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An evaluation of the speed difference between the maximum and minimum speed possible without coins

Discussion in 'Articles' started by Mister Wu, Jan 2, 2015.

  1. Mister Wu

    Mister Wu

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    AN EVALUATION OF THE SPEED DIFFERENCE BETWEEN THE MAXIMUM AND MINIMUM SPEED POSSIBLE WITHOUT COINS
    Mister Wu[1]


    [1]Passons, Italy

    ABSTRACT
    To evaluate the difference in maximum speed between a 1.0 and 5.75 speed combination in Mario Kart 8 a method was devised based on a previous assessment by the MKBoards' user Nefos. The results showed a speed increase between 7.4 % and 7.6%, lower than the expected 10%.


    INTRODUCTION

    Due to the lack of a speedometer, it is difficult to accurately measure the difference in speed between a 1.0 speed combination and a 5.75 speed combination (which will be called "slow" and "fast" combination, respectively) in Mario Kart 8. Previous measurements of this difference were performed by the user flc[3]. Furthermore, the user Nefos suggested a method[1] and posted data[2] that, when extrapolated, indicate that the increase in speed in the fast combination is 5.6% of the speed of the slow combination (measured as 2316.5 frames / 2193 frames, 2193 frames is the actual value measured by Nefos, while 2316.5 is a value extrapolated based on the notion that the time needed to drive the distance indicated by Nefos' is linearly dependent on the speed value of the combination[2]: 2193 + 26 * 4.75). Here a new method is presented to accurately measure this speed increase, and results of the application of this method are shown.


    MATERIALS AND METHODS

    N64 TOAD'S TURNPIKE


    MARIO KART 8 VERSION
    Mario Kart 8 version 2.0 was used

    CONTROLLER
    The Wii U GamePad was used.

    COMBINATIONS
    The following combinations were used to evaluate the speed increase:
    slow combination: Lemmy + Mr. Scooty + Roller tires
    fast combination. Morton + Circuit Special + Slick tires

    STARTING POINT FOR THE MEASUREMENTS
    The starting line of Toad's Turnpike was used as the starting point for the measurements.

    ENDING POINT FOR THE MEASUREMENTS
    The first dashed line met by the vehicle was used as the finishing point for the measurements

    STOPWATCH USED
    The iOS 7 clock application in stopwatch mode was used to measure the time passed between the starting and the ending point.

    METHOD
    The method is based on the one used by user Nefos to measure the coin contribution to maximum speed[1]. Time Trial without ghost was selected. Immediately after the beginning of the time trial, the "B" button was hold until colliding with a vehicle. After colliding, the "ZL" button was pressed to use a mushroom and the "A" button was used immediately after pressing the "ZL" button in order to reach and mainatin the maximum speed. The "A" button was hold until a collision with the guard rail happened and then the time trial was finished normally. 4 independent iterations of this method were performed per each combination. The time trial was watched through Mario Kart TV with the standard camera angle (i.e. behind the vehicle) pushing the "B" button before the beginning of the measurement in order to use the slow motion feature during the whole measurements. The stopwatch was started as the driver passed the starting point and was stopped as the driver passed the ending point.


    TOAD HARBOR


    MARIO KART 8 VERSION
    Mario Kart 8 version 3.0 was used

    CONTROLLER
    The Wii U GamePad was used.

    COMBINATIONS
    The following combinations were used to evaluate the speed increase:
    slow combination: Lemmy + Mr. scooty + Roller tires + Bowser Kite
    fast combination. Morton + Circuit Special + Slick tires + Bowser Kite

    STARTING POINT FOR THE MEASUREMENTS
    The starting line of Toad's Harbor was used as the starting point for the measurements. TH_starting_point.jpg

    ENDING POINT FOR THE MEASUREMENTS
    The last straight segment of the dashed line the drivers meets after the starting line was used as the finishing point for the measurements
    TH_ending_point.jpg

    STOPWATCH USED
    The iOS 7 clock application in stopwatch mode was used to measure the time passed between the starting and the ending point.

    METHOD
    Time Trial without ghost was selected. Immediately after the start, the "B" button was hold until reaching the external part of the sidewalk, without colliding with the barrier. TH_mushroom_point.jpg
    The "ZL" button was pressed to use a mushroom and the "A" button was used immediately after pressing the "ZL" button. The "A" button was hold until a collision with the barrier happened and then the time trial was finished normally. 4 independent iterations of this method were performed per each combination. The time trial was watched through Mario Kart TV with the standard camera angle pushing the "B" button before the beginning of the measurement in order to use the slow motion feature during the whole measurements. The stopwatch was started as the driver passed the starting point and was stopped as the driver passed the ending point.


