This is a bit long & heavy on X's & O's talk. Hope someone out there likes this sort of thing!
As I was considering these ideas more I was struck with a potential insight into the differences between how GK's system &
EP* attack defenses. Both systems attempt to not "tip off" plays. You folks did an awesome job explaining how GK does it both pre & post-snap.
EP is almost the opposite: rather than running a ton of different plays that start out looking the same, you run the same plays from different looks. EP hides information by doing same passing concepts from a variety of formations. You can see an example of it in my avatar. The left side of the play does a three man route concept, and the right side does a two. This can happen even if it starts as a two back set, as in the bottom image. This allows for a ton of offensive flexibility. How the Patriots can look like a completely different style offense week to week reflects that.
The way that you use the EP flexibility is to manipulate match-ups. I believe this is what OB meant. Suppose you think a team's LBs are bad in pass-coverage. You go to 21 personnel (RB, FB, TE) to get their team into their base defense (only 4 DBs). Then you spread the field with 4 or 5 wide, often putting the FB lined farthest wide. The other team either puts a LB in the normal outside CB spot, or wastes a CB on your FB. If they choose the former, the entire defense is playing in roles they are not used to. If they chose the latter, you now have your receivers lined up against their LBs. Furthermore, you can figure out if they are in zone even before you put a guy in pre-snap motion. You can rip teams apart in the passing game like this, and you keep going no huddle so they can't get out of base.
Eventually, they might realize they cannot defend the pass in base against 21 personnel. They swap out a LB for a DB, and you pound them in the running game. This is how scrub running backs put up 200 yards against Colts.
To be able to achieve any of that described above, you need smart RBs, WRs, TEs, etc. Every player needs to understand every part of every route concept. The FB needs to know the inside, middle, and outside of the three man. This is why the Patriots value versatility and game-intelligence in their players. Perhaps OB wants to be flexible like this, but he does not have personnel that can do it.
@steelbtexan has been arguing similar things. The Patriots have moved on from talented players because they could not pick up the concepts.
*(I am talking about EP as the Pats (and sometimes OB) do it. The article linked goes into Pats style EP more. I am not convinced that all teams that use EP actually employ these themes enough. The Steelers' take on EP always
seemed a bit more bland to me.)