It's actually quite interesting using my spreadsheet, how much things can change by changing the percentages a little bit. I found a list of historical percentages between different seed numbers. If I use the historical seed percentages (and assuming that the higher seed wins every round), i come out with only a 1 in 53 billion chance. Changing some percentages up by 5-10 percent can make huge differences. That drop is even with me dropping the chance of winning for the 2, 3, 4, and 5 seeds. A bunch of the rest of the numbers that I used were off 5-10% from the historic averages.
I left the 1 vs 16 at 99%, since it will happen someday. If I change that 99% to the 100% historical average, it jumps down to 1 in 51 billion.
I used historical records from here.