Instead of trying to figure out or reverse enigneer minute details of formulas that 'may' exist, I prefer to go with my own anecdotal evidence. In my very first season of HBD, I was 17-25 with a good hitting C that I moved to DH. I moved my bench C with a PC rating of 86 to a starter (he was not an elite hitter, but made good contact - especially against LHP and held his own just fine as a hitter). My staff improved dramatically from that point on and I finished with 99 wins and a WS title. Furthermore, both SP's I traded for during the stretch run were miles better for me than for the teams they came from.
That was just the first year. Last year, he played an important part of another good staff. The team lost the WS, but the staff was again good.
This year, I let the same catcher walk as a Type A FA. At 5.3M, I couldn't afford him. With his demands down to 1M before the AD, I re-signed him. 77-42 the rest of the way after starting a mediocre 23-20. My 3 main starting pitchers were much better the second half of the season with him catching.
So while I can mathematically try to discern what the formula is, I'm more than happy to watch what appears to be a discernable effect. For context sake, my team has a very strong defense, which is obviously a contributing factor. I thought that was the strongest factor in my newly acquired pitchers' success two seasons ago, but this year, even they struggled more without the high PC catcher. When I brought him back, almost the whole staff was significantly better.
Not scientific, I know, but it sure looks like it has a noticeable effect.