    RESULTS

    N64 TOAD'S TURNPIKE


    RAW DATA
    slow combination: 48.00 s, 48.00 s, 48.06 s, 47.97 s
    fast combination: 44.56 s, 44.60 s, 44.66 s, 44.59 s

    MEAN ± STANDARD DEVIATION
    slow combination: 48.01 s ± 0.04
    fast combination: 44.60 s ± 0.04

    INCREASE IN SPEED ± STANDARD DEVIATION (Referred as % more than the slow combination)
    7.6 % ± 0.1

    TOAD HARBOR

    RAW DATA
    slow combination: 47.74 s, 47.67 s, 47.66 s, 47.64 s
    fast combination: 44.37 s, 44.37 s, 44.36 s, 44.41 s

    MEAN ± STANDARD DEVIATION
    slow combination: 47.68 s ± 0.04
    fast combination: 44.38 s ± 0.02

    INCREASE IN SPEED ± STANDARD DEVIATION
    7.4 % ± 0.1


    DISCUSSION

    It is interesting to note that between version 2.0 and version 3.0 the speed increase due to passing from a slow combination to a fast combination was not altered in a significant way. This increase is not as high as the 10% usually reported, but is higher than the value extrapolated from Nefos' data based on the assumption that the time needed to drive a determined distance is linearly dependent on the speed value. Further experiments whose results are reported as supplemetary information apparently don't agree with this surprising assumption, but the actual nonlinearity in speed increase with respect to speed value measured by Nefos is anyway very slight[2]. The difference between the current results and the ones obtained by interpolation of Nefos' data could have many reasons: in particular, the method currently used to measure the time passed is suboptimal and some systematic errors due to the operator, such as the lag between perception of passing the starting point and ending point and the start and end of measurement, may not always be completely compensated. Methods based on a frame-by-frame analysis of recorded game footage are recommended and suggested as a proper extension of the current methodology.

    CONCLUSIONS

    A new method was proposed and applied for the evaluation of the increase in speed between a slow and a fast combination. Other methods based on this and Nefos' methods may help in the evaluation of other critical parameters in Mario Kart 8.


    COMPETING INTERESTS

    The author declares no competing interests.


    REFERENCES

    [1]posts #9, #10 and #11 of the "Coin Count and Performance" thread in the "Mario Kart 8 - General Discussion" section of MKBoards' forum by Nefos
    [2]post #14 of the "Coin Count and Performance" thread in the "Mario Kart 8 - General Discussion" section of MKBoards' forum by Nefos
    [3]post #19 of the "An evaluation of the speed difference between the maximum and minimum speed possible without coins" thread in the "Mario Kart 8 - General Discussion - Articles" section of MKBoards' forum by flc

    ACKNOWLEDGEMENTS

    The direct help of user Ade in suggesting the formatting, of user Shito Ryu in suggesting the acquisition of further data to perform a linear fitting, and the indirect help of MKBoards' user Nefos in proposing a method for the evaluation of speed differences is acknowledged.


    CONTACTS

    If more information is needed, the user Mister Wu of MKBoards may be contacted.


    SUPPLEMENTARY INFORMATION

    An additional evaluation of the speed increase was done in Toad Harbor with the following combinations:
    2.0 combination: Wendy + Biddybuggy + Standard Tires + Bowser Kite
    3.0 combination: Larry + Sports Bike + Slim tires + Bowser Kite
    4.0 combination: Ludwig + Standard Bike + Slim Tires + Bowser Kite
    5.0 combination: Roy + Mach 8 + Slim Tires + Bowser Kite

    RAW DATA
    2.0 combination: 46.84 s, 46.87 s, 46.90 s, 47.19 s
    3.0 combination: 46.26 s, 46.25 s, 46.18 s, 46.29 s
    4.0 combination: 45.38 s, 45.42 s, 45.65 s, 45.63 s
    5.0 combination: 44.92 s, 44.85 s, 44.99 s, 45.01 s

    MEAN ± STANDARD DEVIATION
    2.0 combination: 46.95 s ± 0.16
    3.0 combination: 46.25 s ± 0.05
    4.0 combination: 45.52 s ± 0.14
    5.0 combination: 44.94 s ± 0.07

    INCREASE IN SPEED ± STANDARD DEVIATION
    2.0 combination: 1.5 % ± 0.4
    3.0 combination: 3.1 % ± 0.1
    4.0 combination: 4.7 % ± 0.4
    5.0 combination: 6.1 % ± 0.2

    Results for all combinations were plotted and a linear regression was performed:
    Increase_in_speed.png
    The R^2 of the regression suggests that the increase in speed is linear with Speed Value. The equation found in this study is:

    %increase = 1.5526 * SV - 1.5514

    The error on the last two digits are an indication the uncertainty of this equation.
     
