How accurate are advertised ride queue times?: A statistical analysis using data from Alton Towers and the UK Merlin parks
Disclaimer: This is a long, geeky post. If you don't like statistics or maths talk, turn back now! If you'd like a more concise summary, a TL;DR can be found at the bottom.
Hi guys. When you go to a park, you will often see advertised queue times all over the place to help you determine how long the ride queues are. But sometimes, you might find that these do not necessarily tell the truth. At times, you might get in a queue with a reasonable advertised time and wait far longer than expected, and at other times, you might get in a queue with a long advertised time and wait far less than expected. With this in mind, you might be wondering; how accurate actually are these advertised queue times? Can they be relied upon? Or are they largely hokum?
Well, dear reader, that is the question I'm aiming to answer today. Through the power of statistics, I am going to work out; how accurate are advertised queue times?
Let's firstly start with the methodology of my statistical analysis...
Methodology
You might be wondering "Matt, how on Earth are you going to get hold of advertised and actual queue time data to conduct this analysis?". Well, the answer to that is that I had an idea... for years, I've been writing trip reports from various theme parks, and within these, I often make reference to the advertised queue time and how it compared to the actual queue time. And I was thinking that I could use my anecdotes from some of these trip reports as samples for the analysis. Yes, there's finally a day where my comparisons of advertised and actual queue times come in handy!
My method entailed reading my various trip reports from the UK Merlin parks from over the years and looking for anecdotes referring to the advertised queue time in comparison to the actual queue time of a ride. I chose the UK Merlin parks because these are where I have by far the most data from, and they are also likely to share similar technology, processes and the like for determining advertised queue times, which removes any uncertainty from working with companies with differing processes.
I should note that I did not count every time I went on a ride. I only counted rides where there was one of:
- An explicit comparison between advertised queue time and actual queue time given.
- A comparison between advertised queue time and actual queue time that heavily hinted towards the actual queue time given. For instance, words like "walk-on" or "I waltzed straight onto the train" would infer a 0 minute actual queue time, and words like "the queue time board stayed true to its word" would infer no discrepancy between the advertised and actual queue times.
There were rides I did not count, as I felt that they would not be representative of the actual main queue. These are:
- Any time where I talk about using a Single Rider Queue or otherwise benefitting considerably from single rider status (such as being called to walk past a long queue to fill an empty seat).
- Any time where I talk about using Fastrack or similar.
- Any time where I talk about waiting longer for a specific experience, such as the front row.
Through these rules, I was able to gather:
- 15 days and 75 rides of data from Alton Towers, dating back as far as 23rd June 2019
- 9 days and 48 rides of data from Thorpe Park, dating back as far as 6th May 2018.
- 3 days and 9 rides of data from Legoland Windsor, dating back as far as 31st August 2017.
- 1 day and 3 rides of data from Chessington, from 17th September 2023.
I should also give a few caveats. These are:
- This is my data and mine only. There are multiple reasons why that means that it may not be a fully representative sample. For example, Chessington and Legoland are under-represented, whereas Alton Towers and Thorpe Park are over-represented.
- The actual level of understatement may be higher than what this analysis suggests, as this only factors in queues I have personally waited in. If a queue looks vastly understated at first glance, there's a good chance I won't join it.
- Where I provided a range of time for the actual queue length, I went with the upper bound. For example, if I described a queue as taking 20-25 minutes, I logged the actual queue time as 25 minutes.
- I should strongly emphasise that this is not a massively exact science. The measurement of actual queue time was me looking at my watch throughout the queue, and for a variety of reasons, the movement of a queue can be affected in ways that the advertised time can't account for.
With this out of the way, let's move onto the actual meat of the analysis...
For each part of the analysis, I'll look at an individual park, as well as all 4 Merlin parks amalgamated together. For the individual park, I picked Alton Towers, as this is the park for which I have the most data.
Let's start with a simple correlation analysis to determine the strength of the relationship between advertised queue time and actual queue time...
Correlation
For those not aware, the correlation between two variables determines whether or not they are inter-related. The magnitude of a correlation lies between 0 and 1, with 0 indicating no correlation and 1 indicating a perfect strong correlation, and a correlation can also be positive or negative. A positive correlation means that as the value of one variable rises, the value of the other rises in unison, while a negative correlation means that as the value of one variable rises, the value of the other falls.
Now that I've explained a bit about correlation, let's have a look at what the data says about the correlation between advertised queue time and actual queue time! I'll consider two different correlation coefficients, Pearson and Spearman. Pearson's correlation coefficient assumes a linear relationship between two variables, whereas Spearman's correlation coefficient does not.
