Diamondbacks starters can't go deep: is it a problem?

It's become something of a joke in the Gameday Threads about how Arizona's starting pitching seemingly can't go deep into games. It certainly seems like a problem, and an average of 5.017 IP/GS seems to be low. But are they really?

The second assumption can be answered fairly easily. Yes, the Diamondbacks have been one of the worst in getting lengthy starts from their pitchers. This table shows each team's innings pitched per game started as kind of a crude measure for the average length starters are lasting per team:

The D-backs weren't much better last year over the full season:

It's clearly not a figment of our imagination. Is it a problem, though? That's a little harder to figure out.

If we look at the last few years to see who has been making the playoffs, it does like most of the teams are in the top 10 for IP/GS: 5 of 10 in 2014; 7 of 10 in 2013; 5 of 10 in 2012; 5 of 8 in 2012, including the Diamondbacks. But if the difference between the 10th best team and the worst isn't dramatically different, instead only showing a gap of less than an inning. Between the top team and the bottom there's more variance, but it's usually only about an inning, and in 2014 was less than an inning.

Spread out over 162 games an inning every game will carry a larger difference, as you're calling on your bullpen earlier every night over potential rivals. But depending on how your bullpen is structured it might be easier to be managed because those extra innings might be absorbed with a good long reliever, or if you have a bullpen that is talented from the top to the bottom.

Of course, using the postseason as a result from starter longevity is problematic because it doesn't represent if the pitching is effective, only if the team played well. The Angels last year were the 6th worst team for getting long starts, yet their offense was so good that they ran away with their division. What if instead we compare IP/GS to starting pitching fWAR?

It seems there's some positive correlation, but not an overwhelming one:

This is only a handful of years, I didn't run any statistical tests beyond simple correlation. This isn't a finished study by any means, but it might serve as a starting point for some of the members of the community that are smarter than me.

Other things I'd like to consider would be a larger data set, comparing IP/GS to a rate stat instead of a counting stat (it makes sense that the longer a pitcher is out the more WAR they can accumulate, and if they're making it into the 7th inning on a consistent basis they probably aren't too terrible in this age of pitcher specialization). And with increased specialization for relievers and the decline of complete games, is this correlation losing any meaning? If I looked at older years would there be a stronger connection?

Obviously the above is closer to a pilot study than a fully fleshed out idea, but it does show you're not crazy for wondering if the Diamondbacks currently aren't very good at going deep into games. It seems to matter some, but how much is still up for debate.