A summary of the latest theme park reports: What do they tell us?


Concept Art of Dubai Parks and Resorts credit:Dubai Parks and Resorts

I’ve been interested in the recent reports released recently by OmnicoGroup and Picsolve, two market research companies affiliated with Blooloop who publishes news and research related to the theme park and entertainment industry. Both have been publicised pretty widely on Twitter and in the mainstream media, but each explore different aspects of the current and future theme park visitor experience.


OmnicoGroup: The Theme Park Barometer

The offering from OmnicoGroup is the Theme Park Barometer, a set of questions based on another of their surveys. The full report is 15 pages long, and offers the responses to 38 questions based on 677 UK, 684 US and 670 Chinese respondents. The questions cover the full pre, during and post visit experience including what visitors do as well as what they’d like to do. Their main focus is on the online activities of visitors before and during their visit (18 questions).

Picsolve: The Theme Park of the Future

This report was based on research for Dubai Parks and Resorts, and focuses on  photos (7 questions) as well as wearables and cashless technology (8 questions). The whole report is 12 pages, and reports the results of 24 questions based on responses from 500 Dubai residents that had attended a Dubai theme park in the last year. Their questions focus almost entirely on future technology, and it seems their research serves as an exploration of some specific ideas more than a full strategic suggestion.

The results

The two surveys cover eight subjects, with four subjects covered exclusively by one survey or the other. The subjects as I can derive are:

Subject Description
During Visit What visitors do and want during their visit
During Visit Online What visitors do and want to do online during their visit
Post Visit What visitors do and want to do online after their visit
Pre Visit What visitors do and want to do before their visit
Photos What visitors do and want to do with the photos and videos of their visit
Wearables and Cashless The current and future usage of wearable and cashless devices
VR and AR What visitors expect from Virtual and Augmented technology during their visit
Merchandise What visitors do and want from their shopping experience during their visit.

I’ve posted the full set of responses to both surveys by subject, as it makes it a little easier to digest it all. However, despite half the subjects being covered by both surveys, it’s difficult to combine the two for many valuable insights.

Probably the most promising subject to look into here is the During Visit Online block, as it has by far the most coverage. Ignoring the different audiences surveyed, we can see that recommendation systems and information applications are highly desirable for a park, however there is still a quarter unable to connect to the internet (24%). While there is a lot of interest in the industry in selling the park online and building the post-visit experience, the two reports suggest that today’s parks may have a long way to go to satisfy the visitor’s expectations during the visit itself.

Another insight is that while Picsolve is reporting a large number of people expecting a range of advanced technology in the future, the OmnicoGroup research shows that they’re not expecting it in at least the next three years. For example, while around 90% have said they would attend a theme park offering Virtual Reality in the Picsolve report, only 65% expect to see this in the next the three years according to the OmnicoGroup report. Another example is 42% of people saying they want holographic entertainment in queues, but only 20% expected to see holographic assistants in the next three years. Admittedly having holograms in queues that just talk at you isn’t the same as the AI suggested by the term ‘holographic assistant’, but it shows that none of these expectations are for the near future.

Other than the few insights we see by crossing the two reports, there is also some evidence that despite some of their expectations of online services at the park not being met, visitors still want to engage with the park after the experience. However, the low positive response to questions asking about what visitors actually do after the experience suggests that these post-experience needs are not being met either. The same pattern holds for OmnicoGroup’s pre-visit questions, indicating that there is still a lot of low-hanging fruit to grab from visitors before and after their visit. This area should be particularly lucrative for parks considering that serving a lot of the needs visitors indicated they had, such as reserving merchandise (71%), ride times (81%) and VIP experiences (82%) really cost very little to develop and maintain compared to physical features during the visit.

Some criticisms

While I’m really interested in the results of these surveys, there are a couple of things that bug me about them as well.

First is that I don’t know how many people the OmnicoGroup report is based on (edit: since posting this OmnicoGroup contacted me with their respondent numbers – many thanks!). I may have missed this and they have been very responsive and helpful, so I can’t hold this against them.

Second, both reports ask very specific questions, then report the answers as if they were spontaneously offered. It’s a very different thing to ask ‘would you accept temporary tattoos for cashless payments’ and have 91% of people say yes than it is to say ‘91% of people want temporary tattoos for cashless payments’. My point here is not that the questions they asked were wrong or irrelevant, it’s that it is very easy to overclaim using this method. As it stands I know certain things about the theme park audience now, but I don’t know what they might have responded to any other question in the world. Given that the questions of either survey don’t cover the full process of the theme park experience (and don’t claim to), I don’t see how these reports could be used meaningfully for any business, operational or strategic decisions without it being something of a magic ball.

Finally, the Picsolve report is so focussed on specific areas of the theme park experience, I really can’t tell if it’s research or a sales pitch. Most of the images were provided by Dubai Parks and Resorts, and the final pages are dedicated to talking in general about how much the Dubai market is growing. Further to this, I don’t know how many people who live in Dubai would actually attend a Dubai Theme Park, so I’m not sure the population is really that relevant. On the other hand, a lot of what they write in this report is corroborated by the comments in the Themed Entertainment Association reports, so they’re either singing from the same songbook or reading the same reports as me.

What I learned

These reports are highly publicised and look like they took a lot of work to put together. However, something I’m learning is the importance of packaging my findings in a very different way from what Tufte would ask us to do. While statistical visualisations provide a very efficient way of communicating rich information in a small amount of time, it seems like for many people sheets of graphs and numbers is drinking from a firehose.

On the other hand, I’ve also learned that even minor crossover between two surveys can provide really valuable and useful insights, if only at a general level. I may spend more time in future looking through these results to see what else I can find, and I look forward to building up more of a database of this type of research as it’s released.

So what do you think? Have I made the mistake of looking too hard into the results, or have I missed other useful insights?

