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Fun with Gantt charts: Is your park maintaining its attraction lineup?

Pokemaniac

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I'm not really sure what made me drop down this rabbit hole, but I guess it's a combination of fascination with statistics, topics popping up in recent conversations, and procrastination. Thesis due in two weeks? Time to do a bit of theme park analysis!

First thing first: what is a Gantt chart? I'll quote Wikipedia here:
A Gantt chart, or harmonogram, is a type of bar chart[3][4] that illustrates a project schedule.[5] This chart lists the tasks to be performed on the vertical axis, and time intervals on the horizontal axis.[3][6] The width of the horizontal bars in the graph shows the duration of each activity.[6][7] Gantt charts illustrate the start and finish dates of the terminal elements and summary elements of a project. Terminal elements and summary elements constitute the work breakdown structure of the project. Modern Gantt charts also show the dependency (i.e., precedence network) relationships between activities. Gantt charts can be used to show current schedule status using percent-complete shadings and a vertical "TODAY" line.
In practice, they look something like this, picture from that same Wikipedia article:
Pert_example_gantt_chart.gif


Never mind the project management stuff, the interesting bit for our purposes is that the chart can be used to show the start and end dates of parallel project activities along a timeline. What else is there that exists in parallell and has start and end dates along a timeline? The lifespans of attractions in an amusement park, of course! This gave me an idea for an interesting new way to analyse how well a park is holding up its attraction lineup.

Suppose a park opens one year with a bunch of attractions. That year, all attractions will be new, with a listed age of zero years. The year after, all the attractions will be one year old. Then two years. Then perhaps it's time to expand the park, building a new attraction. That attraction will then be zero years old while the other attractions are three years old. Over time, some attractions are taken out while others are added. By listing the age of every attraction in a Gantt chart, it's possible to read the age of each attraction at any given moment by going vertically down the chart. Here's an example, using the coasters at Alton Towers:

LSd8wbW.jpg


As you can see, the chart lists the age of every attraction in any given year, starting in 1980. I could have gone back to the start of the park, but 40 years of attractions was enough work already. In the end, I only listed the attractions that existed in 1980, by simply beginning with their age in 1980 and working from there. Doing the entire park, using the list of attractions from Alton Towers' Wikipedia article, resulted in a chart looking like this:
TgphNYg.jpg


You're not meant to read it, just appreciate the emerging patterns. Rides are built and removed, and in the meantime they age. If you squint, you may find that the Rowing Boats reached a ripe old age of 73 before they were removed after the 1996 season - I presume they had swapped out the boats at a few occasions before then, however. At the top of the chart, you also see that all the coasters built in the 1980's have now been removed, and you can notice the mass extinction of Alton's flat rides in the 2010's. Interestingly, the two that survived that purge are the two oldest ones, suggesting that their time may be up soon as well.

Anyway, this data can be condensed further. Using a few simple functions in Excel (or in this case, Google Docs), you can count the number of attractions in the park at any given time. Moreover, you can find and chart the average and median age of the park's attractions at any given time as well (using =COUNT, =AVERAGE, and =MEDIAN, respectively). Behold:

EVDS5Z3.jpg

As you might expect, the attractions age as time passes, so the curve rises steadily by default. But the removal of old attractions (look at the nosedive in 1997, when the 73-year old Rowing Boats attraction was removed) and the addition of new ones (6 new kiddie flats for CBeebies Land in 2014) pushes the mean age back down. The median age of Alton's attractions was the same in 2014 as in 1996, for instance. You may also notice that the median age curve only has two degrees of "steepness" as it rises, depending on whether 0 or 1 new rides were added that year. With more additions than that, the curve flattens or decreases. The four new flats for 2021 are already making a solid dent in the line, bringing the average attraction age at Alton Towers below the level it reached in 2019 and the median back to 2007 levels.

With the exception of 2020, Alton has managed to keep the average age of its attraction lineup between 10 and 15 years since the late 1990's. If not for Covid, I think Gangsta Granny would have opened on time and kept the average attraction age within those brackets that year as well. However, there is a rising trend, suggesting that Alton Towers isn't quite keeping up with time the same way it used to - between 1990 and 2006 or so, the trend line must have been quite flat.

