But we can't just use the standard deviation percentages for a normal curve. Yogg-Saron damage definitely is not normally distributed. The only way to get good numbers out of this is through simulation.
So I ran some numbers using a very simple simulation that ignored killing minions. If you play Yogg with 15 spells into an empty board, your chance of winning versus your opponent's health looks like this:
Unbuffed C'Thun, of course, killed 100% at health 6 or less and 0% at 7 or more. Yogg-Saron at 15 spells has about a 50% chance of beating out C'Thun. If you'd like to generate some output of your own, you can enter the number of spells, number of minions your opponent has out, and the number of trials you want to do and get a cut-and-paste .csv showing the distribution of the results below. I'll work on a better simulator that accurately deals with minion death and so on, but, you know, that's actually work.