Len Testa Crowd Analysis

[tirian]

@lentesta First as you have said obviously something changed to make your modeling (which is wonderful work and a great job that you have done) off this January and February. Now getting down to cause obviously gets tricky as there are a number of inputs.

So you have shown that capacity was throttled down before 2/21 as compared to after that date of this year. I think the point @mikejs78 has made is the big point and really the determining point on how this throttling of capacity is interpreted. Without historical context, sure it looks like Disney has throttled down a bunch and of course this could explain the differences. However, I would humbly say though that this data (a one year look pre and post 2/21) is shaky when trying to figure out why your projections were off as it has no comparison to previous years, and I think you would admit as much when you say the numbers should be viewed with skepticism. Perhaps Disney has always decreased capacity during these times by similar percentages or maybe they haven't. That is the missing piece of data, and I am not sure if you have capacity (actual exit counts) for the same time periods in years past or not. That is huge and has huge effects, especially depending on the magnitude of any decrease in capacity from prior years.

On the flip side another input is attendance and that is something that we don't know and is much harder to measure. As you have mentioned the economy is better, delayed trips due to hurricanes, and also this is the third year of tiered pricing (??? or around there if I remember correctly). So behavior is ripe to start changing. And here is the other only issue I see in the analysis, that wait times will increase linearly with attendance. I think the issue here is complete saturation of the capacity for the day. @MisterPenguin has laid this out very well above.

I will attempt to bolster this in another way with the area of study I know which are drug metabolism, kinetics, the Michaelis-Menten equation, and saturation kinetics. This is an area where loads of modeling and equations exist and great science. Actually, it is great parallel to theme park ride capacity and attendance modeling. I will not go into all the math and equations etc here to save everyone from that, but it is all available if anyone wants it and wants to hear more. Most basically, for this I will say drug molecules are similar to people visiting a theme park and that rides/attractions are the enzyme that eats them up so to speak for the metaphor. So a ride/attraction has a certain throughput that it can do, of course which is dependent on staffing and the amount of vehicles used, which is the same as the velocity of an enzymatic reaction, and even in nature it is not constant. And as people queue up and wait for a ride (and then, even though not a direct relation as we know, ride wait time goes up) this is equivalent to a drug concentration or number of people waiting for a ride. So if a theoretical ride capacity is 1,000 people per hour or an enzyme can take care of 1,000 drug molecules an hour, the actual rate of people going through the ride will increase until the capacity is reached or in kinetics the enzyme is saturated. Then the actual rate of people going through the ride for a certain time period will not change, but you continue to have more and more line up.

If we look at one ride and assume the ride on this day has a 1,000 pph capacity we can see what happens if the the number of people entering the attraction per hour is higher (assumed with higher attendance) and then goes over the capacity. The actual rate of people going through the attraction increases until capacity is hit. Then as you have said yes it is true that the additional number of people in line has a linear relation to the number of people entering per hour, but there is an exponential relationship between the total number people entering the attraction over a certain time period and the number still in line after that time period. Of course this simplifies things and takes out things like human behavior when a ride line gets so long and avoiding it etc.
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So now some pictures for those who are visual. I have just changed the graph axis labels to illustrate the point and the originals and a discussion of the said graphs can be found: http://www.derangedphysiology.com/m...ero-order-and-non-linear-elimination-kinetics

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So as can be seen when considering saturation if attendance increases from A to B, and we are not near complete saturation or near complete park capacity at a macro level or at a single attraction at a more micro level there is almost an equal rise from a to b in people in lines or wait times. However if expected attendance C is closer to the saturation point and is further increased to D there is a much larger rise from c to d in people in line and wait times. As saturation or full capacity is reached there will be greater increases in people in line and wait times then expected. Works in nature and works here as well.

To your point Disney can control how that curve looks to some extent with staffing and capacity. I will look at capacity in a macro whole park sense here. Obviously it is far more complex and would be a fun problem to model, but this is most simplistic for explanation.

