NY6, there have been 3, 2, and 1 at-large berths available. That cycle, more or less, will continue. Meaning that there is an average of two at-large bids per year.
Also, it's not a 1/128 comparison, because the number needs to be reduced by the number of NY6 auto-bids.
On the NCAA tournament, it is not true that BYU and every other team out there has a 24% chance of making the tournament. If that were true, there would be 87 teams in the NCAA tournament . The baseline number would need to be reduced, and the calculation performed from there. All 351 teams have a chance to win their auto-bid, and all 351 teams have a chance to earn an at-large berth. I believe you really are taking 68/351, which equals 19.3. Your calculation would then give you a number of 4.8.
Based on the above, the football percentage would be higher, and the basketball percentage lower. Meaning that the difference between the 5.9% chance of making the NCAA tournament, and the 3.9% chance of making an NY6 would shrink even more, making it about the same.
Based on the above, using your post as a baseline, BYU has a 4.9% chance of playing in an NY6.
I should mention that, as we both know, basketball is a different animal. We're not talking about winning an NY6 game--just playing in one. In basketball, you have to win 2 games to get to the Sweet 16--against tougher competition than your average regular season opponent.
Either way, tell me what you think. I believe that the chances are 4.9% for football vs. 4.8 for basketball.