Admittedly, it's a pain and a half to do this exercise for every attraction a park has ever had. It is much, much quicker to focus solely on the coasters, and it allows for more direct comparisons too. Otherwise, it doesn't register as a loss if a park rips out a B&M Hyper and puts in a bouncy castle instead. Although admittedly, a Big Apple would count as much as the aforementioned B&M Hyper, so it's not a methodology without flaws either. Anyway, here are the numbers for Alton's coasters:

ToJI32O.jpg

Same story here, really: the curve is surprisingly flat, but with a recent rising trend. The median coaster age peaked at 13 in 2001, a number reached again in 2017. Granted, the graphs don't tell the whole story. The thrill coasters are generally above the median age, the family (and dressed-up family) coasters are below. The median coaster in terms of age nowadays is Rita. Oh, and next year, Nemesis will be older than both Corkscrew and Beastie were at the time of their retirement.

Using RCDB and a spreadsheet program of your choice, throwing up one of those Gantt Coaster Charts is a surprisingly quick process. I did one for Cedar Point too:
w9f7I44.jpg

As you can see, Cedar Point doesn't have a habit of scrapping old coasters to the same degree. It has actually only happened thrice since 1980, and they have a lot of coasters. Therefore, the veteran coasters keep dragging the average age up, with new additions only making tiny dents in the average age. 2016 saw the removal of Mean Streak (age 25) and the addition of Valravn, and you barely notice it in the overall stats. That year, Cedar Point had 17 coasters, 5 of them older than 35 years, so the reduction of the total coaster age by 25 years barely registered. You may also see that Cedar Point seems to prefer to keep their coaster count steady at 17, which they reached in 2007. The longest period without any change to the coaster count post 1980 was in 2007-2011.

Cedar Point's current "Median coaster" in terms of age is Rougarou (formerly Mantis), at a spry 25 years old. Put another way, Cedar Point has as many coasters built before Mantis as after it. Raptor, age 27, is the closest to the average.

Oh, and because it wouldn't be like me not to mention my home park in such a long post:

c1sAzSv.jpg

No comment should be necessary, but of course I'll add a few anyway:
  1. The park opened in 1988 and has no attractions older than 33 years, yet the average and median attraction age are above 20 years.
  2. From 2013 to 2021, the average attraction age has increased from 13.0 to 20.5 years. In other words, additions in this period have only pushed back half a year of aging.
  3. The median age curve flattened out a bit from 2000 on, until The Terrible Ones started making decisions from 2010 or so.
  4. The park operates one more attraction today than it did in 2005, but in the meantime the average age of attractions has almost doubled, from 10.7 to 20.5 years.

Aaaaanyway, making such charts is a quite simple exercise, but I don't have the time to do a great number of them right now. If you'd like to give it a try, perhaps we could see how well the various parks out there are holding up? I've always wondered what the average lifespan of a coaster is, and what is the average average age of rides in a park. At some point, logically, the curve would flatten. I suspect TusenFryd is an outlier, but until now I haven't had the tools to prove it for certain. If we could make enough of these charts, we could start making quantitative observations. I suspect there could be a way to make them automatically using some coding with RCDB's database, but it would require a level of knowledge and access many notches above my own. For now, the best we can do is punch numbers manually. What do you think?
 
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Ahhh, this is such a cool question @Pokemaniac! If I were to create a hypothesis going into this, it would be that average ride age for parks is more cyclical, oscillating up and down as rides are installed/removed, moving the average age up and down in tandem. While we do see that to some degree, especially Tusenfryd and Alton; I underestimated the general upward trend of the charts - that rides do essentially stick around for longer periods of time, as we move forward in years.

That makes sense to a certain degree - attractions built in 2021 are probably both more exciting and more reliable than rides built decades before. Still, quite surprising to see, as I've always assumed there is a general space scarcity problem across parks - you reach a certain point when you can't fit more rides in, so you need to replace old attractions with new. While that is also partly true, it turns out parks in these samples are figuring out how to hold/revamp rides to have them last longer.

Would love to work with you @Pokemaniac on widening the sample! My general hunch would be RCDB data look ups, yada yada yada, export to spreadsheet somehow? Granted that doesn't cover general attractions (only roller coasters), but could be a way to sale!
 