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So three things could have happened here:

On the one hand Disney could have moved capacity from the high capacity curve to the medium capacity curve (the middle curve) or even from medium to low. For explanation and illustration lets say from the high capacity curve to the medium capacity curve. They could have done this and you and your team model you are expecting attendance level A with the high capacity curve and thus wait times and people in line of a1, however as the capacity has changed then you end up in a big difference from wait times and people in line that is a2. This is all just Disney trying to improve margins and save money and decrease capacity and staffing.

Option 2 is that if Disney has always been riding the slow season with the low capacity curve and has been close to the saturation point for that slow season. However, if there was even a small percentage attendance bump from C1 to C2 which could be related to the economy, buying behavior with tiered pricing, the hurricanes, etc then as Disney was always playing close to maximum during this season this modest attendance bump (if unexpected and capacity not increased) created a c1 to c2 increase in people in line and wait times, which is not linear to the attendance increase.

And then the most likely senario would be a bit of both. Disney has had a few years of analytics and data and are feeling confident and looking at margins and have a directive to cut operating and capital expenditures. During the slow season they always believed they had extra margin for attendance level A and they believe that they can move say from the high capacity curve above to the medium capacity curve and have a marginal effect (to them) on wait times and people in line (a1 to a2). Now they have a steeper curve which is much closer to saturation and if that is coupled with a more then expected increase in attendance from A to B and we end up with a b2 level of wait times and people in line. Now if you (Len and team) are modeling this and are expecting the high capacity curve then the attendance bump would have been an a1 to b1 bump which is probably within your error and isn't a big deal. Also if this kind of attendance variability had existed for years Disney had been able to absorb it at the high capacity curve. But now you are seeing with the combination of the increase in attendance and the decrease of capacity to close to the saturation of capacity levels that there is a big swing from a1 to b2 which is way off. Disney is also surprised as they are expecting a more modest a2 level of people in line and wait times but are seeing a b2 kind of level. However, this is after Disney has let go of a bunch of seasonal employees, have lower college program numbers, etc. and turning that ship is hard. So perfect storm. This seems the most likely and while Disney is playing too close to having saturated capacity and are having the good news of better then expected business, it isn't just some nefarious lets make the park seem busy so we can charge more tin hat theory. Also means Disney will see a drop in satisfaction scores and attractions per guest scores and will hopefully adjust for next year.

The big problem is all of the above scenarios depending on the actual curve shapes can all look very much the same in the outcome of increase in wait times and people in line and can be very hard to parse out. It all comes back to if we had the actual capacity and exit counts historically and could trend that. Not that you need any advice from a random internet guy who is bored on a Sunday, but it seems like that would be great data to have especially in the historically slower seasons to have best predictions and real time updating of your modeling.

You mentioned something that has been detrimental to staffing: Disney has lost a huge percentage of seasonal (CT—Casual Temporary) CMs. The changing tax laws and Obamacare health care affected that. I won’t get into details because it opens a huge can of worms, but even though some of the changes were based on local people’s working a couple shifts a year and taking advantage of free admission, the majority of CTs were college program alumni who returned during the summer and winter breaks for a dose of the Magic. When the requirements jumped to 150 hours every 6 months (and at least 300 hours/year), most of these college students couldn’t commit. CT staffing plummeted.

 

[xdan0920]

It's not that simple. There's multiple inputs and a single output, and the results can be affected pretty dramatically by minor changes in one or more of the inputs (hence non-linear). The problem is we don't have enough data to make a determination on which input was the determining one, or if there was more than one input that changed, or how the different inputs differed from previous years. @lentesta did awesome research and provided one data point. But there are many more we need to properly determine what happened.

Except it’s literally his livelihood to do that research and figure out what’s going on. We are message board hobbyists. He’s an actual professional. He has been very clear about what he believes is happening. You are saying, you don’t believe him, he’s full of it. I disagree.

 

[mikejs78]

Right! And it’s so simple.