During Visit
Survey Question Overall US/UK China
Omnigroup Expect to see holographic assistants in theme parks in the next three years 20% 15% 32%
Omnigroup Expect to see robots as personal assistants in theme parks in the next three years 31% 22% 49%
Picsolve 3D Holograms and lasers made the visit more enjoyable 48%
Picsolve Want holographic videos in queues 42%
Picsolve Want performing actors in queues 41%
Picsolve Want multisensory experiences in queues 38%
Online services during visit
Survey Question Overall US/UK China
Picsolve Unable to log into wifi during visit 13%
Picsolve Unable to find any internet connection during visit 24%
Picsolve Want apps related to the ride with games and entertainment 40%
Picsolve Would be more likely to visit a theme park offering merchandise through a virtual store 85%
Omnigroup Want ability to buy anything in the resort with a cashless device 82% 77% 91%
Omnigroup Want ability to order a table for lunch or dinner and be personally welcomed on arrival 82% 79% 87%
Omnigroup Want recommendations for relevant deals 85% 84%
Omnigroup Want alerts for best times to visit restaurants for fast service 82% 81% 85%
Omnigroup Providing an immediate response to queries and complaints would encourage more engagement on social media during the visit 54% 50% 62%
Omnigroup Offering a discount on rides for sharing photos would encourage more engagement on social media during the visit 50% 47% 57%
Omnigroup Want recommendations for offers to spend in the park 77% 75% 81%
Omnigroup Want recommendations for merchandise and show tickets 74% 71% 80%
Omnigroup Expect to see voice activated mobile apps in theme parks in the next three years 41% 41% 41%
Omnigroup Expect to see Personal digital assistants in theme parks in the next three years 38% 36% 43%
Survey Question Overall US/UK China
Omnigroup Want ability to review trip and receive offers to encourage return visits 81% 79% 84%
Omnigroup Looked at or shared park videos after the visit 50% 41% 69%
Omnigroup Looked at deals or promotions to book next visit after the visit 44% 37% 56%
Omnigroup Posted a review about the stay after the visit 44% 34% 60%
Omnigroup Ordered further merchandise seen during the visit after the visit 25% 16% 42%
Pre-visit online services
Survey Question Overall US/UK China
Omnigroup Pre-booked dining plans before the visit 32% 28% 39%
Omnigroup Pre-booked timeslots on all rides before the visit 31% 24% 44%
Omnigroup Pre-ordered branded purchase before the visit 18% 13% 26%
Omnigroup Want ability to reserve merchandise online before arriving at the resort and collect it at the hotel or pickup point. 71% 65% 83%
Omnigroup Want ability to pre-book dining options for the entire visit 81% 80% 84%
Omnigroup Want to pre-book an entire trip (including meals, etc.) in a single process using a mobile app 89% 90% 91%
Omnigroup Want ability to pre-book a VIP experience 82%
Omnigroup Researched general information about the Park online before the visit 67% 64% 72%
Omnigroup Got directions to particular attractions at the resort before the visit 44% 35% 62%
Survey Question Overall
Picsolve Want ‘selfie points’ in queues 45%
Picsolve Ability to take photos from rides improves park experience 56%
Picsolve Would visit a theme park offering on-ride videos 90%
Picsolve Would visit a theme park offering AR videos of park moments 88%
Picsolve Would prefer park photos to be sent directly to their phone 90%
Survey Question Overall US/UK China
Picsolve Want to use wearable devices for a connected experience within parks 82%
Picsolve Would use wearables to check queue wait times 91%
Picsolve Agree wearables would be an ideal purchasing method 90%
Picsolve Would use wearables to link all park photography in one place 88%
Picsolve Would use wearables to track heart rate and adrenaline on rides 86%
Picsolve Would use wearables to track the number of steps they take at the park 84%
Picsolve Would be more inclined to visit a theme park offering wearable technology for self-service payments 90%
Picsolve Would consider visiting a park offering self-service checkouts 89%
Omnigroup Want ability to buy anything in the resort with a cashless device 82% 77% 91%
Omnigroup Want the park to offer a wide range of options on mobile apps 84% 83% 87%
Omnigroup Want ability to give their friends/family a cashless wristband and have a mobile app to track a topup payments 75% 73% 79%
Omnigroup Expect to see temporary tattoos in place of wristbands in theme parks in the next three years 27% 23% 35%
Virtual and Augmented Reality
Survey Question Overall US/UK China
Picsolve Would be more likely to visit a theme park with VR 94%
Picsolve Would be more likely to visit a theme park with VR based rides 87%
Picsolve Would be interested in VR headsets to view ride photography or videos during the visit 95%
Picsolve Would visit a theme park offering AR videos of park moments 88%
Omnigroup Expect to see Virtual Reality in theme parks in the next three years 65% 62% 70%
Omnigroup Expect to see Augmented Reality games in theme parks in the next three years 33% 25% 49%
Merchandise and Retail
Survey Question Overall US/UK China
Omnigroup Want stores to find merchandise and deliver it to the hotel room or home if the size, colour or style of merchandise is not available 75% 72% 80%
Omnigroup Want stores to find merchandise and arrange for pickup if the size, colour or style of merchandise is not available 72% 70% 75%
Omnigroup Want ability to buy merchandise in resort and have it delivered to home 74% 70% 82%
Omnigroup Want ability to buy merchandise over an app while in queue and have it delivered to home 75% 70% 84%
Omnigroup Want ability to order anywhere in resort for delivery anywhere 77% 73% 84%
Omnigroup Expect to see 3d print personal merchandise in theme parks in the next three years 36% 29% 51%
Omnigroup Want ability to purchase gifts for friends and family for the next visit 81%
Omnigroup Want ability to split restaurant bills 79%

Using ARIMA for improved estimates of Theme park visitor numbers over time

The entry to Tomorrowland at Magic Kingdom Florida

I’ve now had two attempts at predicting theme park visitor numbers, the first using Holt Winters and the second using Random Forests. Neither one really gave me results I was happy with.

Holt Winters turned out to be a misguided attempt in the first place, because most of its power comes from the seasonality in the data and I am stuck using annual measurements. Given the pathetic performance of this method, I turned to the Data Scientists go-to: Machine Learning.

The Random Forest model I built did a lot better at predicting numbers for a single year, but its predictions didn’t change much from year to year as it didn’t recognise the year of measurement as a reading of time. This meant that the ‘year’ variable was much less important than it should have been.

ARIMA: A new hope

Talking to people I work with (luckily for me I get to hang out with some of the most sophisticated and innovative Data Scientists in the world), they asked why I hadn’t tried ARIMA yet. Given that I have annual data, this method would seem to be the most appropriate and to be honest I just hadn’t thought of it because it had never crossed my path.

So I started looking into the approach, and it doesn’t seem to difficult to implement. Basically you need to at least find three numbers in place of p, d, and q: the order of the autoregressive part of the model (an effect that changes over time), the degree of differencing (the level of ‘integration’ between the other two parameters AFAIK), and the order of the moving average part of the model (the how much the level of error of the model changes over time). You can select these numbers through trial and error, or you can use the auto.arima() function in R that will give you the ‘optimal’ model that produces the least possible error from the data. Each of these parameters actually has a real interpretation, so you can actually base your ‘trial and error’ on some intelligent hypotheses about what the data are doing if you are willing to spend the time deep diving into these parameters. In my case I just went with the grid search approach with the auto.arima()  function, which told me to go with p = 0 , d  = 2 and q = 0.

