HS has max cap at around 75k.
Let's say after RoR settles down it averages: 120 ppl per BG, 120 BGs and 50 back-ups.
That's about 14k guests guaranteed rides, and 6k who have a decent shot.
1/3 of max cap arrives, so 25k ppl out of 75k possible.
There are 20k slots to give 25k ppl, so a 4 out of 5 chance to succeed.
Let's take that to 4 time windows-
Park open: 25k guests there, 5k get a BG. 1 in 5 chance to succeed.
12:30p: 45k guests minus 5k with BGs, so 40k and 5k get BG#2. 1 in 8 chance.
3:30p: 55k guests minus 10k with BGs, so 45k and 5k get BG#3. 1 in 9 chance.
5:30p: 45k guests minus 15k with BGs, so 30k and 5k get BG#4. 1 in 6 chance.
Attending all 4 windows, you now only have a 3 out 5 chance to succeed. For every window you missed, your chances go down further. For guests who are trying during the 2 midday windows, they'll likely have to show up to HS 3 or 4 days before success at BG.