Ahhh, this is such a cool question @Pokemaniac! If I were to create a hypothesis going into this, it would be that average ride age for parks is more cyclical, oscillating up and down as rides are installed/removed, moving the average age up and down in tandem. While we do see that to some degree, especially Tusenfryd and Alton; I underestimated the general upward trend of the charts - that rides do essentially stick around for longer periods of time, as we move forward in years.
The frustrating thing, I think, is that many of the parks we know and love haven't completed a full cycle yet. Take for instance Thorpe Park; most of its current attractions were built between 1995 and 2006, and aren't old enough to be replaced yet. Same with Alton; basically all of its stuff is from 1990 or later and still operating. We don't know how long a cycle lasts, but it's certainly long enough for various external factors to affect them. Financial crises, pandemics, corporate mergers, market situations in general, technological developments ... we can't have a steady state to use as a baseline. Alton had a sizable lineup of attractions back in 1980, which is now mostly removed and technically forms a previous cycle, but it hardly compares to the current lineup. TusenFryd still operates many attractions from its opening year, it will be interesting to see how long that can last. Ideally, their replacement should be spaced out so that they don't have to replace all of it at once when it becomes too old. The alternative is to scrap them without replacement. Regardless of how it happens, the average age graph will reach a maximum value one day.

That makes sense to a certain degree - attractions built in 2021 are probably both more exciting and more reliable than rides built decades before. Still, quite surprising to see, as I've always assumed there is a general space scarcity problem across parks - you reach a certain point when you can't fit more rides in, so you need to replace old attractions with new. While that is also partly true, it turns out parks in these samples are figuring out how to hold/revamp rides to have them last longer.
It's not always about reliability either, but also novelty and marketability (and in some cases IP rights). In many cases, a park will revamp rides to re-launch them as entirely new rides. Take for instance that boat ride at Alton Towers, which started out as Around the World in 80 Days in 1981, was revamped into Toyland Tours in 1993, then into Charlie and the Chocolate Factory in 2006, and is currently Alton Towers Dungeon from 2019 on. From the perspective of a visitor, I'd say the rides are distinct enough to be considered separate.

At the same time, I think many rides simply can't operate longer than a certain lifespan, for technical reasons. Coasters can be replaced one part at a time, in a ship-of-Theseus kind of operation, but flat rides aren't as easy to revamp. They must be retired one day. And as Alton Towers discovered, guests will want to see them replaced when that day comes. It threw out most of its thrill flats between 2010 and 2017, and now it has to hire travelling rides to make up for the resulting holes in its lineup. It's a band-aid solution, and to do anything in the long term it will have to install something more permanent.

Lastly, I think many parks are restricting the number of attractions they operate too. Keeping a ride running costs money, after all, and more rides doesn't always mean more guests. Look again to Cedar Point, which has kept 16-17 coasters running since 2003, even though they'd probably have the room for more. 16-17 could simply be the tolerance limits of coasters they can operate without having to expand their team of mechanics. For cost reasons, they could have a policy of shutting one old ride down when a new one opens, regardless of whether there's room to operate both. In that case, the lifespan of a ride would not be dictated by its technical operating limits, but by the pace at which rides are swapped out. A removed ride may be sold to another park and continue running there for many years. Look to the UK, for instance, where hardly any coasters are ever scrapped, they are just sold on to buyers abroad.

My general hunch would be RCDB data look ups, yada yada yada, export to spreadsheet somehow? Granted that doesn't cover general attractions (only roller coasters), but could be a way to sale!
Yeah, that would be very interesting! Particularly for parks with a long history, so it has thrown out enough coasters for us to determine how long they will last, with the average age graph flattening out somewhat. But it could also be fun to see how parks are currently doing, in terms of which way the trend line for the past 10-or-so years is pointing.

Many parks in the West expanded their coaster lineups rapidly in the 1990's and early 2000's, and will have a slew of coasters whose age is beginning to show these days. Assuming the coasters to have near-identical maximum lifespans, they will require replacement at roughly the same rate at which they were built. For Six Flags in particular, this is a ticking time bomb. They built so many coasters so fast they bankrupted the company, and if they want their parks' lineups to stay the same size in the future, they will have to replace them all within a similarly short time period. And we're talking very big coasters too, not stuff you can replace with Rollerskaters or Free Spins and expect the same marketing draw. However, Six Flags doesn't have the finances to replace so many big coasters so quickly (evidently, they couldn't even afford to build them that quickly in the first place). The second best choice is to start early to spread out the replacements, but they don't have the finances for that either. I wonder whether they will secure funding somehow, or if they will accept downscaling when the time comes. Either way, it will definitely be interesting to follow Six Flags over the next decade or so. The longer they will wait to begin replacing their 1995-2005 coasters, the faster they will have to be about it. Thorpe Park is in a similar situation too on a much smaller scale: It basically has only three permanently installed thrill attractions younger than 15 years, out of a current lineup of 15.