The results

ARIMA seems to overcome both the lack of frequency in the data as well as the inability of Random Forests to take account of time as a variable. In these results I focus on the newly reinvigorated Universal vs. Disney rivalry in their two main battlegrounds – Florida and Japan.

Here are the ARIMA based predictions for the Florida parks:



Both are definitely improving their performance over time, but as both the Holt-Winters and the Random Forest model predicted – Universal Studios is highly unlikely to catch up to Magic Kingdom in its performance. However, unlike the Holt-Winters model, the ARIMA predictions actually have Universal overtaking Disney well within the realm of possibility. Universal’s upper estimate for 2025 is just over 35 million visitors, while Magic Kingdom’s lower estimate for the same is around 25 million. In an extreme situation, it’s possible that Universal’s visitor numbers will have overtaken Magic Kingdom’s by 2025 if we go with what the ARIMA model tells us.

The story for the Japanese parks looks even better for Universal:




In these cases we see Universal continuing on their record-breaking rise, but things don’t look so good for Tokyo Disneyland. This is really interesting because both are pretty close replicates of their Florida counterparts and both exist in a booming market. For Tokyo Disney to not be seeing at least a predicted increase in visitor numbers, something must be reasonably off. The prediction even shows a good possibility of Tokyo Disneyland beginning to get negative visitor numbers, suggesting the park’s future may be limited.

Things I learned

ARIMA definitely seems to be the way to go with annual data, and if I go further down the prediction route (which is pretty likely to be honest) I’ll probably do so by looking at different ways of playing with this modelling approach. This time I used the grid search approach to finding my model parameters, but I’m pretty suspicious of that, not least because I can see myself stuttering to justify my choices when faced with a large panel of angry executives. “The computer told me so” seems like a pretty weak justification outside of tech companies that have the experience of trusting the computer and things going well. There is clearly a lot of better methods of finding the optimal parameters for the model, and I think it would be worth looking into this.

I’m also starting to build my suspicion that Disney’s days at the top of the theme park heap are numbered. My recent clustering showed the growing power of a new audience that I suspect is largely young people with no children who have found themselves with a little bit of expendable income all of a sudden. On the other hand, Magic Kingdom and Tokyo Disney serve a different market that arguably consists more of older visitors whose children have now grown up and don’t see the fun in attending theme parks themselves.

Future things

I’ve read about hybrid or ensemble models pretty commonly, which sounds like a useful approach. The basic idea is that you make predictions from multiple models and this produces better results than any individual model on its own. Given how terrible my previous two models have been I don’t think this would help much, but it’s possible that combining different ARIMA models of different groupings could produce better results than a single overall model. Rob Hyndman has written about such approaches recently, but has largely focussed on different ways of doing this with seasonal effects rather than overall predictions.

I also want to learn a lot more about how the ARIMA model parameters affect the final predictions, and how I can add spatial or organisational information to the predictions to make them a little more realistic. For example, I could use the ARIMA predictions for the years where I have observed numbers as input to a machine learning model, then use the future ARIMA predictions in the test data as well.

Do you think my predictions are getting more or less believable over time? What other ideas could I try to get more information out of my data? Is Universal going to be the new ruler of theme parks, throwing us into a brave new unmapped world of a young and wealthy market, or can Disney innovate fast enough to retain their post for another generation to come?  Looking forward to hearing your comments.


Clustering theme parks by their audience

The conductor of the Hogwarts Express interacts with some young visitors at Universal’s Islands of Adventure.

I had a go recently at running a K-means clustering on the theme parks in the Themed Entertainment Associationreports by their opening dates and locations. This was pretty interesting in the end, and I was able to come up with a pretty nice story of how the parks all fell together.

But it made me wonder – what would it look like (and what would it mean!) if I did the same with visitor numbers?

 Competing for different audiences

Using the elbow method I described in my previous post, I again found that three or six clusters would be useful to describe my population.


Just like last time, I probably also could defend a choice of eight or even ten clusters, but I really don’t want to be bothered describing that many groups. Joking aside, there is a limit to how many groups you can usefully produce from any cluster analysis – it’s not useful if it just adds complication.

But here’s the issue I ran into immediately:

Universal Studios Japan
Year Cluster (3) Cluster (6)
2006 2 3
2007 2 3
2008 2 3
2009 2 3
2010 2 3
2011 2 3
2012 2 6
2013 2 6
2014 2 6
2015 3 1

It moves clusters over the years! I shouldn’t really be surprised – it shows that these theme parks are changing the markets they attract as they add new attractions to the mix. Remember, in this exercise I’m describing audiences as observed by the parks they visit. In my interpretation of these results I assuming that audiences don’t change over time, but their image of the various theme parks around the world do change. Let’s look at the clusters:

Cluster 1: Magic Kingdom Crew

These are the audiences that love the Disney brand and are loyal to their prestige offerings. If they’re going to a park, it’s a Disney park.

Cluster 1
Magic Kingdom 2006-2015
Disneyland 2009-2015
Tokyo Disney 2013-2015


Cluster 2: Local Visitors

These parks are servicing local visitors from the domestic market.

Cluster 2
Disneyland 2006-2008
Disneyland Paris 2007-2009
Tokyo Disney Sea 2006-2015
Tokyo Disneyland 2006-2012

Cluster 3: The new audience

This is an audience that has only emerged recently and offering more profits, with those parks gaining their attention reaping the rewards, as seen by the membership of very successful parks in recent years.

Cluster 3
Disney Animal Kingdom 2006
Disney California Adventure 2012 -2014
Disney Hollywood Studios 2006
Everland 2006-2007, 2013-2015
Hong Kong Disneyland 2013
Islands of Adventure 2011-2015
Ocean Park 2012-2015
Universal Studios Florida 2013-2014
Universal Studios Hollywood 2015
Universal Studios Japan 2006- 2011

Cluster 4: The traditionalists

This group is defined by the type of visitor that attends Tivoli Gardens. Maybe they are more conservative than other theme park audiences, and see theme parks as a place primarily for children.

Cluster 4
Europa Park 2006-2014
Hong Kong Disneyland 2006-2010
Islands of Adventure 2009
Nagashima Spa Land 2006-2010
Ocean Park 2006-2009
Seaworld Florida 2010 – 2015
Tivoli Gardens 2006 -2015
Universal Studios Hollywood 2006-2011

Cluster 5: Asian boom market

This audience seems to be associated with the new wave of visitors from the Asian boom, as seen by the recent attention to Asian parks like Nagashima Spa Land.