If we look at Alton Towers on an individual level, the scatter graph of advertised queue time and actual queue time looks something like this:
And the correlation figures are as follows:
Correlation Type | Correlation Coefficient (2dp) | Correlation Classification |
Pearson | 0.67 | Moderate Positive Correlation |
Spearman | 0.74 | Moderate Positive Correlation |
Whereas if we look at the UK Merlin parks overall, the scatter graph of advertised queue times versus actual queue times is as follows:
And the correlation figures are as follows:
Correlation Type | Correlation Coefficient (2dp) | Correlation Classification |
Pearson | 0.65 | Moderate Positive Correlation |
Spearman | 0.70 | Moderate Positive Correlation |
So if we look at correlation, I think we can conclude that there is a relationship between advertised queue time and actual queue time. Based on correlation alone, we can infer that on a general level, there is a moderate-to-strong correlation between advertised and actual queue time, so if the advertised queue time increases, you can generally expect actual queue time to increase along with it. However, the correlation is far from a perfect positive correlation, so this will not be the case in every scenario. In fact, the fact that the positive correlation does not even quite breach the threshold of "strong" (which I was told was 0.75) would suggest that this is not always the case by a long shot, and the relationship is far from perfectly proportional.
So in general, the correlation analysis would suggest that the advertised queue times are trustworthy to a broad extent to get a gauge of the broader picture, but perhaps with a notable margin of error for exact figures.
Let's now look at the average discrepancy...
Discrepancy (Vector)
Let's now look at the average discrepancy as a vector quantity. Vector quantities have both magnitude and direction, so this form of discrepancy will consider whether the queue is overstated or understated as well as its actual magnitude. Where the queue is overstated, the discrepancy is negative, whereas the discrepancy is positive where the queue is understated.
If we firstly look at Alton Towers on an individual level, here are the boxplots showing the ranges of raw and proportional discrepancies respectively. It's important to consider proportional discrepancy because if an advertised queue time is longer, there's bound to be a larger discrepancy in general:
And the raw and proportional discrepancy stats, as well as average queue time, are as follows. Both mean and median values are provided, as each metric has flaws in isolation and I felt that showing both offered maximum transparency:
Average Advertised Queue Time (minutes, 1dp) | Average Raw Discrepancy (minutes, 1dp) | Average Proportional Discrepancy (1dp) | Adjusted Average Proportional Discrepancy (1dp) | |
Mean (Calculated Average) | 28.3 | 2.2 | 8.8% | 7.8% |
Median (Middle Value) | 25 | 0 | 0% | 0% |
I should clarify that Average Proportional Discrepancy is the average of the proportional discrepancies listed alongside each anecdote, which excludes those where the advertised queue time was 0 minutes and the actual queue time was a different number (you cannot divide a non-zero number by 0, so a percentage proportion cannot be provided). Adjusted Average Proportional Discrepancy is a simpler calculation of Average Raw Discrepancy as a share of Average Advertised Queue Time on an overall basis, which (sort of) takes these into account.
If we now look at the UK Merlin parks overall, here are the boxplots showing the ranges of raw and proportional discrepancy respectively:
And the raw and proportional discrepancy stats, as well as average advertised queue time, are as follows:
Average Advertised Queue Time (minutes, 1dp) | Average Raw Discrepancy (minutes, 1dp) | Average Proportional Discrepancy (1dp) | Adjusted Average Proportional Discrepancy (1dp) | |
Mean (Calculated Average) | 26.1 | 1.3 | 13.7% | 5.1% |
Median (Middle Value) | 25 | 0 | 0% | 0% |
So looking at this, Alton Towers and UK Merlin queue times are understated by up to 1-2 minutes on average.
If we look at the median, that would imply that there's no discrepancy between advertised and actual queue time at all on average, and even the higher mean values infer that there are average discrepancies of less than 10% in some cases. At face value, these stats would give reason to believe that Merlin's advertised queue times are very accurate overall, with an average error of only 1-2 minutes and less than 10%.
However, you should note my use of the term "at face value"... because that's not the full picture. You might remember that earlier, I said about how the discrepancy being shown here is a vector quantity, meaning that it has both magnitude and direction. That means that understated queues have a positive discrepancy value and overstated queues have a negative discrepancy value, so the two balance each other out. So while you'd think that the low average discrepancies shown here mean that the queue times are very accurate... the use of vector discrepancies here mean that all this really shows is that understating and overstating balance each other out quite nicely, meaning that you can't really rely on Merlin parks to understate or overstate their queues. They both understate and overstate to broadly equal extents.
To get the true picture of how accurate these queue times really are, we need to convert the discrepancy values into a scalar quantity and look at the absolute values of discrepancy...
Absolute Discrepancy
To get the true gist of how accurate these queue times really are, let's now look at the absolute discrepancy values. Absolute means that only the magnitude of discrepancy is considered, and that the discrepancy values are scalar quantities rather than vector quantities.