    Last edited: Jan 25, 2015
    Hawk, snoωγ, Exodaire and 5 others like this.
  2. Jake

    Jake I love Meganium

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    Called a study bro.

    Very interesting findings Mister Wu.
     
  3. Rookie

    Rookie

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    This is pretty interesting to do an experiment on, but I'm still kind of confused by the layout. Does the speed increase turn out to be statistically significant, and is there any margin of error with this method?
     
  4. Shito Ryu

    Shito Ryu M32

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    It would be way more enlightening to get data for all the possible speeds sets and fit some function with it (can't guess what it is without seeing the experimental points first).
    Maybe it's just it's pretty late so I'm not very awake, but it looks to me like you considered the moment you shroomed to be the start. The shroom time affects the data, Idk how though.
    Moreover, using a phone to look at times? Where's the human error? You gotta record that and go through the video with some zoom on the time to make it precise.
    It would also be interesting to do the same thing with different amount of coins and see ho does that affect the speed (fit through the data again to find the function)
    I guess I could do some work on it to get some real data out of it.
     
  5. Mister Wu

    Mister Wu

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    The errors are reported as standard deviation, you can directly calculate it from the raw data, just use the propagation of errors for the ratio. The standard deviation is, in this case, 0.1 % on the speed increase, so, if you want a 99 % confidence interval, it is [7.5%, 7.8%] for N64 Toad's turnpike and [7.0%-7.8 %] in the case of Toad Harbor. To put it simply, the real increase in speed it almost sure to be greater than 7.0 % and less than 7.8 %, or in Funky Kong + Flame Runner terms, if Morton is running at 84 km/h then Lemmy is running at 78 km/h (wow, Double Dash!! days return!)
     
  6. Zinthos

    Zinthos

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    Not sure if it is me reading on the phone, but can you layout the thread better? It's a bit cluttered. Being organized will make your report more effective.
     
  7. Mister Wu

    Mister Wu

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    Nope, the point of shrooming is chosen as the farthest from the starting point in order to reach full speed at the starting point by shrooming and holding A. Look at the screenshots if the text is not clear!
    The human error in all aspects (in game/in measurement) is taken into account by doing 4 iterations. They are not many, I know, but this method is quite time consuming because each time I have to finish the time trial. The best method is the capture card and measuring the frames needed to get from starting point to ending point, but I don't have one...
    Yes, I would like to measure the coin contribution too, but this method cannot be directly used because, as far as I know, there are no tracks in which coins can be reached without sterring in Time Trial, and it is very difficult to obtain the same trajectory if you start steering. We should maybe ask Nefos if he can collect more data. But you can be sure that I'm thinking about it!
     
  8. Shito Ryu

    Shito Ryu M32

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    @Mister Wu
    Ok, I didn't read well enough about the starting point, my bad, I'm falling asleep.
    And you're right about the steering part, didn't really think about it. Maybe it's possibile to get the right angle but Idk, haven't tested how many angles are possible (if they are way too many, I guess it can't be done well enough).
     
  9. Mister Wu

    Mister Wu

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    Added some newlines and color coding, do you have any other suggestions about proper formatting?
     
  10. Zinthos

    Zinthos

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    I'll look at this at my laptop when I get home. I'm currently on mobile so that might be the reason of the clutter. Generally space different sections of your research. Don't provide a huge text wall is my general advice.

    EDIT: Looks a bit better now! I'll try to help out the formatting when I get home , which won't be for a while
     
  11. Ryan's

    Ryan's Zealous Staff Member

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    I just looked at the pictures.
     
  12. Luso

    Luso mk8 is the superior game

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    Wow, nice work :eek:
     
  13. Shito Ryu

    Shito Ryu M32

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    btw real MEN use Latex.
     
