If you've read Rising Tide, then you'll understand quite clearly that the Russians had their main communications cable tapped for over 30 years. As soon as they left their Northern Ports, the USN was picking up data and traffic. They knew where they were going to etc...
The classic example is the Cuban Crisis, 5 subs armed with nukes, and 4 were intercepted within 3-4 days of the ASW killer groups going active - in fact they followed them all the way through the Atlantic.
The Russians would always have managed to sink "something" - but their own expectations were that they would be lucky to get 1/10th of all US Carrier Groups - and that was with enormous fleet/land based air support.
For those who think that Russian subs were technological marvels - then the list of russian sub accidents and losses is somewhat sobering - they were invariably more dangerous to themselves than the americans.
The nuke sub that they leased to India for example sank twice prior to handing over and was considered a jinxed boat. it was carved up as soon as India sent it back at the end of the lease.