Would Napoleon's chances in Russia have been better had he split his forces?

Let's say that rather than marching >500,000 men straight to Moscow, Napoleon split his force into 3 columns, marching separately under different commanders: One to St. Petersburg, one to Moscow, and one to Kiev or somewhere else in to the south. This would have made supplies easier, and if each column is of roughly equal size - 170,000 or more, at least - then the Russians still can only just barely raise an army that could rival any of these columns' sizes, so it's not as if the French would be opening themselves up to be defeated in detail. Even better, it might goad the Russians into attacking instead of going for a scorched earth and retreat strategy.
 
I think you've missed the point of Napoleon's strategy for the 1812 campaign. He wasn't marching on Moscow because he really likes the onion domes; he's marching that way because that's where Russia's main army is. His initial moves attempted to trap the Russian army between multiple columns, but the Russians evaded the trap, and past Smolensk, there was only one route forward. Moreover, even if Napoleon did advance along multiple axes, he'd still suffer continuous depletion of his forces, and since the axes would be out of supporting distance, he'd be giving the Russians a chance to get numerical superiority over one of them while more or less ignoring the others.
 
Let's say that rather than marching >500,000 men straight to Moscow, Napoleon split his force into 3 columns, marching separately under different commanders: One to St. Petersburg, one to Moscow, and one to Kiev or somewhere else in to the south. This would have made supplies easier, and if each column is of roughly equal size - 170,000 or more, at least - then the Russians still can only just barely raise an army that could rival any of these columns' sizes, so it's not as if the French would be opening themselves up to be defeated in detail. Even better, it might goad the Russians into attacking instead of going for a scorched earth and retreat strategy.

An issue of his march on Moscow already had been addressed, which leaves the numbers. In 1812 Russian forces consisted of:
1st and 2nd armies on the main direction - 153,000 (758 guns), 3rd army in the south - 45,000 (168 guns), Army of the Danube in Moldavia - 55,000 (202 guns), in Finland - 19,000 (102 guns), near Riga - 18,000. Then deeper in land - 4 corps units of reserve (each of 15 - 20,000 at least on paper). Plus 20 - 25,000 Cossaks (total up to 117,000). Surely, they could join each other in various combinations to deal with the isolated French columns.

Then, of course, comes an obvious question: these 3 isolated armies would be led by whom? Napoleonic army was "Napoleon-centered" and by 1812 the only other figure potentially suitable for an independent command was Davout. Who would be the other lucky guy? As was convincingly demonstrated by the earlier campaigns, the marshals left without Nappy's supervision tended to quarrel with each other and even sabotage each other's efforts (see memoirs of Baron Marbot). Subordinating them to each other was not a trivial thing and it did not work well in Spain (according to Marbot, Ney practically sabotaged Massena). Not to mention that out of the whole bunch available in 1812 only Davout was able and willing to perform the duties related to administration of the corps. The rest were doing only what they were explicitly ordered to do.
 
But Napoleon did split his forces. The Prussians, about 20 000 under Yorck advanced towards St Petersburg, but were stopped outside Riga. The Austrians and Saxonians under Schwarzenberg advanced towards Kiev with about 50 000 men but never got far against the southern army under Tomasov.

The French also dispatched a Corps to Polotsk, which later re-joined the main army as it retreated.
 
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