Cluster 5
Disney California Adventure 2006-2011
Europa Park 2015
Everland 2008-2012
Hong Kong Disneyland 2011-2012, 2015
Islands of Adventure 2006-2008, 2010
Nagashima Spa Land 2011-2015
Ocean Park 2010-2011
Seaworld Florida 2006-2009, 2012
Universal Studios Florida 2006-2012
Universal Studios Hollywood 2012-2014


Cluster 6: Family visitors

These all seem like parks where you’d take your family for a visit, so that seems to be a likely feature of this cluster.

Cluster 6
Disney Animal Kingdom 2007-2015
Disney California Adventure 2015
Disney Hollywood Studios 2007-2015
Disneyland Paris 2010-2015
EPCOT 2006-2015
Tokyo Disney Sea 2011
Universal Studios Florida 2015
Universal Studios Japan 2014

I tried a couple of other methods- the last cluster for each park and the most frequent cluster for each park, but these really were even less informative than what I reproduced here. In the first case the clusters didn’t look much different and didn’t really change interpretation. This is probably because my interpretation relies on what I’ve learned about each of these parks, which is based on very recent information. In the second case, I reduced the number of clusters, but many of these were a single park (damn Tivoli Gardens and it’s outlier features!)

Lessons learned

This work was sloppy as anything – I really put very little faith in my interpretation. I learned here that a clustering is only as good as the data you give it, and in the next iteration I will probably try and combine the data from my previous post (some limited ‘park characteristics’) to see how that changes things. I expect the parks won’t move around between the clusters so much if I add that data, as audiences are much more localised than I’m giving them credit for.

I also learned that a simple interpretation of the data can still leave you riddled with doubt when it comes to the subjective aspects of the analysis. I have said that I am clustering ‘audience types’ here by observing how many people went to each ‘type’ of park. But I can’t really say that’s fair – just because two parks have similar numbers of visitors doesn’t imply that those are the same visitors. Intuitively it would say the opposite! I think adding in the location, owner and other information like the types of rides they have (scraping wikiDB in a future article!) would really help this.

Future stuff

Other than the couple of things I just mentioned, I’d love to start looking at the attractions different parks have and classifying them that way. Once I have the attraction data I could look at tying this to my visitor numbers or ownership data to see if I can determine which type of new attractions are most popular for visitors, or determine which attractions certain owners like the most. In addition, I can’t say I really know what these parks were like over the last ten years, nor what a lot of them are like now. Perhaps understanding more about the parks themselves would give some idea as to the types of audiences these clusters describe.

What do you think? Am I pulling stories out of thin air, or is there something to this method? Do you think the other parks in Cluster 3 will see the same success as Islands of Adventure and Universal Studios Japan have indicated they will see? I’d love to hear your thoughts.

Record numbers at Universal Studios Japan: The continued rise of Universal, or a story of the Asian Boom?


 The Universal Studios Japan main entrance credit: Travelcaffeine.com

Today Universal Studios Japan released a report showing that they had received a record number of visitors last month. The news led me to wonder – was this new record the result of Universal Studios’ meteoric rise as of late, or was it more a symptom of the renewed interest in Asian theme parks in the last few years?

Pulling apart the causes of things with multivariate regression

One of the most basic tools in the Data Scientist toolkit is multivariate regression. Not only is this a useful model in its own right, but I’ve also used its output as a component of other models in the past.  Basically it looks at how much the change in each predictor explains the change in the outcome and gives each variable a weighting. It only works when you have linear data, but people tend to use it as a starting point for pretty much every question with a bunch of predictors and a continuous outcome.

Is the Universal Studios Japan record because it is Universal, or because it’s in Asia?

To answer this question I ran a multivariate regression on  annual park visitor numbers using dummy variables indicating whether the park was Universal owned, and whether it was in Asia. After a decent amount of messing around in ggplot, I managed to produce these two plots:

Black is not Universal, red is Universal
Black is not Asia, red is Asia

In these two plots we can see that the Universal parks are catching up to the non-Universal parks, while the Asian parks still aren’t keeping pace with the non-Asian parks. So far this is looking good for the Universal annual report!

This is confirmed by the regression model, the results of which are pasted below:

Estimate Std. Error t value p-value
(Intercept) 7831953 773691 10.123 2.00E-16
year 126228 125587 1.005 0.3158
universal -3522019 1735562 -2.029 0.0435
asia -1148589 1228394 -0.935 0.3507
universal*asia 3044323 3341146 0.911 0.3631
year*universal 234512 280112 0.837 0.4033
year*asia 31886 193528 0.165 0.8693
year*universal*asia 267672 536856 0.499 0.6185

In this we can see that firstly, only Universal ownership has a significant effect in the model. But you can also see the Estimate of the effect is negative, which is confusing until you control for time, which is the year*universal row of the table.  We can see here that for each consecutive year, we expect a Universal park to gain 234512 more visitors than a non-Universal park. On the other hand, we’d only expect and Asian park to have 31866 more visitors than a non-Asian park for each consecutive year over the dataset. This suggests that being a Universal Park is far more responsible for Universal Studios Japan’s record visitor numbers than it’s location. However, the model fit for this is really bad : .02 , which suggests I’m doing worse than stabbing in the dark in reality.

Lessons learned

The main thing I learned is that it’s really complicated to get you head around interpreting multivariate regression. Despite it being one of the things you learn in first year statistics, and something I’ve taught multiple times, it still boggles the brain to work in many dimensions of data.

The second thing I learned is that I need to learn more about the business structure of the theme park industry to be able to provide valuable insights based on models from the right variables. Having such a terrible model fit usually says there’s something major I’ve forgotten, so getting a bit more knowledgable about how things are done in these areas would give me an idea of the variables I need to add to increase my accuracy.

Future things to do

The first thing to do here would be to increase my dataset with more parks and more variables – I think even after a small number of posts I’m starting to hit the wall with what I can do analytically.

Second thing I want to try is to go back to the Random Forest model I made that seemed to be predicting things pretty well. I should interrogate that model to get the importance of the variables (a pretty trivial task in R), which would confirm or deny that ownership is more important than being in Asia.

What do you think? Are my results believable? Is this truly the result of the excellent strategic and marketing work done by Universal in recent years, or is it just luck that they’re in the right place at the right time? One thing is certain: the theme park world is changing players, and between Universal’s charge to the top and the ominous growth of the Chinese megaparks, Disney is going to have a run for its money in the next few years.


A spatio-temporal clustering of the world’s top theme parks.

The ‘Mickey’s Friends’ or something show I saw at Magic Kingdom. My niece loves Elsa.

