sorry for the delay to answer ; I got a lot of complicated days lately, and I wanted to focus my work on other things.
As I was not sure about what you described, I just tested 6 CPU vs CPU matches on BG-Cement with exactly the same high skills, except for the confidence being at 100% for the 1st player and 0% for the 2nd one.
The result is 3 matches won by each, and 12 sets won by the 0% confidence player vs 10 sets for the other one.
So the conclusion is that the Self Confidence influence is very low and you shouldn't worry too much about it...
My guess is that out of 100 sets, the 100% confidence player would win something like 51~53 sets, but I'm not sure as I didn't test further. (hopefully it doesn't make him weaker to have high confidence