Disney lowered capacity. Say from 10k guests per hour across all attaractions(made up #) to 8k. That has a destructive impact on wait times, crowding in public areas, lines in QSR. When you try and walk the perfect staffing right rope that’s hard. When you then try and see how far you can push the lower staffing models, that’s just wrong. They should not be doing that.

We don't know that they lowered capacity from previous years. We know capacity was lower in Jan/early Feb than later in Feb. That's what Lens data shows so far.

 

[mikejs78]

Except it’s literally his livelihood to do that research and figure out what’s going on. We are message board hobbyists. He’s an actual professional. He has been very clear about what he believes is happening. You are saying, you don’t believe him, he’s full of it. I disagree.

I'm not saying that at all. I admire @lentesta quite a bit and his work. But he's a data scientist, and like anyone in this field will tell you, it's all about the data. He has a hypothesis based on some valid experiments. I'm not even challenging his hypothesis (not a statement of fact, which he himself postulated), I'm pointing out alternative scenarios and I'm curious to see what his data says about those possibilities.

 

[MisterPenguin]

Except it’s literally his livelihood to do that research and figure out what’s going on. We are message board hobbyists. He’s an actual professional. He has been very clear about what he believes is happening. You are saying, you don’t believe him, he’s full of it. I disagree.

Is Len your cult leader now and declared infallible?

Len himself posted in this thread about how he wasn't sure off the top of his head about the relationship of overall attendance to lines. He's scratching his head over the cause of 60% jump in wait times and trying to figure it out. NASA scientists can lose hundreds of millions of dollars worth of a satellite by forgetting to convert imperial to metric. Argument by Authority is a fallacy.

Len has great data and analysis. But Disney isn't transparent. We don't have their hard numbers on attendance or parkhopping or staffing. At some point, there are guesses. But from the math I know and the model I used (and no model is perfect), I caught something Len wasn't aware of: overall attendance increases can indeed lead to spikes in waiting in a non-linear way.

Disclaimer: I've given Len money through his website. Have you?

 

[lazyboy97o]

"An attraction with 1,000 pph capacity will take 66 minutes to get through 1,100 people."

Correct. However, this means in the first hour, there will be 100 people still waiting to get on. In the next hour, when another 1,100 people show up, they all have to wait for the 100 people left over from the first hour. And when the second hour is done, there will now be 200 people waiting in line. Once you pass the tipping point, the queue backs up hour over hour.

If it's 1,320 people per hour showing up, then for each hour that ride can not accommodate 320 of those 1,320 people. Hour by hour, 320 people unaccommodated is 320% more than 100 people per hour unaccommodated.

Let's look at a 10 hour day. If 1,100 people show up per hour, that is 11,000 people. A 1,000 pph capacity will take 11 hours to get through.

If 1,320 people show up per hour, then that 13,200 people. A 1,000 pph capacity will take 13.2 hours to get through.

So, yes, that's a 20% increase in pph and a 20% increase in time.

But... people aren't going to show up after the end of the 10th hour, let alone during the 13th hour in a ten hour day. The time to deal with the people that arrive each hour can't be solved by extending the time (actually, that's exactly what WDW does occasionally). But, if you're going to consider the case of a limited set of hours for the park's opening and closing, you have to consider the impact of everyone showing up within the park hours and not after the park has closed.

With 1,100 pph, the ride needs to accommodate 11 hours worth of guests in 10 hours. That's 1,000 people more in the line during the day, and not showing up for the 11th hour.

With 1,320 pph, the ride needs to accommodate 13.2 hours worth of guest in 10 hours. That's 3,200 people more in the line during the day, and not showing up after the park closed in the 11th-13th hours.

Now, of course, when lines get that long they are self-limiting because guests refuse to wait that long and rather stroll around or eat or shop. And the numbers fluctuate during the day. And there are other limiting factors. But, here's the point: once you hit your tipping point, an overall increase in guests will have an exponential effect on lines.

Demand is not constant. It is curved.

 

[MisterPenguin]

Demand is not a constant, it is curved.