Anyway, I wonder which park was the first one to "boom" in the wave we saw in the 1990s. The state of its coasters nowadays might indicate where the other parks will be a few years from now. I have a hunch SFMM will be an interesting one to see.
 
This is fascinating and I haven't even begun to digest it properly, but I just have to say the thread title is the biggest abuse of the word "fun" I've seen in a LONG time!

Gantt charts just bring back memories of creating them 5-minutes before project deadlines at university 🤣
I'll grant you that, charts can be boring, but they're also an incredibly useful way to collect and display information. If the information is interesting, the chart will be too.

The aging-and-decay aspects of parks is very fascinating to me, because it gives a look into the future. It's this kind of information parks use to make future decisions, after all. If we can spot that a park's attraction lineup is aging, we can tell that it's due for replacement soon. Well, that or the park is about to lose a bunch of rides and subsequently guests, but that can be interesting too in its own way. The direction of the trend lines in these charts tells us whether the status quo is sustainable. A flat trend line means the park will add attractions at its current rate, a lowering trend line means they'll probably put on the brakes sometimes soon, and a rising trend line means they will have to step up their game unless they want to jeopardize their market position.

Or to summarize the three parks from the OP:
  • Alton is not where they were 20 years ago, but a few new attractions would put them back on track. Looking purely at the numbers, they're not in a bad situation, but it's easy to see the limitations of the methodology - its thrill sector is not keeping up. Probably still salvageable, though.
  • Cedar Point has historical "baggage" skewing the numbers, with five coasters older than 40 years and a further four older than 25. For how long can they hold on to all these aging coasters, before it's time to replace them? The park to conclusively answer the question "how old do modern coasters get?" may very well be Cedar Point. They do have a healthy lineup of younger rides to fall back on, however. And unlike Alton's situation, the oldest coasters at Cedar Point would not be the most expensive ones to replace.
  • TusenFryd is heading deeper and deeper into a situation it is becoming increasingly expensive to get out of. The number of rides in the park is dropping while the age of the rides is increasing - not a good combination. This status quo can't be sustained for many more years, as the rides decay faster than the park is currently replacing them. A change of pace - or complete collapse - seems inevitable.
The next parks I'd like to look at would be Thorpe Park (all rides, not just coasters) and SFMM (just coasters would suffice here). I don't think I have time to make the charts right now, however. Anybody up to the challenge?
 
EDIT: I'm leaving this post here as it's a reminder of how not to post. Warning issued. Hixee

Well, Herschend now owned Kentucky Kingdom to help the park to keep maintaining its attraction lineup because the park located near the Louisville International Airport. The height restriction that rides and attractions can’t be over 185 ft tall in order to build the tower, roller coaster, water ride, etc.

Current coaster lineup:
1. RMC Raptor - It was originally planned to open as Raptor as a clone Wonder Woman or Railblazer. It was scrapped due to financial problem of the pandemic and we will have this coaster to open in 2022 or 2023 season.

2. B&M Batman clone - Originally opened as Lightning at the Kuwait Entertainment City in 2004 become the last of its kind before the re-clone begins later on. It closed down in 2016 to stand but not operating until it is to put up for sale last year. Kentucky Kingdom fans want the park to buy this B&M Batman clone and named this coaster as T4.

3. Mack Blue Fire clone - I guess that Kentucky Kingdom will get Mack Xtreme Spinning Coaster soon. Mack will work with Kentucky Kingdom for the very first Blue Fire clone to have Xtreme Spinning Coaster trains.

4. Gerstlauer Takabisha clone - It would be cool for Kentucky Kingdom to break the record of the steepest roller coaster in the world but it would be the exact clone to the TMNT Shellraiser.
 
