Now that the title race is over, I decided to check out a stat that I thought I must have misheard from a few weeks back - I think it was in the build-up to the Aberdeen-Celtic SF.
They were discussing Scott Bain's promotion to the starting line-up, and someone came up with his shut-out stats in all competitions this season. I think he was running at something like 80%, which seemed far too high for me. I'm not sure how much you can trust the published numbers, but here's the record for this season's Premiership goalies from the first source I found:
This appears to confirm what the pundit was saying on the radio. It's also notable that Gordon and McGregor are just about the same level on the clean sheets front, and Celtic and Ranges were battling it out in the first half of the season; but Bain is miles ahead in percentage terms, and has been playing during the part of the season when Celtic pulled ahead.
I suspect you could find similar correlations between individual player' performances and their teams' successes; but the size of the difference here and the comparison with Gordon make me think that Bain's personal record may have made a big contribution to Celtic's title win.