CERA and OPS Against don't need defining. They are what they are.
To me, the issues are how the numbers are used, and why some big differentials exist.
Since many pitchers pitch almost exclusively to one catcher, which to me proves it makes a difference to the pitcher and manager who makes that call, so it's hard to count those pitchers who pitch 180 innings with one guy and 9 with the other. Looking at overall CERA numbers does not factor in who catches who way more and way less. It's next to useless, and this is why many poo-poo the stat. It's not like BA or OPS or ERA.
You have to look at each pitcher individually, and this creates new problems, like unbalanced or small sample sizes. You look at the numbers with each catcher and then compare the overall results. To me, the results were highly conclusive. Almost every pitcher, with large enough sample sizes with 2 or more catchers, did better with catchers not names Vaz and Swihart, of late. Some of the differentials were staggering. To just chalk it up as luck, or to throw the whole idea out, just because the reasons can't be pin-pointed, to me, is being short-sighted.
I've provided research many times, even going back to VTek vs his back-ups. I even did one on Posada vs his back-ups that showed that despite his great hitting, pitchers did better with his back-ups and the team often had a better winning % without him.
I'm 100% convinced a catcher may make a big difference, beyond his hitting, throwing, framing and blocking skills. I can't say why, but that does not mean it's not real.
It's best to go season by season/ pitcher by pitcher, but these career numbers are shocking:
Sale
2.52 AJ Pierz. (226- most with CWS)
2.79 w Leon (436 Innings)
2.87 w Wong (47)
4.08 w Vaz (132)
Price
2.96 Leon (204)
4.27 Vaz (360)
Porcello (not a big swing)
4.19 Leon (576)
4.93 Swi (122)
4.96 Vaz (211)
Nate
3.39 Plawecki (183)
4.64 Vaz (176)
4.90 Leon (61) kinda small sample
Only ERod didn't seem to care who was catching:
4.05 Leon (118)
4.18 Vaz (614)
4.44 Swi (75)
But Vaz was almost his exclusive catcher.
These are not cherry-picked pitchers. These are the Sox leading IP pitchers since 2014- Vaz's first year in MLB.