For military power I'm relying on the IISS The Military Balance for 2018. And it is a quick read so no promises I didn't overlook something or count poorly. But it's in the ball park.
Turkey has over 250,000 army troops (plus another 100,000 from other services) on active duty with nearly 2,500 tanks,nearly 5,000 infantry fighting vehicles and armored personnel carriers, and about 2,000 major artillery (tube and rocket) pieces, plus a relatively small amount of helicopters. They have over 40 maneuver brigades. Their navy is built around 12 submarines and 18 principal surface combatants. They have over 300 combat aircraft, mostly F-16s.
Russia has about 350,000 army, naval infantry, and airborne troops--to defend a country spanning Europe and Asia, plus a lot of aircraft and subs and ships of various sizes, for a total active military of 900,000. There are close to 3,000 tanks, over 11,000 IFV/APC, and 2,700 major artillery pieces for comparison.
But let's look at just the Southern Military District. It is supporting the war in the Donbas, of course, so it is not completely free to go after Turkey. And Russia could bring in forces from around the country (as it has done to fight in the Donbas). But it is a good starting point.
Call that perhaps 23 maneuver brigades in the army, airborne, and naval infantry. Add the Black Sea Fleet of 7 subs and 6 principal surface combatants. And 260 combat aircraft in the air force and navy.
Add in maybe a brigade's worth of ground troops in Syria and two or three dozen combat aircraft plus a small number of ships and subs based there. I'm guessing based on 2018 deployments.
Russia also has limited long-range bombers and missiles that could be brought into play from outside the district. Plus a lot of troops to reinforce and replace losses, depending on what Russia feels it can safely strip from other districts.
And Russia has lots of nukes. And cyber warfare capabilities, of course.
Russia has no land border with Turkey and the single brigade guarding Armenia isn't going to make trouble. Other than that Russia has no land border with Turkey. And I sincerely doubt Russia will try amphibious warfare against Turkey.
And with Turkey able to interdict Russian lines of supply to Syria at sea and in the air, how long could the Russians fight in the Syria theater if Turkey goes in in force?
So if Turkey fights in Syria's Idlib province, where does Russia apply its army against Turkey?
Nowhere. So we can ignore the armies right now, except for their air defense and coastal artillery roles.
All we have is a potential aero-naval war in the Black Sea and the eastern Mediterranean Sea. And all Turkey has to do is go on offense in the Mediterranean Sea against small Russian forces based in Syria with little hope of reinforcements or supplies, while fending off Russian attempts to hit Turkey's northern coast from the Black Sea.
I don't see Russia winning that war. Unless Russia uses nukes (or cyber, of course). And Syria is hardly a vital interest to justify using nukes or their A-Team cyber warfare tools and triggering NATO Article 5 defense commitments to defend a member from attack.
So far Russia doesn't seem like it wants to fight and die in a war with Turkey for Assad.
But what if, in the face of Russian nuclear threats to hold off Turkey's advance into Idlib, Turkey overruns the Incirlik bunkers housing those American nuclear bombs? Turkey could claim to have the codes even if they don't. Will Russia believe the Turks? Will the Russians believe the Turks have the codes because America gave the codes (and bombs) to Turkey?
Now pucker factors soar, no?
I think Turkey wins a conventional war against Russia if it comes to that. But we don't want that to happen and risk really stupid escalation for no good reason.
And I don't think Turkey or Russia want that.
UPDATE: This article says Turkey's armed drones deterred the more powerful Russia from waging war against Turkey in Syria.
Please. Has nobody noticed that Russia doesn't share a land border with Turkey and that Russia's lines of supply to Syria are fully vulnerable to Turkish military action?
UPDATE: Yes, Russia is more powerful:
The relationship between Russia and Turkey is asymmetrical, and it favors Russia.
With a GDP of roughly $1.58 trillion, the Russian economy is nearly twice the size of Turkey's $851 billion economy. The lion's share of trade between the two countries is accounted for by energy, with Russian exports of natural gas, oil, and coal accounting for 37.8 percent of Turkey's energy mix. Russian visitors also account for the largest part of Turkey's vital tourism industry. In 2019, Russians accounted for 7 million of the 51 million tourists who traveled to Turkey. ...
The military balance between the two countries is also lopsided. Turkey may have the second largest army in NATO after the United States, but at $61.4 billion, Russia’s defense budget is more than three times that of Turkey, which spends just $19 billion.
But while the asymmetrical relationship favors Russia, Turkey has a much greater stake in what happens in Syria. This is because for Moscow, the conflict in Syria is aspirational. Vladimir Putin's regime is seeking to preserve a client state that it can both monetize and use as a geopolitical asset.
But for Erdoğan, the conflict in Syria, which is on its border, represents a vital–if not existential–interest. There are already approximately 4 million refugees from the Syrian war in Turkey. And as Assad seeks to forcefully reunite the country with Russian and Iranian assistance, millions more will follow.
But. On the GDP, twice isn't necessarily decisive. And if Turkey needs Russian energy, Russia needs Turkish payments for that energy. And I suspect Turkey can get alternative suppliers more readily than Russia can get new customers if Russia cuts off Turkey.
As for the defense budget disparity, all of Turkey's budget is essentially right there. Russia has strategic nuclear weapons and must disperse military spending across a country that spans two continents. That's why I only looked at Russia's closest district. Turkey can afford to focus almost all of their military power against Russia while Russia has to look over their shoulders in a number of directions if the Russians want to wage war on Turkey.
Russia must also factor in NATO if Russia goes directly after Turkey rather than just in Syria. And as the author notes, Turkey has higher interests than Russia has.
And I will note again that despite the lopsided Russian record in wars against Turkey, a new war would be a first with no common land border.
I just don't see Russia being able to deploy decisive force against Turkey if Turkey wants to fight.
Finally, while the ceasefire is lopsided in the sense that it ratified Assad's gains in Idlib province, Turkey has an interest in a buffer zone that prevents more refugees from flooding Turkey. How far back could Turkey fall back and maintain an effective buffer zone? So I won't call that a Russian victory until Turkey caves in and surrenders an effective buffer zone.
NOTE: I forgot the possibility of typos. Russia has about 11,000 IFVs and APCs--not the 1100 I typed in originally. Why that didn't leap out at me when I wrote it I do not know.
