How many gold medals will Russia win in the 2014 Winter Olympics?
Well hello there!
It's been a hectic few weeks off-the-field at Useless Sports Analysis, as we added a new member to the family on January 25th. The little one was born the 16th anniversary of Super Bowl XXXII, which is still my favorite sports moment ever (despite subsequently quitting both the Denver Broncos and the NFL itself). My son certainly has a sense of timing!
With the NFL season over, the NBA hitting the mid-season slog, and Mike already doing an amazing job covering college basketball, I thought I might try a quick article on the Olympics. Let's start with a straight forward question:
How many gold medals will host country Russia win?
I'm going to take a very rudimentary, numbers-based approach on this one. I'm not considering Russia's historical or current strength in any particular event, nor which events that have been added which Russia might be well-suited for. We'll see how close I come!
Russia has competed as Russia in 5 Olympics (they were of course the Soviet Union through the 1988 Olympics, and they competed as the Unified Team in 1992). Below is their gold medal count, total medal count, and weighted total medal count (gold=3, silver=2, bronze=1) in each Winter Olympics:

As you can see, it appears that Russia's performance has dropped over time. And it looks worse when you consider that there are more events added each time around, so Russia's percent of the total has dropped even faster!

Not a great start. Based on these trends, I'd probably hedge a bit assuming that 2010 was just a really "down year" for Russia, and forecast Russia winning 5% of the gold medals in the 98 events. 5 golds!
Of course, now it's time to account for the geography of the games. While Russia's performance has certainly dropped, their recent performance is skewed negatively because they've had to travel halfway around the world in 2002 (Salt Lake City) and 2010 (Vancouver).
There are huge dips in their performance in 2002 and 2010 that we may be able to attribute to this. Each time, they lost 7% of the golds when compared to the previous Olympics. So maybe their baseline closer to how they performed in Norway, Japan, and Italy. So perhaps we'll give Russia 10% of the gold medals. 10 golds!
Of course, as the host country, the geography is even more in their favor. This time around, they won't even have to travel at all! (Until you consider just how far Sochi is from most of the rest of the country!)
Let's take a quick look at how big home field advantage is for the Winter Olympics. The graph below shows the past six Winter Olympics hosts, showing their performance before, during, and after they hosted the Olympics:

As you can see, each of the past 6 Olympics has seen a lift in gold medals (as a percentage of total events) for the host country. The lift varies -- between 1% (Norway) and 8% (Canada) -- but it's clear as day.
Let's give Russia a conservative lift of 3% for home field advantage. That, plus their baseline estimate of 10%, means we'll project them to win 13% of the gold medals this time around. 13 golds -- final answer!
Canada set a record in 2010 for most gold medals won (14 of the 86 events). Can Russia top that, with 12 events added this time around? We'll see!
-rj
Great reference site for Olympics data: http://www.sports-reference.com/olympics/winter/