If we firstly look at Alton Towers on an individual level, the boxplots showing the range of raw and proportional absolute discrepancy values are as follows:
And the raw and proportional absolute discrepancy stats, as well as average queue time, are as follows:
Average Advertised Queue Time (minutes, 1dp) | Average Raw Absolute Discrepancy (minutes, 1dp) | Average Proportional Absolute Discrepancy (1dp) | Adjusted Average Proportional Absolute Discrepancy (1dp) | |
Mean (Calculated Average) | 28.3 | 14.1 | 39.3% | 49.6% |
Median (Middle Value) | 25 | 10 | 27.5% | 40% |
If we look at the UK Merlin parks overall, the boxplots showing the ranges of raw and proportional absolute discrepancy are as follows:
And the raw and proportional absolute discrepancy stats, as well as average queue time, are as follows:
Average Advertised Queue Time (minutes, 1dp) | Average Raw Absolute Discrepancy (minutes, 1dp) | Average Proportional Absolute Discrepancy (1dp) | Adjusted Average Proportional Absolute Discrepancy (1dp) | |
Mean | 26.1 | 13.5 | 58.7% | 51.6% |
Median | 25 | 5 | 33.3% | 20% |
So looking at these stats, UK Merlin queue times are wrong by 5-15 minutes on average, and broadly, the average proportional absolute discrepancy ranges between 20% and almost 60%.
This would imply that the advertised queue times are not phenomenally accurate, and may not be 100% correct in terms of the exact figure on average. However, it would suggest that they are still quite good at a more general level to get a general gauge of how long a queue might be. If a queue is advertised at 100 minutes, it's unlikely to be walk-on, and vice versa. These figures suggest that the advertised queue times can generally be used as a broad gauge of the length of the queue, but should not be taken as gospel and the exact figures should be taken with some degree of caution.
Let's now look at some final conclusions...
Conclusion
So in conclusion, how accurate are these advertised queue times? Well, I think these results show that they're overall reasonable as a gauge of the broad ballpark the queue time is likely to fall into, but have somewhat weaker accuracy at determining exact queue times.
In terms of the correlation analysis, the advertised queue time and the actual queue time have a reasonable correlation, but not a perfect one. The two are moderately positively correlated, with a correlation coefficient of around 0.6-0.7, which would suggest that the two variables are broadly related and do increase in unison with one another in general, but this is far from a perfectly proportional increase and is not a perfect rule by any means.
On average, the vector discrepancy between advertised queue time and actual queue time was to be understated by 1-2 minutes, and the percentage margin of error was often to be understated by less than 10%. This suggests that understating and overstating overall happen to roughly equal degrees, and you can't really rely on Merlin to reliably do either.
On average, the absolute discrepancy between advertised queue time and actual queue time was 5-15 minutes, and the percentage margin of error for the advertised queue time was between 20% and 60%. This would suggest that the advertised queue times are rarely 100% accurate and should be treated with a degree of caution and a margin of error, but that they're generally decent as a way of gauging broadly how long a queue will be. If a queue is advertised at 30 minutes, for example, you can assume that it will probably be between about 15 minutes and about 45 minutes. That is quite a wide margin, admittedly, but the advertised queue times are unlikely to be amazingly wrong, on the whole. A 30 minute advertised queue, as an example, would indicate a roughly "middle of the road" queue time with a reasonable degree of reliability; the queue is unlikely to be obscenely short, but it's unlikely to be obscenely long as well.
So in conclusion, I think this analysis suggests that the advertised queue times are decent for getting an idea of broadly how long a queue is likely to be, but are worse at pinpointing the actual exact queue time, and the estimates should be considered with a good margin of error and not taken as exact estimates.
If you'd like to look at my data, here are the full spreadsheets for Alton Towers and UK Merlin queue times respectively:
https://docs.google.com/spreadsheets/d/1c2b05czi2xwwDxKRVBMJ9qyB3_-_b0RyMdc-N8n8JJI/edit?usp=sharing
https://docs.google.com/spreadsheets/d/1jpqqpu2pErHY41vHTpDP_NEZqnjuMwgtVVp99JexjvI/edit?usp=sharing
So that brings us to the end of this statistical analysis! I hope you enjoyed reading it as much as I enjoyed concocting it, and I hope you found it interesting! I'd be really interested to hear your thoughts; I'm receptive to any feedback, good or bad!
TL;DR: I performed a statistical analysis to try and determine how accurate advertised queue times are, using datasets of advertised vs actual queue times in Alton Towers and the UK Merlin parks taken from my past trip reports. A correlation analysis showed that there was a moderate positive correlation of magnitude 0.6-0.7 between advertised and actual queue time, indicating that they do generally increase in unison, but that this is far from a perfect trend and this is not necessarily a proportional increase. An analysis of average vector discrepancies showed that Merlin parks do not reliably understate or overstate queue times, with both understating and overstating happening to broadly equal degrees. An analysis of average absolute discrepancies showed that the queue times can provide a broad idea of roughly how long a queue may be, but are unlikely to be too accurate at determining the exact queue time.
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