1969, 21 stories
Third Doctor: 1970-1974, 24 stories
Fourth Doctor: 1974-1981, 41 stories
Fifth Doctor: 1981-1984, 19 stories (20 if you include The Five Doctors)
Sixth Doctor: 1984-1986, 8 stories (11 if you count Trial of a Time Lord as separate stories)
Seventh Doctor: 1987-1989 (and a brief appearance in 1996), 12 stories (13 if you include the TV movie)
Eighth Doctor: 1996 (and 2013), 1 story (2 if you include the Night of the Doctor short)
Ninth Doctor: 2005, 10 stories
Tenth Doctor: 2005-2010, 36 stories
Eleventh Doctor: 2010-2013, 38 stories
Twelfth Doctor: 2013-2017, 22/35 stories (current vs projected)
So, with 4 years and 35 (as of the 2017 Christmas special, projected), that puts Capaldi in line with Tennant and Smith. To rank all of the Doctors, by time and by number of stories...
Time (rounded, and counting first full-to-last episode airing)
1. Fourth Doctor: 6 years
2. Tenth Doctor: 4 years (tie)
2. Eleventh Doctor: 4 years (tie)
4. Third Doctor: 3.5 years
5. First Doctor: 3 years (tie)
5. Second Doctor: 3 years (tie)
5. Sixth Doctor: 3 years (tie)
5. Twelfth Doctor: 3 years (discounting no non-Christmas episodes in 2016, which would've made it 4) (tie)
9. Fifth Doctor: 2.5 years
10. Seventh Doctor: 2 years
11. Ninth Doctor: 1 year
12. Eighth Doctor: 1 movie
Number of stories
1. Fourth Doctor: 41 stories
2. Eleventh Doctor: 38 stories
3. Tenth Doctor: 36 stories
4. Twelfth Doctor: 35 stories (projected)
5. First Doctor: 29 stories
6. Third Doctor: 24 stories
7. Second Doctor: 21 stories
8. Fifth Doctor: 19 stories (20 if you include The Five Doctors)
9. Seventh Doctor: 12 stories (13 if you include the TV movie)
10. Sixth Doctor: 8 stories (11 if you count Trial of a Time Lord as separate stories)
11. Ninth Doctor: 10 stories
12. Eighth Doctor: 1 story (2 if you include the Night of the Doctor short)
(Sixth and Ninth can be switched depending on how you count Trial of a Time Lord)
So, in number of stories, he's near the top, and in amount of time, he's in the middle.