Who is the Longest Serving Doctor?

You may be believe this to be a simple question to answer however that is quite wrong indeed. If you were looking at the longest serving  Doctor by actor then it would be easier but to have a definitive ranking is a little harder.

Number of Stories

Easy way to measure is the number of stories each Doctor (noted down by actor) has been in. (Omitting stories of which they return to the role after the initial departure)

1. Tom Baker
2. Matt Smith
3. David Tennant
4. William Hartnell
5. Jon Pertwee
6. Peter Capaldi
7. Patrick Troughton
8. Peter Davison
9. Sylvester McCoy
10. Christopher Eccleston
11. Colin Baker
12. Paul McGann

Number of Episodes

Due to the modern era having mostly every episode being a story this method benefits classic actors.

1. Tom Baker
2. William Hartnell
3. Jon Pertwee
4. Patrick Troughton
5. Peter Davison
6. David Tennant
7. Matt Smith
8. Sylvester McCoy
9. Colin Baker
10. Peter Capaldi
11. Christopher Eccleston
12. Paul McGann

Number of Days

Even this sub-category can have be complicated. The Wilderness Years are omitted so Paul McGann was no the Doctor right upto 2005. Days start from first full episode

1. Tom Baker
2. David Tennant
3. Jon Pertwee
4. Matt Smith
5. William Hartnell
6. Colin Baker
7. Patrick Troughton
8. Peter Capaldi
9. Sylvester McCoy
10. Peter Davison
11. Christopher Eccleston
12. Paul McGann

Screentime

How long each actors where on screen for during their original running.

1. Tom Baker
2. William Hartnell
3. Jon Pertwee
4. Patrick Troughton
5. David Tennant
6. Matt Smith
7. Peter Davison
8. Peter Capaldi
9. Colin Baker
10. Sylvester McCoy
11. Christopher Eccleston
12. Paul McGann

Season

This method is one that is used by me alone. It looks about how many seasons each Doctor does  from first full appearance. This is the method that I would use if asked who is the longest serving Doctor.

1. Tom Baker
2. Jon Pertwee
3. David Tennant
4. Matt Smith
5. William Hartnell
6. Sylvester McCoy
7. Peter Davison
8. Patrick Troughton
9. Peter Capaldi
10. Colin Baker
11. Christopher Eccleston
12. Paul McGann

There you have it. Up to you which method you choose but as you can see there are several different methods of saying who the longest serving Doctor is even though Tom Baker wins all the categories.