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.

may-bumps-2010
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.

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

Results

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.

bumps

BLACKPOOL PLEASURE BEACH BLPB NAGASHIMA SPA LAND NASL
BUSCH GARDENS BUSG OCEAN PARK OCEP
CHIMELONG OCEAN KINGDOM CHOK OCT EAST OCTE
DE EFTELING DEEF PLEASURE BEACH PLEB
DISNEY ANIMAL KINGDOM DIAK PORT AVENTURA PORA
DISNEY CALIFORNIA ADVENTURE DICA SEAWORLD SEAW
DISNEY HOLLYWOOD STUDIOS DIHS SEAWORLD FL SEAF
DISNEYLAND DISN SONGCHENG PARK SONP
DISNEYLAND PARIS DISP SONGCHENG ROMANCE PARK SORP
EPCOT EPCO TIVOLI GARDENS TIVG
EUROPA PARK EURP TOKYO DISNEY SEA TODS
EVERLAND EVER TOKYO DISNEYLAND TOKD
HONG KONG DISNEYLAND HOKD UNIVERSAL STUDIOS FL UNSF
ISLANDS OF ADVENTURE ISOA UNIVERSAL STUDIOS HOLLYWOOD UNSH
KNOTTS BERRY FARM KNBF UNIVERSAL STUDIOS JAPAN UNSJ
LOTTE WORLD LOTW WALT DISNEY STUDIOS PARK AT DISNEYLAND PARIS WDSPADP
MAGIC KINGDOM MAGK YOKOHAMA HAKKEIJIMA SEA PARADISE YHSP

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

africaak
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:

universalhwmkhw

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:

universalforecast

mkforecast

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!