Demand is not constant. It is curved.

1. I have acknowledged such.

2. Your counterexample didn't include any curvatures. You just linearly expanded the time of the park hours.

3. Models aren't perfect representations. They illuminate a point. The point being that increase in overall attendance can lead to non-linear spikes in wait times.

 

[EPICOT]

If there is an exponential relationship between attendance and wait times then that would mean each additional person in line over the hourly capacity would be adding more time to the overall wait time then the person in front of them. That does not make any sense. A linear model would say that each additional person adds X amount to the wait while an exponential model would say that each additional person would add X+C, where C is some value that increases for each person in line.

Say the 1st person in line over the capacity adds 30 seconds to the wait time. Would the 100th person in line over the capacity also add 30 seconds to the wait or a value greater than 30 seconds. It wouldn't make sense for a person in line to add more wait time than another person in line, regardless of when they entered the line.

 

[briangaw]

Right! And it’s so simple.

Disney lowered capacity. Say from 10k guests per hour across all attractions(made up #) to 8k. That has a destructive impact on wait times, crowding in public areas, lines in QSR. When you try and walk the perfect staffing tight rope that’s hard. When you then try and see how far you can push the lower staffing models, that’s just wrong. They should not be doing that.

Well that and maybe attendance changed or not. Disney is the only one who knows the entire answer. Well I would argue that Disney should be walking the perfect staffing tight rope as a stock holder. I believe if they don't do a good job of that and get it wrong then that is obviously bad. I think there is something to be said of @tirian response about causal temporary employees too. If you used to have some slack where you could fill shifts with more as needed workers that helps your elasticity. That goes away and if you get it wrong you have less room.

 

[lazyboy97o]

1. I have acknowledged such.

2. Your counterexample didn't include any curvatures. You just linearly expanded the time of the park hours.

3. Models aren't perfect representations. They illuminate a point. The point being that increase in overall attendance can lead to non-linear spikes in wait times.

You acknowledge it in words after the fact. It is completely ignored in your argument and math.

My counter example looked at a single hour, not a day, because that is how capacity modeling is done. Hourly park capacity is based on the peak design day hour.

Your model illustrates a non-existent condition, constant demand, and then conflates a daily metric with instantaneous and hourly metrics.

 

[MisterPenguin]

If there is an exponential relationship between attendance and wait times then that would mean each additional person in line over the hourly capacity would be adding more time to the overall wait time then the person in front of them. That does not make any sense. A linear model would say that each additional person adds X amount to the wait while an exponential model would say that each additional person would add X+C, where C is some value that increases for each person in line.

Say the 1st person in line over the capacity adds 30 seconds to the wait time. Would the 100th person in line over the capacity also add 30 seconds to the wait or a value greater than 30 seconds. It wouldn't make sense for a person in line to add more wait time than another person in line, regardless of when they entered the line.

There are posts above that show the relationship. Can you show where the math is wrong?

As to your example, you're not accounting for continually increasing wait times as the ride's capacity is exceeded and the backup from one hour gets added to the next hour's line which has its own baked-in excess and they keep progressing geometrically. Overall growth in attendance doesn't mean there are extra people the first hour, there are extra people each hour and the back-up keeps growing.

 

[brb1006]

RetroWDW recently uploaded home video footage of the Magic Kingdom in the 1970's showing crowd differences and the old school way of meeting characters.

Not sure if this video is relevant, but it really shows the differences between WDW then and now.

 

[briangaw]

If there is an exponential relationship between attendance and wait times then that would mean each additional person in line over the hourly capacity would be adding more time to the overall wait time then the person in front of them. That does not make any sense. A linear model would say that each additional person adds X amount to the wait while an exponential model would say that each additional person would add X+C, where C is some value that increases for each person in line.

Say the 1st person in line over the capacity adds 30 seconds to the wait time. Would the 100th person in line over the capacity also add 30 seconds to the wait or a value greater than 30 seconds. It wouldn't make sense for a person in line to add more wait time than another person in line, regardless of when they entered the line.