I’ve been playing a lot lately with my dataset of the locations, opening dates and other information about the top theme parks in the world as measured by the Themed Entertainment Association. I mentioned that I wanted to try clustering the parks to see if I can find groups of them within the data. When I built my animation of theme parks opening I thought there might be some sort of ‘contagion’ effect of parks opening, where one opening in an area increased the likelihood of another one opening in the same area within a short time. My idea is that companies and people try to reduce risk by opening parks in areas they understand, and that the risk they’re willing to take in a new market increases as time passes. This second idea comes from my contention that these companies are always trying to open new parks, but won’t do it if the current market is too competitive. Their two options are to build their share of the market they know, like they do in Florida, or to try and find a new market that looks promising. As the home market gets more and more competitive over time, those foreign markets start to look more attractive.


K-means clustering

K-means is one of the most popular methods at the moment of grouping data points of any type  – so popular that the algorithm comes packaged in base R. In short, the model makes points on a surface with N-dimensions, where N represents the number of variables you’ve put into the model. This is pretty easy to imagine with two or three variables, but once we get to six or so (having used up colour, size and shape in a graph) you have to start bending your brain in some pretty specific ways to keep up.

Then it picks K points on that surface that minimise the distance between all the data points in the set. The distance between the point that is chosen (or ‘centroid’) is called the ‘within Sum of Squares’, and is used to determine how well the points group the data points. (Here’s another explanation if you’re interested in the details)

An example of centroids (represented as stars) grouping data points (represented as circles) on a two-dimensional surface.

 Choosing K: Slap that elbow

The main question that K-means clustering wants you to answer before you start is how many clusters you want it to make. It sounds weird, but the best way I know to do this (without moving to Bayesian mixture modelling) is basically trial and error. Usually with the Big Data I’m used to, this can take a long time unless you do some parallelisation work but with only 30 or so entries this is a pretty trivial task. So basically I run a loop in R building a cluster model with 2 – 15 clusters (more is kinda useless to me) and measure the Within Sums of Squares error of the model at each stage and get ready to slap that elbow.wsserrortheme

You can see from the graph that the error reduces massively from 2 to 3 clusters, but then eases off between 3 and 4 clusters creating an ‘elbow’ in the line plot. That indicates that 3 clusters give a good explanation of the data, and while 4 clusters is slightly better, they don’t explain that much more about the data. When trying to name and describe clusters it always gets more difficult with more groups to describe, so we don’t want to clog up our communication with clusters that don’t really mean much. Looking at this graph I could probably make two justifiable choices – three clusters is the strongest choice but six clusters is probably defensible as well. This is one of the issues with this method – the results massively rely on K, but choosing K is a really subjective procedure.

The code

Here’s some code that does the within sums of squares loop:

# xxx is a data.frame or data.table object of only numbers
wss <- NULL
for (i in 2:15) {wss[i] <- sum(kmeans(xxx, centers=i)$withinss)}

plot(wss, type = "l", xlab = "Clusters",ylab = "Within SS Error",
 main = "Error with different number of clusters")

The results

This was another experiment like my adventures in Holt Winters modelling that looks promising but really needs more data. Here are the plots of parks with three and five clusters:


The results of the three cluster model are pasted below. Tivoli stands out on its own as expected due to its opening date being so far before everyone else. The other two groups though I’m struggling to describe the other two groups by anything particular.

Cluster 1 Cluster 2 Cluster 3

So I thought the six cluster model might do better in describing the parks. The results of the model are pasted below:

Cluster 1 Cluster 2 Cluster 3 Cluster 4 Cluster 5 Cluster 6

This one is a bit more descriptive, so I had a go at giving the clusters names. Remember that even though they are clustered by date amongst other variables, the groups aren’t organised chronologically because the algorithm is unsupervised.

Cluster 1 Cluster 2 Cluster 3
The Bright Future The Cold War The Start of it All
Cluster 4 Cluster 5 Cluster 6
The Asian Boom Pre-GFC growth The Classics

The Bright Future

These parks all seem to be built in times where the owner was looking to take a bigger risk because they knew their future was looking good. The reasons for their optimism are probably different by location and owner, but if I had to pick something that made these parks similar, I’d say it was the spirit of optimism in which they were built.

The Cold War

These parks were generally built in places and times where governments were spending a lot of time and attention on trying to show off how awesome they were, especially in the 60’s and 70’s. The Cold War was at it’s height throughout this period, and having a park Magic Kingdom on your books was a massive draw for high-profile defectors and a boon for propaganda. Having said that, Magic Kingdom was notably built with very little Government support, so I’m probably totally off here.

The Start of it All

Tivoli Gardens will always be a unique gem of this theme park world. Long live Tivoli!

The Asian Boom

These are the massive new Asian superparks, with OCT owned by the Chinese Government and the other two heavily sponsored by public interests. With these parks rocketing up the ranks, it’s very possible that this group will grow in the list of top 25 parks in the coming years.

Pre-GFC growth

Most of these parks were built in booming economies that (in retrospect) were growing because of the growing deregulation in financial markets – in the late eighties and early nineties. These were built in a spirit of optimism like the Bright Future parks, but that optimism stemmed from regulatory environments in this case rather than real business growth. A lot of these parks have done less well in the ranks in recent years, possibly as a result of the market adjustment in these economies.

The Classics

These are the parks that really established the theme park industry. After Tivoli Gardens had gestated the idea of amusement parks, Walt Disney introduced the concept to Los Angeles and everything went mental. These parks were mainly those that made up this first wave, riding on the buzz caused by Disneyland.

Stuff I learned

The first and most obvious lesson of this exercise is that K-means clustering is a minefield of subjectivity and over-interpretation. As a statistician I really don’t like having to make a decision without  a solid numerical threshold on which to rely, so slapping the elbow of the within groups error isn’t very nice. The other part of the process is naming an describing the clusters, which is pretty difficult to do from an analytical perspective. In writing my descriptions I had to be pretty creative, and as I wrote I could see all sorts of ways the list didn’t really fit what I was saying. The common excuse of people using this method is ‘you’ll never get it perfect’, but I should at least be able to say why I chose the things I did with more backup than ‘it felt right’.

The second lesson is that as always more data is better. I’ve done this clustering on around thirty parks,  but it might make the clusters more clear if I added more parks and included more variables in the model I train. In addition, I only trained this model on four variables at the moment, while normal Data Science clustering models should contain at least 50 or 60 to really start looking valid.

Things I’ll look at in the future

The next thing I’ll probably do is a different approach to clustering using visitor numbers in combination with the locations of the parks. This would tell me if the different parks are catering to different markets that have unique patterns of attendance, which might contribute to my machine learning approaches.

