WARNING: IF MATH GIVES YOU HEADACHES, THIS POST MAY BE HAZARDOUS TO YOUR HEALTH!
OK, here are my attempts at quantifying the level of human misery, in which splitting one opening time BG-drop into drops at different times of the day would be likely to result. All of the below is of course based on assumptions and very rough estimates. Though the actual numbers will be different, this makes some of the tendencies I wrote about earlier in this thread a bit more obvious.
First of all, here is my list of assumptions, where I got those numbers, and what potential problems in using them for calculating could be:
Guessed number of total BG-spots: 7500 (there is no information as to the actual size; estimates thrown around here range between 75 and 100 spots per group—who knows, they may even vary them based on how well the ride is doing on any given day—7500 would cover a relatively decent day of 100 called group of 75 people each or 75 BGs, which is pretty close to their average number of guaranteed groups, at 100 people each; even if the actual number of spots is higher or lower, the tendencies we find in comparing different BG-drop scenarios should more or less hold up to that).
Number of visitors at different times of the day: ~10,000 at opening, ~20,000 at 11am, ~40,000 at 1pm. These numbers are guesses. According to the Orange County Register, the average number of daily Disneyland visitors is around 50,000. In my experience (during summer visits; I don’t know if that pattern would hold during the rest of the year) there is a good size influx of guests between 10:30 to 11, and things get really crowded around midday and stay like that until fairly late in the afternoon). So, just that I have some numbers to work with, I’m proposing that the hypothetical day that underlies the below calculations has 10,000 people in the park upon opening, 20,000 around 11am, and 40,000 around 1pm (I’m not using the full 50,000, since I figure some locals will come once the evening to hang out or eat and some families with small kids will leave early, so I don’t expect the estimated 50,000 to be all in them park at once).
I have absolutely no idea how many of those guests are children, so I’m taking a very wild guess and say 25% (by common sense understanding of the term rather than Disney’s ticketing policies which of course count anybody over 10 as an “adult”). In order to come up with something to visualize I’ll also boldly assume that 10% of those kids will cry if they don’t get to ride.
I neglect a number of factors such as differences according to weekday/weekend, school holidays, AP block calendars, people who visit the park & couldn’t care less about Star Wars & this ride, differences in phone speed and Disboards-reading-frequency, etc. etc. Since I am not looking for actual accurate numbers but tendencies that become visible at different possible scenarios of BG-distribution, I figure that all of the above would be affecting the three scenarios more or less evenly.
Here are the three cases I’m looking at:
(A) distribution as it’s currently done—one BG drop upon opening; (B) splitting all BG slots into three equal chunks and distribute those at 1.) opening, 2.) 11am, and 3.) 1pm; (C) splitting all BG slots into three differently sized chunks, trying to keep the odds relatively constant by releasing the largest chunk when we expect to find the largest number of people in the park
Here it goes:
(A) Given the above made assumptions, this would result in 7,500 out of 10,000 participants (either by using their own phone or, in case of many younger kids being part of somebody else’s “boarding party”) being successful in snagging a spot. This also means that 10,000 - 7,500 = 2,500 people won’t get one. If we, per our above estimation, assume that 25% of those 2,500 disappointed people (625) are children and that 10% of those children are upset enough that they cry, then we would in this case end up with 63 crying children spread out all over the park (rounded from 62.5).
Let’s look at the (suggested by some posters in this board as better) alternative (B): Three equal drops of 2,500 slots each, one at opening for 10,000 people, one at 11am for 17,500 people (20,000 minus the 2,500 who already got a BG at the first drop), and one at 2pm for 35,000 people (40,000 - 5,000).
B.1. Eerie silence settles over the park, while people frantically operate their phones. However, instead of the happy 75% we had in scenario (A), two thirds of the slots are held back for the later two drops, meaning we get only 25% “winners,” resulting in 7,500 disappointed people and, if we use the same ratios as above, 1875 very, very sad children, 188 of which—three times the number of those in scenario (A)—start crying.
B.2. 11am — The same number of BGs is released, but by now there are far more people in the park (20,000, according to our above estimate). Subtract the initial 2,500 who already got a BG and you get 17,500 eligible visitors competing for 2,500 slots. This results in 15,000 disappointed guests, 3750 of which are children, 375 of which are now crying. What’s worse, out of the 7,500 people who were already disappointed in the first round 7,500 (15,000/17,500) or 7,500 * 85.7%, namely 6428 people, among which would be over 1600 disappointed children, would now have gone through the experience of hoping for a BG and missing out twice.
B.3. 2,500 BG for 35,000 (40,000 minus the 5,000 who already got one) people => 32,500 broken hearts, 8125 children, 813 of which are now crying. Children who had to go through this three times now: (7,500 * 85.7% * 92.9%)4 = 1,493
Well, how about adjusting the size of the drops according to the expected crowd sizes? Would that work?
(C) If we try to keep the odds fairly constant, we arrive at a BG slot drop size of 1150 (11.5%) for the first drop, 2168 (11.5%) for the 20,000 - 1,150 people placing their hopes in the 2nd drop, and 4,182 (11.4%) for the third. The resulting numbers of crying children would be: 2213 disappointed children in round one, 221 of which are now crying—more than in scenario (B), since we’re keeping more BG for later than in either of the first two scenarios. Round 2 leaves us with 4171 very sad children, 417 of which are crying, and 1958 children, crying or not, who had to go through this agonizing process twice. In Round 3 we again get 8125 disappointed children, 813 of them crying. The number of children who would have now experienced this disappointment three times would be 1,735. Because we held back the largest number to the end, the number of multiple disappointments becomes higher. Thus, what may intuitively strikes us as “fairer” way of distribution is actually likely to cause fat more misery.
Compare this to the 625 children in (A), and the current BG drop procedure doesn’t look as bad after all, does it?
But she knew all along that there was a good chance we wouldn’t ride - I always present things that way: plan for the worst, hope for the best! She had decided her back-up plan would be to get Lunar New Year face paint if we failed to ride, so she had something to look forward to either way. 