The frustrating thing, I think, is that many of the parks we know and love haven't completed a full cycle yet. Take for instance Thorpe Park; most of its current attractions were built between 1995 and 2006, and aren't old enough to be replaced yet. Same with Alton; basically all of its stuff is from 1990 or later and still operating. We don't know how long a cycle lasts, but it's certainly long enough for various external factors to affect them. Financial crises, pandemics, corporate mergers, market situations in general, technological developments ... we can't have a steady state to use as a baseline. Alton had a sizable lineup of attractions back in 1980, which is now mostly removed and technically forms a previous cycle, but it hardly compares to the current lineup. TusenFryd still operates many attractions from its opening year, it will be interesting to see how long that can last. Ideally, their replacement should be spaced out so that they don't have to replace all of it at once when it becomes too old. The alternative is to scrap them without replacement. Regardless of how it happens, the average age graph will reach a maximum value one day.
That's a brilliant point; that many parks probably haven't completed a full ride replacement cycle. I guess I always assume European parks, like everything else European, are way older than American parks. :p

To your open question on "first park to boom in 1990", there was a ton of activity going on for sure - would wager on something like Cedar Point or Six Flags Great America; especially is widen the search a bit to late 80s, especially 88-89 when we saw Arrow rolling out big, bad multi-loopers and other coasters. (Aka before the dawn of B&M et al.)
 
That's a brilliant point; that many parks probably haven't completed a full ride replacement cycle. I guess I always assume European parks, like everything else European, are way older than American parks. :p
The parks themselves are older, but the modern ride types in them aren't. An Arrow loopscrew or a Mondial Top Scan are recent enough inventions that they're the same age on both sides of the pond. I guess we could tell from the Alton data how long an Astroglade, cable cars, or a model railway can last in a park (evidently about 20 years), but that information isn't particularly relevant to the current lineup of any major park out there. I think the biggest and most important question is what is the service life of a B&M. As I mentioned above, next year, Nemesis will be older than Corkscrew was when it was decommissioned.
 
Small bump, but I decided to have a look at a few other parks. Only coasters this time too, of course:

xaj3Ae5.jpg

It's really interesting to see that long, constant slope on the "Number of coasters" chart. Between 1997 and 2003, SFMM added a new coaster every single year. Look how the average age of coasters stayed almost entirely flat throughout the period as well. The number of coasters peaked in 2014 and has been relatively stable since. SFMM's coasters are younger than those of Cedar Point on average, but it's a much younger park too.


FJhypR5.jpg

I think that if we were to make such plots for all the Six Flags parks, SFGAm would be the odd one out. Its number of coasters has not peaked yet, in fact there is only one decline in the entire period since 1980. It has kept scaling up even as the other Six Flags parks have plateaued or scaled down. That sudden drop in the median age in 1992 happened because until then, the park had had four coasters built before 1981 and three built after 1988. The coaster ages in 1991 were 15, 15, 13, 10, 3, 2, and 1. In 1992, Tidal Wave (built 1978) was removed and Batman: The Ride was built, and instead of an 11-year old coaster being the median one in terms of age, the four-year old one suddenly was.

aXEHjbI.jpg


Kings Island is another one of those parks that expanded rapidly around the turn of the millennium and then plateaued. Like at SFMM, you can see a period where one coaster was added every year (1998-2001), making the average age of coasters flatten while the median was steadily pushed down. The trio of coasters built in the seventies kept the average fairly high, though. This period of expansion kept the park quite young on average for a long time. In 1986, the average/median age of coasters was 9.20/9 years and it had only risen to 11.46/9 by 2001. Nowadays, however, it's 23.93/23.5, which is quite a bit higher, but as you can see by the dips in the curve, aging is kept at bay somewhat by the retirement of old attraction and the installation of new ones.

UxSERg2.jpg

This one is a fun one. A park with the same number of coasters today as it had in 1980. Where the removal of two rides aged 19 and 24 in 2008 caused the median age to increase by 11 years from one year to the next (a jump that was almost exactly nullified back in 2018, you may notice, when Wild Mouse was removed and Icon added). Even Cedar Point today, during its longest new coaster drought in years, doesn't match the lowest average coaster age BPB has had since 1980. Taking the year of manufacture into account, BPB currently only operates one coaster younger than 22 years, and that's Icon. The current median age is the average of Steeplechase (built 1977) and Revolution (built 1979) - or 43 years. The average age is a full decade above that again, at 53 years. And the park is still much younger than it was in 2017. I don't count at a high enough resolution to tell for sure, but I think the park's coasters reached a median age of 50 years at some point before Wild Mouse was removed, and an average of 55 years. The four woodies are so old that even if any of them were removed, the average age would only go down by about 5 years, and the median would barely budge (it's defined by Steeplechase and Revolution, remember). In fact, you could remove the seven oldest coasters at BPB and the park would still have a median coaster age above that of SFMM.