Another idea is to play with the different results produced by changing K, which gives progressively more detail about the groups as it increases. This is based on the work I saw once at the Australian Statistical conference in a Peter Donnelly lecture where he did this with Genetic data to move back in history and show the gradual introduction of different genetic groups.

What do you think of my attempt at grouping theme parks? Do you think the clusters make sense, or did I just pull a bunch of meaning out of nothing? As always, I’d love to hear any critique or analysis you might have.

The code

Here’s some code in case you want to do something similar:

#Load libaries

# Load the data
info <- read.csv("~/myspatialdata.csv", stringsAsFactors = FALSE)
info <- info[complete.cases(info),] #Get rid of any empty trailing rows
setDT(info) #Make it a data.table because Data Science
info$opened <- as.Date(info$opened) # Tell R this is a date
setkey(info, park) # Order by park
setkey(info, opened) # Order by Opening date
cols = c("opened", "lat", "long", "operator")

xxx <- info[,cols, with = FALSE] # Select only the columns we'll cluster 
xxx$opened <- as.numeric(as.Date(xxx$opened)) #Convert this to a number 
because K-means only takes numbers.
xxx$operator <- as.numeric(as.factor(xxx$operator)) # Same for the 
operator factor.

# Slap that elbow
wss <- NULL
for (i in 2:15) {wss[i] <- sum(kmeans(xxx, centers=i)$withinss)}
plot(wss, type = "l", xlab = "Clusters",ylab = "Within SS Error", 
main = "Error with different number of clusters")

# Create models with 3 and 6 clusters based on the elbow approach.
parksclusterreal <- kmeans(xxx, 3, nstart =10)
parksclusterfun <- kmeans(xxx, 6, nstart =10)

# Add the cluster labels to the data frame
info$cluster <- parksclusterreal$cluster
info$clusterfun <- parksclusterfun$cluster

### Plot the parks by cluster on a world map

# Three cluster model
mp <- NULL
mapWorld <- borders("world", colour="gray10", fill="gray10") 
# create a layer of borders
mp <- ggplot(data = info, aes(x= long, y= lat , 
    color= as.factor(cluster))) + mapWorld + theme_bw()
mp <- mp+ geom_point(size = 5, shape = 5) + ylim(c(0, 60))
    + ggtitle("Clusters of theme parks by location, operator, 
    and opening date") + labs(colour='Cluster')

# Six cluster model
mp <- NULL
mapWorld <- borders("world", colour="gray10", fill="gray10") 
# create a layer of borders
mp <- ggplot(data = info, aes(x= long, y= lat , 
    color= as.factor(clusterfun))) + mapWorld + theme_bw()
mp <- mp+ geom_point(size = 5, shape = 5) + ylim(c(0, 60))
    + ggtitle("Clusters of theme parks by location, operator,
    and opening date")+ labs(colour='Cluster')

An animation of theme parks opening around the world


I’ve been collecting a lot of data to be able to do my last few posts, and I’d mentioned that I wanted to try more with time series data. A few years ago I got to sit in a lecture at Queensland University of Technology by Sudipto Banerjee on Bayesian spatiotemporal modelling. At the time the material was way too advanced for me, but the idea of analysing data points with time and space treated correctly has always stuck.

As I dug into different things I could do with spatiotemporal , I realised that I needed a lot more understanding of the data itself before I could do fun tricksy things with it. I needed something that would maintain my interest, but also force me to mess around munging spatiotemporal data

An idea born of necessity

In the first year of my postgraduate research, I was really interested in data visualisations. Thankfully at the time a bunch of blogs like FlowingData were starting up, reporting on all types of cool data graphics.’Infographics’ also became a thing, threatening to destroy Data Science in its infancy. But what caught my eye at the time were the visualisations of flight paths like this one.

So now that I have some data and a bit of time and ability, I thought I’d try a more basic version of a spatiotemporal visualisation like this. My problem is that I hate installing extra one-time software for my whims, so the idea of using ImageMagick annoyed me. On top of that, when I tried I couldn’t get it to work so I determined to do what I could using base R and ggplot.

The result

This is probably the first article I can say I’m pretty happy with the result:



The first thing you can see is that Europe, not the US is the true home of theme parks, with Tivoli Gardens appearing in 1843, and remaining in the top 25 theme parks since before there were 25 parks to compete against.

Beyond that, you can also sort of see  that there is a ‘contagion’ effect of parks – when one opens in an area, there are usually others opening nearby pretty soon. There’s two reasons I can think of for this. First, once people are travelling to an area to go to a theme park, going to two theme parks probably isn’t out of the question so someone’s bound to move in to capture that cash. Second is that the people opening new parks have to learn to run theme parks somewhere, and if you’re taking a massive risk on opening a $100 million park with a bunch of other people’s money you’ll want to minimise your risk by opening it in a place you understand.

Future stuff

Simply visualising the data turned out to be more than a data munging exercise for me – plotting this spatially as an animation gave some actual insights about how these things have spread over the world. It made me more interested in doing the spatio-temporal clustering as well – it would be really cool to do that then redo this plot with the colours of the points determined by the park’s cluster.

Another direction to explore would be to learn more about how to scrape Wikipedia and fill out my data table with more parks rather than just those that have featured in the TEA reports. I know this is possible and it’s not exactly new, but it’s never come across my radar and web scraping is a pretty necessary tool in the Data Science toolkit.

What applications can you think of for this sort of visualisation? Is there anything else I could add to this one that might improve it? I’d love to hear your thoughts!

The code

Just in case you wanted to do the same, I’ve added the code with comments below. You’ll need to add your own file with a unique name, latitude, longitude and date in each row.

# Load the required libraries

info <- read.csv("***.csv", stringsAsFactors = FALSE)

info <- info[complete.cases(info),]
info$opened <- as.Date(info$opened) # S
setkey(info, park)
setkey(info, opened)

# Setup for an animation 
a_vec <- seq(1840, 2016 , by=1) # Create a vector of the years you will 
animate over

# Create a matrix to hold the 'size' information for the graph
B = matrix( rep(0, length(a_vec)*length(info$park)),
 nrow= length(a_vec), 
 ncol= length(info$park))

for (i in 1:ncol(B))
 for (x in 1: nrow(B))
 { #I want to have a big dot when it opens that gets gradually smaller,
    like the alpha in the flights visualisation.
  open_date <- as.numeric(year(info$opened[i]))
  c_year <- a_vec[x]
  #If the park hasn't opened yet give it no circle
  if ( open_date < c_year)
  {B[x,i] <- 0} else
  # If the park is in its opening year, give it a big circle.
  if (open_date == c_year)
  {B[x,i] <- 10}

