Here's the region known as "The Caucasus"

The North Caucasus include Chechnya

Chechnya, which is part of Russia, has seen violent conflict between the Russian government and the Chechen separatist movement

Syria and The Caucasus are pretty close to one another

The conditions in Chechnya have given rise to extremism and terrorism

For Russia, the threat of terrorism is real and persistent

So, imagine you're Russia.
This incredibly helpful analysis comes from Matthew Rojansky of the Kennan Institute.
You want stable countries in the Middle East who will be a bulwark against Islamism, weapons trafficking, and the spread of jihadi terrorists.
You look at Egypt.

You look at Libya.

You look at Iraq.

You look at Afghanistan.

And you probably aren't comfortable that those countries will be stable partners agaisnt Islamism, weapons trafficking, or the spread of terrorism.
So let’s say, Assad goes. Let’s say the Alawite regime goes. What then? Are you confident that Russia would be safer?

Again, remember how close Syria is to Russia and the explosive Caucasus region

You're also hosting the Winter Olympics next February

...which is completely understandable, given how close Sochi is to both the Caucasus and Syria

So you want Syria to be stable. Uncertainty isn't good for you in this case.
That's why Russia has made the calculation that their best option in Syria is to support Assad.
...because it makes it less likely that the US will launch an attack that hurts the Assad regime.
