What started out as an effort to rank my Top 10% coasters a while back has ended up getting carried away into so much more (I really need to find more to do during Lockdowns)…
(Warning - I got
really carried away and did some maths-y stuff in this post. I'll say when that starts and finishes so people can skip over it if you want..
)
So here’s my current Top 10% (aka Top 20):
1. Taron
2. Taiga
3. Untamed (Walibi Holland)
4. Helix
5. Oz’Iris
6. Balder
7. Lost Gravity
8. Nemesis
9. Joris en de Draak
10. Troy
11. Goliath (Walibi Holland)
12. Black Mamba
13. Hyperion
14. Lech Coaster
15. Lisbergbanan
16. Van Helsing’s Factory
17. Pulsar
18. The Swarm
19. Nemesis Inferno
20. Colorado Adventure
My rankings are very much based on the philosophy of asking the question “What cred would I most like to ride out of this list?”. It’s not a perfect way of doing it, but it works at this high level.
I then started to wonder if there was any trends with my favourite rides. More specifically, if there was any correlation between how much I enjoy a cred and its stats. So I started have a think and play around with plotting some graphs. But that wasn’t going to be good enough, as it would only show if there was any interesting correlation with my favourite rides.
In the end, I went through and gave a ranking to all my coasters (fortunately 200 isn’t that many). And even then, I didn’t bother ranking the kiddie creds and all the stupid little +1s which wouldn’t really affect my rankings. So that left me with 134 coasters to rank, again with the logic of “Which one would I most like to ride right now?”. Whilst that was fine and a bit more clear cut with my favourites, that was much harder towards the middle and bottom - how do you compare a specific Vekoma looper, Maurer spinner and a woodie all from different countries and decide what you’d rather ride? The short answer is you basically just wing it and hope for the best..! (One day I'll move my Excel spreadsheet onto a Google spreadsheet so I can edit it anywhere, then maybe I can share that list in all its glory...
Then I pulled all the key ride stats (length, height, speed, inversions), which fortunately I track in my cred count sheet. The stats mostly comes from rcdb, unless I think it’s wrong…Untamed’s 270 Double Inverting Corner Stall is 2 inversions, not 1 thank you very much. So far so good.
*Now for some scary-ish maths...*
Now trying to come up with a correlation between several different things is…tricky. Fortunately during my PhD I had to self-teach myself how to use a statistical programming language, R (who says that a Maths PhD doesn’t have real world applications?!). Basically what this would let me do is put in all the data I had, and it would spit out all the possible correlation details I could want. The downside is that I needed complete data for each ride; so the length, height, speed and number of inversions. A fair few had incomplete data, meaning I’d be looking at 110 different coasters and their stats. That leaves a few gaps, but largely it’s okay.
So, putting all that data in and running some magic stats stuff that I don’t really understand properly, I got this lovely graphic:
This shows individual correlation between Ranking and each stat, as well as between the stats themselves. The closer the number is to +1, the better the correlation. The closer the number is to -1, the better the “anti-correlation” (basically, the higher the value of the independent variable, the lower the dependent variable). It also gives plots against each variable. So on these individual cases, it seems:
-The longer the length of the cred, the less likely I am to rate it.
-The height of the cred doesn’t matter too much, but I seem to prefer slightly shorter creds
-Creds with higher speeds might detract from the experience for me.
-Number of inversions doesn’t matter too much, but some might help.
There’s issues with this, of course. Most of the creds in this list are in very short range of height (about 80-120ft), and speed (around 40-50mph). This makes it hard to get a good view of any correlations. Equally, number of inversions is a difficult one given its discrete data (0, 1, 2, etc) rather than continuous, and a huge proportion of these creds have no inversions.
But what about combining all these together? Well, R is able to calculate that (though I don’t *really* know how..), and gives a few different measures.
-The first is an adjusted R-squared number (like an
R-squared number, but for multiple variables). The closer to 1, the better all the model explain the ranking. This was churned out to be 0.2266, which is low (but in these situations, ie - ones which are less scientific, lower numbers are to be expected).
-We then get a
F-statistic value, and a p-value, which are related. The F-statistic’s ‘goodness’ is only seen when compared to another number which comes from the number of pieces of data you have, and the p-value effectively indicates the probability that the F-statistic’s value is wrong. Effectively you want a large F-statistic and a low p-value. The F-statistic is 8.984, which given the size of the data is good, and the p-value is 2.799*10^(-6), which is good.
(NB: I know very little about all this, so I could very much have been talking out my backside during this..)
*End of most of the scary maths stuff*
So basically, what this means is that the model I have (which can be put into an equation; see below) isn’t particularly good at predicting where I’d rank a coaster. But there exists something, perhaps a much more complicated formula, which might be good at such predictions! None of that is too surprising - I'm more likely to like a coaster with good stats after all. But obviously things like theming, location, manufacturer, restraints, etc all come into play too.
So, without further ado, the current formula I have…
Rank = 131.777733 - 0.010833*L + 0.254006*H - 1.607595*S + 4.531214*I
where: L = length in feet, H = height in feet, S = speed in mph, I = inversions
Side note: the stuff which is also churned out from the programming suggest that the current formula puts too much of an incorrect emphasis on height, and that number of inversions is problematic for the formula.
As a random example to show this, this would suggest something like:
Maverick (L=4450, H=105, S=70, I=2) could be my 6th favourite ride, but..
Steel Vengeance (L=5740, H=205, S=74, I=4) might only just squeeze into my Top 20.
Hmmm, maybe not...
Fun fact as well: this formula suggest that a "no-cred" (ie something with no length, height, speed or inversions) would be more fun than my bottom 3 coasters. Those are Ukko at Linnanmaki, as well as MP Express and Condor. Hard to disagree there.. ?
It’ll be interesting to revisit this after riding some new creds, and maybe redoing this whole thing after getting a lot more creds under my belt, to see if I get something which is perhaps better!
