This one’s a bit on the wonky side. Via John Sides we have a newish paper, The Rising Incumbent Reelection Rate: What’s Gerrymandering Got to Do With It?.
The answer in brief: less than nothing.
Some background. The reelection rate of Congressional incumbents has always been high, but over time it has gotten higher, as shown by this graph from the paper:
Why is this? The authors aren’t willing to say for sure, but they are willing to say that it’s not because of increased or technically improved gerrymandering. Decennial census-based redistricting has actually decreased incumbents’ reelection rate, while other overriding factors (whatever they might be) have increased it.
A reasonable conclusion (and no real surprise to many of us) is that new independent-commission redistricting schemes such as California’s are not going to do much to change the incumbent advantage.