There was a reference recently to CNA (Center for Naval Analysis) paper titled Russian Forces In The Western Military District on combat ratios between Russian and US divisions. There, on page 17 such statement was made.
In a classical sense, the Russians assess that they need to possess at least a force ratio of 3:1, preferably 4:1, to defeat a US division (three brigade combat teams)in an open battle. Naturally, the outcome of a battle also depends on asymmetrical means of combat, such as electronic warfare; however, in terms of force correlation, Moscow would like to possess enough fire superiority in the initial period of war to ensure an immediate breakthrough of front lines. Before 2012,the Russian Land Forces would have required at least seven to nine combined arms brigades just to defeat a US division. As a result, and given the complexities of commanding combined arms brigades, a decision was made to return to the pre-Serdyukov model of C2 of regiment-division-army to match NATO’s potential in the western operational direction.
It needs to be stated that this conclusion is made based on the assessments, as the end note suggests, of Marek Depchinsky who passes in Warsaw for military specialist on Russia. Let's start with legitimate assessments: Russia's divisions are smaller than American ones. This is a hard cold fact, not to mention the other fact that US division can fluctuate between one to five Brigade Combat Teams, in this case US division can range anywhere from 14,000 to 27,000+. That is why it is always a fool's errand trying to figure out the actual size of any US division. It could be 15,000 it could be hell knows what, depending on the circumstances. Russian divisions are also capable to be augmented but they are pretty hard-set in terms of numbers of personnel and TOE. Here is an example of Russian (4th Tank) Division.
But, of course, main point in Depchinsky's analysis is the fact that, as he himself defines it, this whole thing is about "classical sense". What is this Depchinsky's "classical sense"? I will go out on a limb here and state that the "classical sense" is a two opposing divisions taken out of the overall structure of armed forces, placed on the imaginary huge plateau and being compared on purely isolated TOEs in a hypothetical battle with each-other. Obviously, this is not how real war works, not to mention the fact that any references to brigade-structure are absolutely irrelevant, since Russians decisively returned to a division structure. Depchinsky writes about "open battle"--I have news for him, "open battles" ended up with the WW II. Today's battles are not only conditioned by the strategic aims--strategic offensive, strategic defense--but by the fact that some "abstract" Russian division today, in 2020-2021, can do what American division can not--it has a separate air-defense regiment. In fact, Russia has what is a separate air-defense arm for her ground troops--Troops Air Defense system (Voiskovaya Systema PVO).
Why it is important? Because the air component of US 1st Tank Division, as an example, 501st Aviation Regiment of the US 1st Armored Division, which is a a striking stand-off force for US division (as an example) never operated in the environment where it had to face such systems as S-300V4, Buk-M3 or Tor-M2, and others, which are a standard issue for Russia's ground troops. When taken into "NON-classic" combat consideration, among many other things, including integration into combat networks, the picture changes dramatically. Including the fact that no American unit ever fought with an enemy capable to strike to operational and even strategic depth. In other words, US Army never experienced the situation where its rear logistic, headquarters and other C4 systems are attacked and destroyed. But this is precisely what fighting Russian abstract division entails not in a "classical sense" but in reality. And this is just a brief shallow overview of only some key capabilities which turn modern warfare into a stochastic process with myriad of variables popping up and disappearing from combat reality.
As per ratios--this is what General Staffs do, including, "in a classical sense", but the reality of the warfare which will be fought is always shrouded by secrecy and is never disclosed. So, all those 3:1 ratios are just talking points required for public discussion and, as I already stated, Russian divisions are smaller and the actual force required is calculated quite differently from comparing TOEs of respective units. Ask yourself a question: can US division fight without its air component or how effective is air-defense of any US division, or the ground troops in general? I'll give you a hint--it is not even in the same league with Russian ground troops air defense. Not even close. If you think that you can stop Iskander with Stinger, think again. So, when I wrote my second book I peeked not into the "classical sense", but into the actual war with all its modern complexities. That is why I called my book The Real Revolution in Military Affairs. I hope this short clarification on ratios helps. So, in general, Depchinsky's own clarification in terms of complexity of factors influencing force ratios is a correct one but any warring side ON the offensive will always try to create a large numerical (force) superiority at the breakthrough point and this is nothing new--enough to take look at Red Army's Deep Operations in WW II.