The Top 10 Shortcuts in Mario Kart Wii, definitively

A few notes:

I used 1.22^x on the denominator for a few key reasons, although changing the base to anything close to 1.22 won't make much of a difference. Since I believe that difficultly isn't as important as how much time the shortcut saves, I wanted to use something that increases slower than a linear function y=x so that the score is A) affected by the difficulty less and B) has output smaller than y=x for all x between 1 and 5 (although this essentially just inflates the scores). The derivative of 1.22^x is less than 1 when x is between 1 and 5, and it actually equals 1 at ~5.02, so this checks out. Any higher base (rounded to the nearest hundredth) has a derivative higher than 1 when x is between 1 in 5, so we can't use those. bases between 1 and 1.22 would have worked too, but the closer the base is to 1, the less the difficulty affects the score because (base)^x would grow slower. Therefore, I chose the highest value (1.22) so that difficulty is still aptly accounted for, while not affecting the overall score as much as y=x does. I think this was successful in the experiment because there were some shortcuts that got higher scores than others for having a low difficulty score, but the shortcuts trended toward being more difficult in general.

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[PiCoinEarlyAdopter]

The only other factor I think that could be considered in a part 3 to this is the risk reward ratio rather than just time save. For instance, if you fail the grass cut you might lose 2 seconds. But if you fail a rainbow road track skip you might lose 5 seconds. This factors in how risky a given cut is.

[hinakremec]

You forgot the coolness metric in your calculations

[jurriankoning]

worst shortcut is a lie. It's been speculated the hippity hoppity strat improves luck by 200% making it worth it every single time

[bicrowave]

i think that another factor to consider is the proximity to the end of the lap: mg gap jump can take you from 7th to 3rd and you finish immediately after. however for pg grass cut, it's right at the start of the lap, meaning there's more time for you to be shocked/blued and for you to lose your position. proximity to end of lap makes mg gapjump much stronger and pg grasscut much weaker

[BlueGrovyle]

I like metric-based rankings like this because they're objective once the admittedly subjective, but concrete criteria are determined. Then the numbers can be adjusted if we think they did a poor job.
I think that, instead of giving a bonus to shroomless cuts, you should have introduced what I'll call an "accessibility" stat to generalize based on the number of shrooms the cut takes (e.g. dock points from Delfino double cut for requiring 2 shrooms).

Excellent video!

[spencergains]

one slight methodological critique is the choice to use absolute time versus something like shortcut time save divided by total track time. Shortcuts which save less time, but in short tracks will be disadvantaged to shortcuts that save an average amount of time on a long track.

[joshualiley]

Maybe a max vs min time save/loss based on if you succeed or fail. The grumble volcano rock hop might be harder than the respawn, but if you fail it you're probably still going to respawn on the other side and save time. Compared to the peach gardens flower cut, even though it's easy to pull off, if somehow you fail it by crashing into the hedge and ending up in the flowers, for example, then you're losing time overall.

The formula would be very similar, but would also factor in an unsuccesful attempt. The probability of failure score is just 5 minus the difficulty of the shortcut, meaning the GV rock hop with a difficulty of 3.62 has a failure score of 1.38.

Let's assume that failing the rock hop saves the same amount of time as simply attempting the respawn, minus 0.5 seconds for arguments sake. That means it saves 3.1 seconds if failed and 5.2 seconds if succeeded.

Using my new system, the success score remains the same as yours at 2.532, and the unsuccesful score is 3.1/1.22^(1.38) = 2.356, so the total score of the shortcut is 2.532 + 2.356 = 4.888

Let's contrast that to the current system's best shortcut, the BC3 regular cut. The successful shortcut remains the same at 4.161, an unsuccesful shortcut we'll say loses 4 seconds (the time it takes to respawn, I believe, and the respawn is back where you started). The unsuccessful cut saves -4 seconds (because it loses time), so the unsuccesful score is -4/1.22^(2.28) = -2.542. Therefore the shortcut has a total score of 4.161 - 2.542 = 1.619. That feels a lot more appropriate given the high cost of failure compared to the GV rock hop.

I also believe you should remove 0.5 seconds from the score per mushroom if it takes more than 1 mushroom. For example, it doesn't feel fair giving the Delfino square double it's full time save when you blow through 2 mushrooms to complete it when the mud cut only uses 1. You should also subtract any possible remaining mushrooms from a failed shortcut that may result in you losing the mushrooms via falling off. For example, failing the rock hop would possibly lose you 2 mushrooms, so 1 second, whereas failing the GV respawn wouldn't really lose you any mushrooms because why would you try it when you still had some? Because of these, these additions/subtractions should be done before dividing by 1.22^x, so that the likelihood could be factored in.

These 2 cuts would then have the adjusted scores:
GV rock hop - 4.128
BC3 regular - 0.782

Shortcuts where you could fall off are going to have much worse scores now, but that feels appropriate in all honesty

[Metagross]

I like the idea, but I have two things I would have done differently in your metric:
1. For the shroomless/shroom distinction I would not have just subtracted a fixed amount, but I would have tested how much time a Shroom on a straight piece of road saves in comparison to driving normally and then subtracted that from the "time saved" variable. This way you can really see how much time is saved by the SC and how much is saved by the shroom.
2. I would have also taken into account if a shortcut takes multiple shrooms. This way the Delphino Square double SC would have been deduced the shroom score twice, since it takes 2 shrooms.

[upMKW]

best shortcut (not really a shortcut but a strategy) is the method where u release a miniturbo into the wall once u enter the waterfall on koopa cape and then turn left and release another minturbo and ride the left wall at nearly shroom speed. i think its the best because its consistent and satisfying. bonus is that it can save you from red shells!! yay!!

[FrogInShorts]

I feel how close to the end of a track should play a factor. Sure peach gardens is easier than mushroom gorge gap jumps but I guarantee far more people have won a race thanks to the gorge jump at the finish line than the peach gardens cut that is on the start of lap 3.

Edit: I see my exact comparison has been made already but ill leave this up cause that's funny to me.

[Foster]

when you blow up this should be redone, imagine like 25k ppl taking the poll

[sketero]

Funky Kong is an affront to science and thus cannot be determined with it

[Seltaeb_]

Commenting for algorithm. GL on this popping off!

[doraemon]

Saving 5 seconds in a short track is more beneficial than in a long one

[nebnoobgeometrydash]

I expected the gap jump to be higher but others werent too surprising lol

[mrsnrub]

i was expecting shrooming over the grass at the start of moonview highway to be number 1

[KlydeRiolu]

just so you know, bc3 shroom cut saves more than ultra does

[JanNiediek]

I think it could be a cool idea to place the shortcuts on an xy graph instead of converting everything into one number ;)

[nixisawesome]

I’m surprised the Toads Factory Shroomless lake jump didn’t make it

[jeikobu]

I think you should add a factor of how many shrooms it takes into the formula as the double dock needs 2 but the single needs 1