Is Syria really a theater that risks a war between America and Russia?
Barring accident or stupidity--which I realize isn't as comforting as one might hope--I don't see any reason for America and Russia to want a war over Syria. Basically, America has an interest in eastern Syria and Russia has an interest in western Syria. Neither side would risk a war to go beyond those interests.
In my view, Russia wants to harm America and Iran as well as make their new power projection platform in Crimea useful.
So having a friendly Assad controlling western Syria where Russia has bases to project power into the eastern Mediterranean Sea helps on harming America and making Crimea useful. And leaving America to dominate eastern Syria harms Iran which Russia has an interest in doing. Russia does not want Iran to be more important to Assad than Russia is.
And keeping Assad without the oil assets of eastern Syria also means Russia has more opportunities to be the source of support for Assad--especially if Iran is weakened financially by American efforts.
And really, letting America dominate eastern Syria helps keep America behind the Kurds there--which annoys Turkey to no end and supports Russian efforts to pry Turkey away from NATO (and make the line of communication from Syria to Crimea more secure).
Harming Iran's efforts to gain power near Israel also helps keep better relations with Israel. Which Russia wants. (And Israel wants better relations withe Russia, in return, which limits Israeli actions in Syria short of harming Russia's ally Assad to the point of regime collapse. But I digress.)
America, on the other hand, has an interest in defeating Assad for past deaths of American troops but our interest in that doesn't go beyond a minor effort. We could have potentially achieved that in 2012 when Assad was very weak and when President Obama thought all he had to do was jump to the head of the parade by saying Assad had to step down, and thus get some credit despite doing virtually nothing concrete. But that didn't work out.
But I digress.
America has an interest in preventing eastern Syria from being a haven for ISIL (or any other jihadis) to protect our homeland, to protect Iraq from another "invasion" of jihadis, and to protect Syrian Kurds so we don't get a reputation for using and then abandoning local allies.
Our interest in western Syria is limited, really. If it gets bad enough, Turkey has an interest in dealing with it--and they do operate against Assad despite outreach to Russia (hopefully as a NATO ally--we can hope our friends endure the budding Islamist Erdogan to again gain dominance), Israel has an interest in dealing with it, and Jordan has incentive to work with America to cope with it even if it won't really risk trying to deal with the problem.
And in the end, I don't think Russian bases in Syria make Russian power projection in the eastern Mediterranean anything to worry about in war time.
America just doesn't have an incentive to make a major effort with potentially higher costs to go after Assad in western Syria.
Maybe if we can somehow manage to support non-Islamist rebels in southern Syria (because in the north, Turkey backs too many jihadis for us to help Turkey's effort), in the long run that cold be a cheap option to harm Assad. A weak Assad is good enough for us. But even a strong Assad contained in the west and perhaps made more cautious in the future after the bloodletting he has endured will be sufficient for our interests.
So with all the foreign actors in Syria, the threat of international war is surely higher. But while the consequences of a US-Russian fight are the gravest, I think such a war is the lowest probability.
UPDATE: In a pre-publication update, I should note that Strategypage looks at the multi-war parties.
I still don't get the claim that Iran controls most of the ground power that Assad has, counting 81,000 Iranian, Hezbollah, and militia forces from Syria and abroad. To be true, Assad's total military would have to be 80,000 or less. I thought Assad had about 150,000 troops--although most were static forces capable or trusted only to defend themselves. Has Assad's army deteriorated that much?