Why FP increases waits: a mathematical example.
BACKGROUND:
- We have a theoretical ride that has a capacity of 2000 guests per hour, or 500 per 15 minutes.
- Every 15 minutes, 1000 guests walk up to that ride (or look at their phone) to check the wait time.
- Of those 1000 guests, 100 are willing to wait 10 minutes to ride that ride, 100 are willing to wait 20 minutes for that particular ride, 100 are willing to wait 30 minutes, and so on to the final group of 100 who are willing to wait 100 minutes for the ride. We will call these groups of 100 "wait groups"
- In scenario 1, we do not have Fastpass, and everyone is admitted through Standby
- In scenario 2, 75% of guests are admitted from the Fastpass line
- These guests (375 per 15 minute block) are pulled evenly from all willingnesses to wait (because the FP wait time is supposed to be max 5 minutes and they're all willing to wait 5 minutes) so each wait group is contributing 37 riders per 15 minutes to the FP queue, and thus only has 63 guests per wait group per 15 minutes walking up or checking their phone for the wait time.
- For simplicities sake, we're doing this in 15 minute blocks (even though Disney updates wait times every 5 minutes or so)
Scenario 1:
As you can see in below, at 9:00 when the park opens, the posted wait time is 5 minutes, and all 1000 guests who walk up in the first 15 minutes enter the queue. 500 ride the ride, leaving 500 in line. So at 9:15, the posted wait time becomes 15 minutes.
This means that all the people willing to wait only 10 minutes no longer want to get in line, so only 900 people enter the queue (the people willing to wait 20-100 minutes). 500 ride the ride, and at 9:30, with 900 people in line, the wait time is set at 25 minutes, and the people only willing to wait 20 minutes no longer want to enter the queue.
This continues for a while but it hits a balancing point. Eventually at 10:45, the posted wait time becomes 55 minutes. At 50 minutes, 500 people enter the queue, and 500 people ride the ride, with 1700 people in line,
so the wait time stays at 55 minutes for the rest of the day. You can see this in the table below.
View attachment 546770
Scenario 2:
As you can see in below, at 9:00 when the park opens, the posted wait time is 5 minutes, and again, all 625 guests who walk up in the first 15 minutes enter the standby queue (remember, the other 375 guests who would have walked up have Fastpasses). In this scenario though, only 125 ride the ride in that first 15 minutes, because 375 ride spaces are going to FastPass. So after 15 minutes, there are 500 in line, just like in scenario 1, but that represents a wait time of 1 hour instead of 15 minutes, because with FastPass, only 125 people come our of the Standby queue every 15 minutes. That 1 hour is already longer than we
ever see in scenario 1.
With a posted wait time of 60 minutes, only those willing to wait 60-100 minutes will enter the queue, so we get 313 guests entering the standby queue between 9:15 and 9:30. Again, however, only 125 board the ride from the standby queue, leaving 688 in line, which represents a wait time of 85 minutes.
With a posted wait of 85 minutes, we actually hit the FastPass equilibrium. only people willing to wait 90-100 minutes are entering the ride (125 per 15 minutes), and 125 people are riding from standby per 15 minutes, so the line remains at 688 people, and
the wait time stays at 85 minutes the rest of the day, as you can see below.
View attachment 546772
This is obviously an oversimplification, but hopefully it explains why wait times HAVE to be longer with FastPass.
TL : DR, FP increases wait times because people who wouldn't have waited the posted wait time are cutting the line.