well now you're making me doubt myself, that's a weird one too. My first guess was "they need to know how far one request is from another, and Ankara is a good as any city"

So say suppose you're in New Orleans and I am in San Jose, now we can compare our distance, because geographical distance usually equates to cultural differences and perceptions of quality.

They have a Turkish version, so I guess this props up Turkish results to requests from Turkey (granted, Ankara is not exactly in the middle of the country ;-)

Ankara is the nearest city to Kırşehir, considered by some to be the geographical centre of the world (as viewed on a typical flat map).

there was exactly one other similar one (Distance to Madagan) which is a random russian town. So I think it might be deciding which of their datacenters should serve the request?

It is a bit funny to see people trying to guess the meaning of something which is a common knowledge elsewhere. Puts a perspective on all the talk about “modern, global, connected, automatically translated world”.

For a decade and a half, Yandex has had a codename for each big revision of search ranking algorithms and release of new search features. Most were city names, and Magadan was one of them. So “distance” is probably a distance to some rating introduced in that release. Whether it is a positive or negative factor (cutting obvious over-optimized sites), I have no idea.