The Pats also run a helluva lot of plays so I'd expect they'd be way there in terms of rushing attempts.
A better stat would be how NE's rushes as a percentage of offensive plays compare to other team's rushes as a percentage of offensive plays. That's the true measure of how run- or pass-oriented NE is.
Actually, I ran the numbers on this after last season. It wasn't what I'd call a "thorough study" but it does address the point. Although I can't find my spreadsheet at the moment, the takeaways were ...
- the league average was a couple ticks above 58% passing
- most seasons, since 2007, the Pats have been between 52% and 56%, averaging just under 55% (2015, with all the OL and RB injuries was the Pats outlier at 62%)
- there are always a few teams that get above 60% passing to as high as 65%. Until last season's debut of the Kamara-Ingram tandem, the Saints were one of them for several consecutive seasons.
- there were also always a few teams that were under average (IIRC, the Vikes were regularly under average when AP was healthy)
- since 2007, there were a very few teams that hit a 50-50 balance or that ran more than they passed for an entire season (mostly teams with running QBs, e.g., the Titans when they had Young)
The Pats aren't alone in "running more plays". They did set a record (I think) in 2012 with nearly 1200 offensive plays for the season, when they went balls-to-the-wall with the no-huddle and hurry-up. But the Pats have since dropped back to around 1050 or so - which is about where most of the league is now (teams that pass more, generally have more plays).
There were two things that happened in 2006 that helped to turn the NFL into "a passing league" beginning in 2007.
1) "The Polian Rule", which was actually Polian insisting on a "re-emphasis" on the enforcement of existing rules regarding defender contact with receivers (but also some other actual rule changes since).
2) The league changed its policy regarding "ownership" of game balls. Prior to 2007, all game balls were provided directly by the league. Before the game, the refs would take brand new footballs (complete with their slippery wax coating) out of their original packaging and give them to the teams. Several QBs (including Peyton and Brady) had been lobbying the league to allow the teams to "own"/control the game balls up until game time, so that the balls could be "broken in". This was really about removing the slippery factory coating and changing the surface texture to something closer to suede - making the footballs easier to grip (AFAIK, it had nothing whatsoever to do with PSI, at least not at that time).
So, since 2007, the total number of passing plays per season has increased substantially - IIRC something around 10% (might be a bit more). However, the total number of running plays has only declined by around 2% or so. IOW, there are now more total plays per game. This can happen because a failed pass play stops the clock, whereas a "failed" running play does not. This is also the main reason why games have gotten longer in real-time since 2007 - a lot more clock stoppages on incomplete passes (roughly 1/3rd of all pass plays).
Finally, the Pats 2018 pass-run ratio is currently about 55-45. However, it has varied quite a bit from game-to-game (it always does ... opponent-specific game plans):
47% pass, 53% run v. MIA
66% pass, 34% run v. IND
48% pass, 52% run v. KCY
Meanwhile, the Pats opponents in the last three games have passed substantially more:
MIA = 58% passing
IND = 74% passing (59 pass attempts by Luck)
KCY = 68% passing (the Chiefs ran the ball only 17 times; the Pats ran 38 times and dominated ToP).