BPB shows that a park can attain a very high median and average age if its old coasters are looked after well enough. But again, those are mostly woodies, where worn parts can be replaced quite easily. We still haven't seen a park define how old a lineup of modern steel coasters can get before the wrecking ball comes a-knocking. Maybe there's some fun data to be collected from Wiener Prater, but that one clearly isn't representative.
 
As @Pokemaniac lays on more parks:

Now you have my mind turning on overlaying all park charts as sortable; maybe even by park chain to see if there's broad trends/preference for how chains develop their parks?
 
There's more.

One thing kept irking me as I collected data and looked at curves. How would an ideal park lineup age? Not ideal as in "perfect", but rather as in "regular as clockwork". Imagine a park with a very strict pattern of investment, which keep building new coasters with exact regularity, and retiring them all at the same age. Say the park started up with three coasters in 1980, of which one was retired precisely on its use-by date, one was retired five years early, and another five years late (to avoid tanking the lineup by removing three coasters at once). Apart from that, coasters are built and retired by clockwork regularity. What would the charts look like under such idealized conditions?

This is very quick to model in Excel, as there's no need to punch in data from parks. So I took the liberty to model a few ideal scenarios, making a few assumptions about investment intervals and coaster ages. Let's go:

dFPt3Uq.jpg

If a coaster lasts 25 years, this is the pattern that emerges. The median age stays above the average for a while, but they converge over time and eventually become the same. Not a surprising result, when you think about it. In this scenario, the number of coasters in the park plateaus at 9, when all opening day rides are removed and the ones built later are steadily replaced by new ones. What's interesting is what happens at the end of the life cycle of the first three coasters. The mean ride age peaks, then drops as the oldest rides are retired, rises again to a new peak (or perhaps, plateaus at a level somewhat higher than the first peak), then slowly drops again before stabilizing in a repeating pattern.

However, this model does not seem realistic. The average and median ride ages never reach 15 years, which is not observed in any of the real-life parks (except Alton Towers, it seems - I didn't expect that, really). Also, the real-life parks tend to have more coasters. Obviously, parks are keeping their coasters for a bit longer than our model 25 years. Let's try 30.

WjaTVRz.jpg

Not much to add here, really. I extended the X axis by 10 years to allow the repeating pattern more room to emerge. The patterns are otherwise the same. The park keeps oscillating between 10 and 11 coasters, after briefly reaching 12. That's roughly the level of many big regional parks in the US today. The same peak-valley-plateau-drop pattern is seen when the opening day rides are retired.

However, in real life, we have yet to see many late-80's coasters retire en masse out there. Let's do 40 years too, but spreading out the investments for a bit longer: One coaster every four years.

vE1IpIw.jpg


Same pattern, same convergence of the median and average ages, and the number of coasters swinging between 10 and 11. The interesting thing, perhaps, is that the median and average coaster ages converge around 20-25 years, roughly 35-40 years after the park began adding coasters at regular intervals. Scroll up and have a look at the real-life parks we've collected data for so far. I think the model is starting to match reality.

Of course, it's still a model. An approximation based on rough assumptions. I don't even know whether the assumptions are realistic. But perhaps we can turn it around and suggest that some parks behave rather like the model. Look at the chart for Kings Island again:
aXEHjbI.jpg

Plateauing number of coasters, convergence of the median and average age, and we've seen the first peak-and-drop-and-climb of the converged graphs from the model. If Kings Island continues with a regular investment schedule, we may see the plateau, the second drop, and the repeating pattern emerge over the next 10-20 years. Of course, the existence of very old rides at a park will throw the average age line all out of wack (again, see BPB), so it's unlikely the park will behave exactly like the model, but at least we know what it will look like on the very remote chance that they do.

I'd like to try this exercise with a degree of randomness. It shouldn't be too hard to throw in a standard normal deviation for the lifespan of coasters, maybe a classic ride or two that never retires, or factor in increased modern coasters having a longer service life, and then run the simulation a bunch of times to see what kind of patterns emerge then. I've got a suspicion this is the kind of thing @Hyde can throw together without breaking a sweat. Or are there other takers out there?
 
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