I would NOT say there isn't an exponential relationship between attendance and wait times. There is a far more complex relationship then that. Prior to reaching the maximum capacity provided for that time period on a specific day that is definitely not the case. Once capacity is reached then wait times will increase at some exponential value as long as a constant rate of people continue to get in line. Of course at certain wait times people will no longer get in line and will go to something shorter, but if nothing is shorter they will suck it up and get in line to do something for the most part. And saying wait time increases exponentially at a saturation point isn't saying that the individual who gets in line at that point is adding more and more time. It is saying that more and more people will continue to back up in the line adding increasingly to the wait time. It isn't that they individually add a greater wait time, but more that they are coming in with 500 of their closest friends while the ride individually and more importantly the entire park of rides/attractions can't keep up with the demand. Of course this will happen until people start leaving the park and then the per hour entry of people trying to ride gets under the capacity and the line goes down.

 

[xdan0920]

Is Len your cult leader now and declared infallible?

Before I get to anything else. Grow up.

 

[xdan0920]

Is Len your cult leader now and declared infallible?

Len himself posted in this thread about how he wasn't sure off the top of his head about the relationship of overall attendance to lines. He's scratching his head over the cause of 60% jump in wait times and trying to figure it out. NASA scientists can lose hundreds of millions of dollars worth of a satellite by forgetting to convert imperial to metric. Argument by Authority is a fallacy.

Len has great data and analysis. But Disney isn't transparent. We don't have their hard numbers on attendance or parkhopping or staffing. At some point, there are guesses. But from the math I know and the model I used (and no model is perfect), I caught something Len wasn't aware of: overall attendance increases can indeed lead to spikes in waiting in a non-linear way.

Disclaimer: I've given Len money through his website. Have you?

Now. On to the basics here.

Your formula is wrong from jump. Lines don’t work the way you say they do. They don’t continually build up through out the day. They level off, they decrease, they surge.

Attendance and wait time SHOULD correlate. What that correlation is, I don’t know. I do know it’s not your example. Because lines don’t work that way.

Like I said. You are a hobbyist. Which is fine, so am I. But I’m not postulating that I’m more then that.

 

[mikejs78]

My counter example looked at a single hour, not a day, because that is how capacity modeling is done. Hourly park capacity is based on the peak design day hour.

That's a poor way to model park capacity, if that's how they do it.

 

[mikejs78]

Now. On to the basics here.

Your formula is wrong from jump. Lines don’t work the way you say they do. They don’t continually build up through out the day. They level off, they decrease, they surge.

Attendance and wait time SHOULD correlate. What that correlation is, I don’t know. I do know it’s not your example. Because lines don’t work that way.

Like I said. You are a hobbyist. Which is fine, so am I. But I’m not postulating that I’m more then that.

Do you know @MisterPenguin's expertise or profession? I sure don't. It's a bit presumptive to label him a hobbyist.

Attendance and wait times do corrolate. The question is how. And @MisterPenguin's model is mathematically sound as far as I can see.

 

[lazyboy97o]

That's a poor way to model park capacity, if that's how they do it.

How is it poor? That represents the hour(s) during which the most people are in the park on the design day. That is the hour(s) during which attractions will be most in demand. Demand during the first part of the day builds up to this hour(s) and then decreases after it.

 

[mikejs78]

How is it poor? That represents the hour(s) during which the most people are in the park on the design day. That is the hour(s) during which attractions will be most in demand. Demand during the first part of the day builds up to this hour(s) and then decreases after it.

But if you look at trend charts, ride time doesn't work that way. There are peaks and valleys, and desigining for a single hourly capacity doesn't really work.

 

[lazyboy97o]

But if you look at trend charts, ride time doesn't work that way. There are peaks and valleys, and desigining for a single hourly capacity doesn't really work.

I don’t even know what you are talking about with trend charts and ride times. Are you talking about changes in hourly demand? One of those hours is going to have the biggest demand.