I don't believe it is significantly harder for BYU to make the Sweet 16 compared to a NY6 game. I think it is equally as hard if not harder for football to reach a NY6 game (at least by my math).

You wouldn't set up the Sweet 16 equation as 16/351 and the NY6 equation 12/128. We would have to acknowledge the differences in each sport.

For BYU to make the Sweet 16, they need to make the NCAA tournament. They can accomplish this by winning 3 games in a row in their conference tournament. Assuming you have a 50% chance to win any game you play this would give BYU a 12.5% chance of making the tournament this way (50%*50%*50%= 12.5%)

They can also make the tournament by being selected as an at large. There are 319 candidates for an at large berth for 36 at large spots. This gives BYU an additional 11.28% chance of making the tournament this way.

Overall, BYU has a 23.78% chance of making the tournament. Once they make the tournament, they need to win 2 games in the tournament to make it into the Sweet 16. Therefore 23.78%*50%*50%= 5.945%. So BYU has about a 6% chance of making the Sweet 16. About a 3% chance if they have to play in the play in game.

For BYU to make a NY6 bowl, they have to make the playoff or an at large berth. This year, there was only one at large berth. They could not have played in the Rose Bowl, Sugar Bowl, or Orange Bowl given the way the contracts are structured. Therefore BYU is competing for one of 5 spots in a NY6 game. Any team can occupy any of these spots. So there are 5 spots for 128 teams. That gives BYU about a 3.9% chance of making a NY6 bowl.