# Make the circle fade from size 10 to size 1, then stay at 1 until 
the end of the matrix

for (i in 1:ncol(B))
{ for (x in 2: nrow(B))
  {if (B[x-1, i] > 1){ B[x,i] <- B[x-1, i] - 1}else
   if(B[x-1, i] == 1){ B[x,i] <- 1}}}

B <- data.frame(B)
B <- cbind( a_vec, B)
names(B) <- c("years", info$park) #Set the column names to the names of 
the parks

xxx <- melt(B, "years") # Convert to long format

# Create a table of locations
loc <- data.table("variable" = info$park,
                   "lat"= info$lat, 
                   "long"= info$long)

#Join the locations to the long table
xxx <- merge(xxx, loc, by = "variable", all.x = TRUE)
setkey(xxx, years)

# Create a ggplot image for each entry in the a_vec vector of years we
 made at the beginning. 
for (i in 1: length(a_vec))
    {mydata <- xxx[years ==a_vec[i]] # Only graph the rows for year i.
     mydata <- mydata[mydata$value!=0,] #Don't plot stuff not open yet.
     #Write the plot to a jpeg file and give it a number to keep the 
      frames in order.
     jpeg(filename = 
     paste("~/chosenfolder/animation", i, ".jpeg", sep = ""),
     width = (429*2) , height = (130*2), units = "px") 
     mp <- NULL 
     # Plot a world map in grey and entitle it with the year.
     mapWorld <- borders("world", colour="gray50", fill="gray50") 
     mp <- ggplot() + mapWorld + theme_bw() + ggtitle(a_vec[i])
     # Add the points on the map, using the size vector we spent all that
       time building matrices to produce.
     mp <- mp+ geom_point(aes(x=mydata$long, y=mydata$lat) ,
     color = "orange", size = mydata$value/1.5) + ylim(c(0, 60))


Using machine learning to improve predictions of visitor numbers

The torii at EPCOT with the globe thing in the background

I wrote previously about using the Holt Winters model for time series analysis, particularly to predict the number of visitors to two of the world’s top theme parks next year. I am using annual data from the last ten or so years (which is all that’s available from the Themed Entertainment Association at this point), and unfortunately we could see quite easily that this sort of frequency of data (i.e. annual) was too sparse to make a decent prediction.

So the data are horrible, what are you going to do?

This kind of annoyed me -it takes ages to put together all this data in the first place and the results were disappointing. So I started thinking about other ways I could potentially model this using other data as well, and it was pretty easy to get general information about all these parks like their location, opening date and company ownership. I can imagine that parks that are close to each other are probably serving a similar crowd, and are subject to the same factors. Same with park ownership – the parent companies of these parks each have their own strategies, and parks with the same owner probably share in each other’s success or failures. But to allow for these sort of assumptions, I needed some way of adding this information to my model and let it use this sort of stuff to inform its predictions.

Machine Learning to the rescue

In current Data Science, Machine Learning is sort of a go to when the normal models fail. It allows us to take a vast array of complex information and use algorithms to learn patterns in the data and make some pretty amazing predictions. In this case we don’t really have Big Data like we would at a major corporation, but given that the numbers are pretty stable and we’re only trying to predict a few cases, it’s possible that this approach could improve our predictions.

Machine what now?

I know, it’s both a confusing and kind of ridiculous name. The whole idea started when Computer Scientists, Mathematicians and Statisticians started using computers to run equations millions of times over, using the results of each round, or ‘iteration’ of the calculation updating the next. It started with doing some pretty basic models, like linear and logistic regression over and over, testing the results and adjusting the weights of each factor in the model to improve them each time. Soon people started using these as building blocks in more complicated models, like Decision Trees, that evolved into Random Forests (which are the result of thousands or millions of decision trees). The sophistication of the building blocks improves daily, as does the ability to stack these blocks into more and more complex combinations of models. The winners of many Kaggle  competitions now take the most sophisticated of methods, and combine them for ridiculously accurate predictions of everything from rocket fuel usage to credit card risk. In this article I’m going to use one of the most popular algorithms, the Random Forest. I like these because they can be used for both numeric and categorical data, and do pretty well on both.

The results

This time we actually started getting pretty close to a decent model. Below you can see the graph of predicted and actual (labeled as ‘value’) visitor numbers for each park in 2015:


It’s not too far off in a lot of cases, and pretty much everywhere it’s predicting just below what really happened, except for in the case of Disneyland Paris. In a few cases I’m way off, like for Universal Studios Japan, which could possibly due to the stellar performance of all the Universal parks recently. So with this information in hand, here’s my predictions for 2016:

DISNEYLAND 15850608.32
EPCOT 11048540.24
EUROPA PARK 4600339.552
EVERLAND 7108378.079
MAGIC KINGDOM 17124831.22
OCEAN PARK 6860359.451
SEAWORLD FL 5440392.711
TIVOLI GARDENS 4249590.638
TOKYO DISNEY SEA 13529866.78

If you want to see how these relate to my 2015 predictions, here’s a graph:



Future stuff

As usual, I can still see a whole lot of things I can do to improve this model. At the moment there’s only two variables ‘moving’ with each row – the date and the visitor number. I could add a few more features to my model to improve things – the GDP of the country that park is in for example.

Second, Random Forests are notoriously bad at predicting time series data. In this case I converted the year of the data into a numeric vector rather than a date, adding 1 to the variable for the prediction. Given that each entry for each park was an even number of days apart (365 each row) I think that’s fair, but maybe I can’t treat annual entries that way. But to be fair, there doesn’t seem to be many models particularly good at predicting time series. There are suggestions of using artificial neural networks , but these aren’t particularly noted in time-series or spatio-temporal modelling. I think ‘Data Science’ needs to draw a bit more from Statistics in this case, and I’ll probably look in that direction for improved results in future. Given that it’s annual data I have the advantage of having a long time to process my model, so things likeMCMC using STAN might be promising here.

Finally, I need to get more practice at using ggplot2 for pretty graphs. I know a few tricks but my coding chops really aren’t up to building things with the right labels in the right places, especially when there are really long names. In this article I spent ages trying to fit the names of the parks into the first graph, but in the end I really couldn’t figure it out without making it really ugly. I’d love to be able to add my predictions as extensions on a line plot of the observed data, but that seems like epic level ggplot ninja-ing.

I’ll probably continue to attempt improving my predictions because it makes me feel like a wizard, but at this point I’ll most likely try this by playing with different models rather than ‘feature engineering’, which is most popular in Kaggle.

I’m always keen to hear people’s feedback and I’d love to improve my analyses based on people’s suggestions. Do you think my estimates are accurate, or is there something major I’ve missed?


