Top 3 rushing teams: 9-10
Top 3 pass rating teams: 13-4
Top 5 rushing teams: 17-14
Top 5 pass rating teams: 21-6-1
Top 10 rushing teams: 33-27
Top 10 pass rating teams: 40-16-1
There are three teams that rank among the top 10 in pass rating, but are bottom 10 in rushing yards (GB, Den, SD), and they're a combined 13-4.
There are three teams that rank among the top 10 in rushing yards, but are bottom 10 in pass rating (NYJ, Hou, Min). None of them has a winning record.
And no, that doesn't mean that how well you run the ball is completely unimportant. Running well obviously benefits a team. But if you can't throw it, you won't win many games. You'd rather be good at both, but if you can only be good at one, it's obvious which one you would choose.
Yes, it's obvious that teams must be able to pass to win consistently. When the average game is around 100 yards rushing and 300 yards passing it's obvious that 300 is bigger than 100.
Team's with terrible QBs just throw off the stats. The Jets could run for 200 yard per game and it's not going to make Geno Smith a great QB. What's important is how a specific good QB does with and without the
threat of a strong rushing attack.
The issue is that rushing and passing are not independent variables. They're interdependent.
The other issue is that it's the threat of a good rushing attack that's important, not the total yards gained. Defenses adjust dynamically to contain rushing which makes passing easier. That's very difficult to measure statistically.
How do you statistically measure the following things that a strong rushing threat causes?
8 men in the box vs 7.
DL that delay their pass rush to play run 1st style defense.
LBs that play closer to the line to defend the run which causes more space to complete passes behind them.
Defenses that play more base personnel (3 LBs) vs Nickel (more DBs) to contain a strong rushing attack.
Examples:
Game 1: Winner has 50 yards rushing, 300 yards passing. Losing defense plays 8 men in the box the majority of the game.
Game 2: Winner has 50 yards rushing, 300 yards passing. Losing defense plays 7 men in the box the majority of the game.
It's obvious that the game 1 winner has a stronger rushing threat than the game 2 winner, but
it's impossible to ascertain this information just looking at passing and rushing statistics. The game 1 winner is highly likely to have had more than 50 yards rushing if playing against 7 men in the box. The game 2 winner is highly likely to have had less than 50 yards rushing if playing against 8 men in the box.