Of all defensive stats, defensive points allowed has the biggest correlation to wins. Pretty obvious, and on that criteria alone ranking by points allowed is far superior to ranking defenses by yards.
The only argument for yards comes when you factor in on the offense side, offensive points scored also has the biggest correlation to wins of any offense stat -- and has been argued to be slightly more valuable than defensive points; i.e., it's more important to score than prevent points.
So how do you score more points on offense? Obviously "being good", but it's also shown that starting field position has an effect. One study even suggested for every 3 yards of extra average starting field position you give to your offense, you add 2 wins.
Seems crazy, but that might suggest if a defense prevents yards, it could be a big factor in its offense scoring points by giving them better field position. However, a college study broke down the factors that create field position as:
* Punt Margin (22%) -- have a great punter (Rams get to check this one off having the best damn punter)
* Kick Margin (22%) -- have a great kickoff kicker (Rams are good here with GZ)
* Turnover Margin (21%) -- very random/luck based (Rams suck in anything lucky)
* Success Rate (37%) -- how efficient are the offense & defense at successful drives
So the last category is where an inefficient defense could factor into it. And note two things -- it's only a small percentage of what makes field position; and it's split with the offense. So perhaps instead of the defense worrying about conceding yards, it's more logical the offense should worry about sustained drives to help itself out...?
Applying these factors, the Rams already have good kicking/punting, if they could get a damn turnover once in a while and increase their lack of 3-and-outs and stop giving up so many yards, then the Rams could improve their average starting field position.
However, the Rams weren't awful on field position -- they ranked 13th! To boost their average starting field position that magical 3 yards to get those extra 2 wins, they would have to rank 1st or 2nd in the NFL -- which would put them equal to Carolina (#2 in field position).
But before we get too excited, Denver was a very bad 26th in field position. This suggests what we all probably know -- there is no one secret recipe. Bottom line at the end of the day both Carolina and Denver didn't give up points.
It's a tough one... Most "advanced" stat systems value every event in football by a yardage equivalent. For example, a turnover is worth about 40 yards. The theory being points don't just happen magically, they come from a sum probability of opportunity times successful plays times field position, etc.
But defense yards allowed seems to be just "a factor on other factors" that might lead to more wins, where we know for sure that preventing points directly leads to more wins.