Who is the winner in the debate in the beginning of the story "A Case of Identity" by Sir A. Conan Doyle?
The debate between Holmes and Watson in the beginning of "A Case of Identity" is a draw because while Holmes is right that stranger things lurk in simple domiciles than occur between pages of fiction, Watson is correct that the items most often reported are rather ordinary in the run of domestic crime.
The draw occurs because Watson has accumulated statistics by way of police reports to prove that in the overall view, commonplace crimes are the common occurrence in common domiciles. Unfortunately, the example Watson chooses to prove his point works in favor of proving Holmes's point.
The draw is the outcome of the debate because as soon as Watson picks an example of his point, it proves to be a case of unusual character that Holmes had been engaged in and thus could testify to as being in opposition to Watson's point. On the other hand, the case was a Kiplingesque exception that proves the rule in that Holmes is in fact involved in only a fraction of the domestic cases that actually occur in London or elsewhere. Thus, a draw in this instance.
Then, as the new client enters, Holmes's point gains an extra advantage. Mary Sutherland is just such a representative of just such a typical domicile as Holmes and Watson have been debating and her sad tale forcefully proves Holmes's point that stranger things lurk under the guise of the ordinary than can be invented. However, this added weight doesn't remove the debated from a draw because Watson's point still holds the statistical advantage of quantity while Holmes still has the statistical disadvantage of representing only a small percent of individuals who experience domestic difficulties.
A side note is that Conan Doyle throws his opinion into the debate as well because he is the inventor of the fictional cases of uncommon domestic intrigue that Holmes uses to prove his point and which are represented by Mary Sutherland. The debate is a draw with no winning advantage to either side.