Theme park ranks over ten years

I’m interested in understanding the competitive landscape of theme parks, and showing their ranks from year to year is a good way of seeing this. The best way I know of is to use everybody’s favourite chart – the bumps chart!

What’s a bumps chart?

This was invented in Cambridge to keep track of one of the most mental sporting events you’ll ever see – the May Bumps.

The May Bumps (credit Selwyn College)

In true Cambridge style, the May Bumps are a rowing race held every June. Apart from their timing, the series of races involves all the college rowing teams (usually around 20 of them at once) racing down the river Cam at high speeds trying desperately to run into (or ‘bump’) each other. If a crew catches up to the one in front, both crews pull over and in the next race they swap positions for the start. This means that over a week a crew can move from the front to the back of the race, and this tells a story of that year’s Bumps. The original bumps chart hangs in the Cambridge University Union building.

A bumps chart of a May Bumps series, showing Oriel winning the competition.


The bumps chart I created was based on the Theme Entertainment Association reports published online each year since 2006. The data were read into R, and I used the ggplot2 package to draw a line plot of visitor numbers over the years. The directlabels package was used for the labels.



There are a few really noticeable things when we plot out the ranks of parks this way. This first is that Disney dominates the industry, and they keep a tight ship. Their parks don’t compete with each other for audience, and they don’t tend to move up and down relative to each other.

The second noticeable thing about the plot is the recent rise of Universal through the ranks, to finally crack the Disney lockout. This probably explains the buzz within Comcast (Universal’s owners) at the moment, and all their talk about an aggressive growth strategy.

Finally we can see really clearly here that the Asian parks, particularly the Chinese ones, are making a claim in the industry as mega players. Particularly Songcheng and Chimelong mega parks are growing at an incredible rate and are showing no signs of stopping. If the trend continues, it is very possible that our children will be pleading us to take them to China for the rides.

Future stuff

There are a whole lot of problems here around missing data. In particular we only get the top 20 – 25 parks each year and TEA only recently started publishing year-to-year figures recently, so the data are really patchy for some parks. On the other hand, in the true spirit of Data Science, the missingness could probably be used to tell us something as well if we could derive any meaning from the patterns of dropping in and out of the top 25.

I’d also be really interested to aggregate the data in different ways to see other patterns in the rankings. We could aggregate parks by location to see which areas are most popular at the moment, or we could aggregate by owner to look at who’s actually performing the best on a budget level. Looking at ownership companies brings forward whole new dimensions to the data – for example none of the Merlin Entertainment parks feature in the top 25, yet they have appeared in the top ten entertainment companies in income for the last ten years.

Do you think Universal can continue its rise? Will the Chinese parks continue to grow to be larger than the might Magic Kingdom, or will Disney retain it’s seat as the unchallenged leader?

Predictions of Disney and Universal visitor numbers

Africa area of Disney’s Animal Kingdom

When thinking about theme parks, one of the most obvious questions is how to predict the number of visitors expected for the coming years. This is not easy to do, but even an approximate answer would help in planning ride maintenance and staffing levels.

Why is this so difficult?

There are a bunch of reasons it’s difficult to predict visitor numbers to any large attraction.

First, all theme parks around the world are subject to global economics – if a park attracts lots of visitors from an area that happens to have a war or a recession then all bets are off.

Second, in places like Orlando where there is a high concentration of parks the number of visitors at a specific park depends heavily on the popularity of other parks in the area.

Finally, when we are talking about a global audience, there are any number of issues that can arise that destroy a park’s precious season. In 2010 when Icelandic Volcano Eyjafjallajökull erupted unexpectedly, Danish park Tivoli Gardens saw a drop of 20,000 visitors.

How is it done?

When forecasting pretty much anything, the go-to method is called the Holt-Winters model. There is a whole lot of clever maths behind this, but what you need to know is that it looks at data collected over time (annually in our case), placing more importance on values it saw more recently than on the ones it saw a long time ago.

The data come from the Themed Entertainment Association annual reports, which are sort of canonical for the theme park industry. In this set we go back as far as their published reports allow – to 2006. This isn’t a particularly long time, especially considering that all we get is annual data, but at least we might be able to get some idea of what we could expect.

Who cares?

We have data for the top 22 or so parks for that time (the bottom few tend  to drop off every couple of years), but to show what we’re doing we’ll just look at the two major competitors in the theme park industry – Disney’s Magic Kingdom, and the first non-Disney competitor Universal Studios Florida. This is interesting because Universal has recently announced an aggressive new strategy, likely based on the success of its recent Harry Potter attractions. But can Universal expect its rise to continue, or will Magic Kingdom maintain it’s unbeatable position?

The results

Well, it doesn’t look particularly good for Universal’s strategy. Here are plots of Holt-Winter’s fitting of visitor numbers to the Magic Kingdom and Universal Studios:


We can see that both parks are steady, but Universal Studios performs massively below Magic Kingdom. The redline shows the fitted Holt-Winters model, and to be honest I’m not that happy with it. Really we’re just predicting the value from the previous year, so I’m interested to see how it does with forecasting.

To see how the two parks might do against each other into the future, we use the Holt-Winters model to predict the next ten years of visitors:



We can see here that our (dumb) Holt-Winters model is predicting the Magic Kingdom to sustain its massive lead over Universal Studios. We can see this in the 80% confidence intervals for both parks at the ten year period – between 7 and 12.16 million visitors for Universal, and between 18.5 and 22.4 million for the Magic Kingdom. This isn’t even close to an overlap, and suggests that Universal has next to no chance of overtaking the Disney powerhouse.

The lessons

The main thing I learned from this exercise is that the Holt-Winters model is best suited to data that is more frequent than annual. The power of the model comes from estimating seasonal variations, so with monthly or even quarterly data our predictions would become a lot more interesting.

I also learned that Universal Studios may have been a little excitable by their recent success. It’s been many years since they were able to crack the Disney fortress of top ranks, and the Harry Potter world attraction seems to have had a bigger effect than they realise even at this point.

Future stuff

There is is whole lot more I’m intending to do with this data. Most immediately I’d like to be able to try and improve my forecasts by adding in information about the parks, such as their location. As I mentioned at the top of the article, the success of parks in places like Orlando and arguably the Benelux region are highly dependent on the performance of their competitors, so a model would likely be able to gain a lot of information from the performance of nearby parks.

I also want to see if there are groupings of parks according to their visitor numbers over time. Seeing different clusters of parks by this metric would suggest they are catering to different populations, and might indicate which parks were truly competing against each other.

This was fun to do, and a great experience to play around with some time series data. Hope you learned something!