Josh has done exactly what no one else has done here: compiled data, and provided a logical analysis.
Not true. Others have provided analyses, including the one I will provide later in this post. I agree that Josh is relatively uniquely privileged to have access to the data.
You mention "other factors" besides crowd levels that might have contributed to changes in wait times, but I don't see the list of what you think those other factors might be.
I was trying hard to keep my post short and to the point, which I occasionally have difficulty with, and what the specific other factors are aren't actually relevant to my point. The failure to consider the crowds implies strongly that no consideration was made for other factors that might have affected the results. Many of these factors are hard to gather data on, so it might not have been possible to include them in the analysis. But it was an omission to exclude any consideration of them when interpreting the data.
I was curious about the increase in crowds, so I tried googling it. Does Disney even release attendance numbers broken down by park and by month? I could only find annual attendance numbers through 2013. Best I could do was Disney's 2nd Quarter Fiscal 2014 earnings report (covering Jan/Feb/Mar 2014): http://thewaltdisneycompany.com/sites/default/files/press-releases/pdfs/q2-fy14-earnings.pdf which says nothing about WDW attendance.
It is a big problem in these discussions that crop up on the boards that nobody who is posting has any real access to this data at the level that would be required to support an analysis.
By comparison, press releases and web news articles for Q4 2014 and Q1 2015 talk about WDW record attendance, and a record quarterly attendance increase of 7%. Safe to assume that if there was a large attendance increase at WDW in Q2 2014, Disney might have mentioned it? Note that a 7% increase to a 15 minute wait time would make it 1 minute longer. I would also suspect a 7% increase in crowd levels to increase standby wait times across the park somewhat uniformly.
Your analysis is somewhat flawed, as it fails to take into account the capacity threshold -- that is, a 7% increase cannot be calculated directly on the wait time. Consider the following analysis, where only 500 more people wanting to ride Figment on a given day, an increase of only 3%, results in bumping the average posted wait time from 5 to 10 minutes. I've chosen Figment because it is commonly cited as a ride that was always a walk on and now has a line.
According to Touring Plans, the wait per 100 people in line in front of you at Figment is 2 minutes per 100 people. That means the ride can handle 3000 people per hour. Most days FutureWorld is open from 9 to 7, so that's 10 hours or ideally 30,000 people that can ride Figment with nobody having to wait. Obviously this assumes they all arrive at the "right time", because 30,000 people who arrive at 9AM will definitely have to wait (and 15,000 of them will be scared off by the size of the queue) and if the whole 30,000 don't show up until 6 PM they're not all going to get on.
Let's assume we have 300 people over capacity there from the very beginning, and the rest of the 30,000 arrive at the right time throughout the day. Now Figment will experience a 5 (really 6) minute wait all day. At every point, the ride will be at capacity, with 300 people in the queue causing a 5 minute wait. The average will be five minutes.
This is quite unrealistic as we all know that crowds are light in the morning, increase towards the middle of the day, and taper off at the end. So let's consider a different scenario -- in this scenario we will assume that nobody rides Figment until 11 AM, and they all stop at 4 PM. Now we need more people in the queue at all times to give us our 5 minute wait; to be precise we need 500 people and the ride is now going to process 15,500 people over the course of the day and we will still have an average wait of 5 minutes.
Now let's add 500 more people into our same scenario riding between 11 AM and 4 PM. That's a 3% increase (500/15500), and we'll get an increase in the posted wait time of 5 minutes to 10 minutes, just like Josh showed. Note that 400 extra people would be only 2.5%, but would still show the average ride time as 10 minutes because it's rounded to the nearest 5 minutes.
Now, obviously there are some omissions in this analysis, obviously there are people on the ride before 11 AM and after 4 PM. Those people would only lower the % increase in overall ridership for the day that is required for the given bump, let's say it's exactly at capacity in those hours -- now we're looking at 500/30500 (1.6%) instead of 500/15500. That's not really true of course, it's going to be under capacity some of that time. And also if we only have 500 more people than the day before, some of them are going to ride in those hours where it's under capacity. And we all know that the line will be bouncy, and they won't all show up at the "right time" as they did in this analysis, although that smoothing assumption doesn't really affect the analysis badly since we are looking at averages.
The difficulties of assessing the affects of a a given boost on the spread is why there is an entire branch of mathematics called queuing theory. However, given that ignoring the riders who are out of window when calculating the % increase and assuming that all of those riders are riding in the window are assumptions that create inaccuracies in the opposite direction (they compensate for each other), then the numbers from this analysis are not an unreasonable simplification. So taking the # of people that results in a 5 minute average wait and increasing it by only 3% has the potential to increase the average wait to 10 minutes.
OK, not all of those 7% are going to want to ride Figment. And we made some assumptions. Etc. But 3% is definitely close enough to the right range that no matter how much arguing you do about the assumptions and who lines up at different times etc., I don't think you can readily dismiss the idea that the increase in crowds on its own and in the absence of FP+ could account entirely for the changes in observed wait times on this ride.
As for other factors when comparing wait times between Jan/Feb 2013 and Jan/Feb 2014, some possibilities would be ride additions, ride closures, holidays, special events, vastly different park hours? Any special discounts or weather events that would affect attendance? Major recent addition at MK was 7DMT, but that was May 2014? I believe Splash Mountain had extended refurbs both years? The study period doesn't include Easter, so it's not affected by Easter being earlier. I'm not aware of any huge differences. That's also the slowest time of the year, would a June/July comparison yield different results?
Regardless, I can't picture any of those other factors having as much of an effect on wait times as FP+.
You've done a good job thinking of other factors, but in the light of the above analysis on how crowds might (note use of the word might) have an effect, you might not even need to consider any of these.
And again, I'm not saying that the bump wasn't due to FP+. I'm not saying it was due to the crowds. I'm saying there's enough uncertainty that you can't dismiss the effect of crowds and other factors without demonstrating that the effects are not as significant or more significant than the effect of FP+.