Really, I thought you knew more about football than just stats.
So a team decides to focus on taking away the run, now you have a better passing day. A team decides to focus on stopping the pass, guess what happens.
Um, that exactly proves my point, if it happens that way.
Let's assume the opponent decides to focus on taking away the run -- the offense has poor rushing stats, but it has a better passing day, as you said. And we know that when a team has a better passing day, it has a much better chance of winning. Thus, having poor rushing stats does not prevent the team from having a better chance of winning, because it passed better. And for the opponent, focusing on taking away the run and stopping the run did not help it stop the pass or increase its chances of winning.
Now let's assume that the opponent decides to focus on stopping the pass. As you say, the offense then has a better rushing day but a worse passing day. And we know that when a team has a worse passing day, it has much less chance of winning. Thus, having great rushing stats did not help the team pass better or increase its chances of winning. And for the opponent, focusing on taking away the pass at the expense of allowing the opponent to run better greatly increased its chances of winning.
So, by your own words, a defense that focuses on shutting down the run increases its chances of losing, while a defense that focuses on shutting down the pass and doesn't worry about allowing the opponent to run the ball increases its chances of winning.
Let me guess, you want to change your mind about what you said?