  14. Mister Wu

    Mister Wu

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    Don't worry, and sorry if I was a bit rude! Oh, and by the way, the effect of the mushroom is finished well before the starting point! This is very important because, judging by the sound of the engine of the Gold Standard, vehicles with tier 1 acceleration don't apparently reach full speed immediately after the effect of the mushroom is finished. I just checked with the Gold Standard and I found out that in Toad Harbor the full speed is reached a bit before the starting point while the situation in Toad's Turnpike is a bit more murky, but still the results show that this aspect was not very influential on the final results (yes, someday I'm going to make a thread about how can one know if he's reached full speed because the situation with vehicles such as the Mach 8 or Circuit Special is maddening since both the smoke out of the engine and the sound of the engine apparently have a "peculiar", if any, relationship with the actual speed!).

    One thing that can be done is 2 player split screen in N64 toad's Turnpike. The second player can get coins without steering. One thing that can be done is using a 5.75 acceleration combination I used to reach full speed before the starting line and then measuring the time from starting line to the ending point of my method. the results can be compared directly with my method. The caveats:
    1. Full speed must be reached before the starting point. Based on the sound of the engine, the time needed to reach full speed is pretty long in MK8. One possible soultion is again Nefos' method: triple mushrooms with player 1. With this, you could also do measurements with a 5.75 speed combination, but please use the Gold Standard so the sound of the engine tells you whether the kart is at full speed or not at the starting line (which curiously doesn't happen with the other speed karts!)!
    2. If the ending point can't be reached by the second player beacuse of the guard rail, my method must be reapplied to N64 Toad's turnpike using another ending point reachable by player 2
    3. MKTV in versus mode uses cinematic angles which are not very good for this kind of measurements
    Of course, if you want to do measurements in Toad Harbor, then you have to use the whole Nefos' method: palyer 1 hits himself to give coins to player 2, then he gets triple shrooms to give the boost that leads to full speed.
     
  15. Mister Wu

    Mister Wu

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    You're right but I don't know if I really want to learn yet another language...
     
  16. Mister Wu

    Mister Wu

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    Except not! In Double Dash!!, if i remember correctly, the speeds were 78-82 km/h in plains (i.e. Baby Park) and 79-84 km/h downhill (e.g. the internal part of the turns of Luigi Circuit)
     
  17. Mister Wu

    Mister Wu

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    Added some information about other speed values, corrected the discussion section and my location.
    And oh, if we were talking again in Funky Kong + Flame Runner terms (5.75 Speed = 84 km/h max speed), then the plot would be like this:
    Speed.png
    With the equation describing the max speed being:
    MAX SPEED = 76.973 km/h + 1.2139 * SV
     
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  18. Din

    Din

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    Very nice work you have going here! I've been waiting for someone to do something like this for a while, wasn't sure how many of us studied Statistics in school and its clear you do :) Fantastic study, I'll have to show this to a few people :D
     
  19. flc

    flc Professional Site Breaker

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    this is similar to how I tested this noise to begin with and it's the same result by the looks of things. wasn't aware people had said that there was a change in how speed works after the 3.0 patch (seriously wat)

    how I was testing coins was recording @ 60fps and checking frame data on the same TH straight you used. also, you say 44 seconds for 5 speed using mktv slowdown... but how much slowdown is that? if lightweights are losing almost a half second on one straight... lol

    recording & frame by framing to see exactly what the speed changes are will be important I think, especially with how momentum works in this game.
     
  20. Mister Wu

    Mister Wu

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    Oh, sorry for not citing you, I didn't do much research about who also tried to mesure this difference in speed.:oops:

    Nobody said that, but the first measurements were done before version 3.0 was released. Since Nintendo usually doesn't publish the full release notes for its games (and MK8 is no excpetion) this was an easy check!

    Well, if on real time is 0.5 seconds and here is pretty much 3.5 seconds, I would say that the slowdown is 1/7 of real time, but probably it is 1/8.

    Absolutely! I personally don't own a capture card nor a HDMI recorder, but I'm more than willing and happy to collaborate with someone who has these devices and has the time and patience to capture and send me the raw streams which will be analyzed.
     
  21. flc

    flc Professional Site Breaker

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    don't worry about not citing, it was more or less just a quick test for curiosity's sake

    so ~0.15 seconds on the TH straight for each point of speed... no wonder lightweights are fucked, they're basically being hit with an item every 30 seconds. not sure how one would test momentum + speed + miniturbo in this game but I'm pretty sure lightweights would have even more problems lol
     
  22. Mister Wu

    Mister Wu

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    Well, I would like to quote and to see your results, but I cannot find where is your post, could you please point me to it?

    And oh, if you did similar studies to the ones I write, please tell me! I am very awful at finding previous studies and many of you who posted results have equipment which is much better than the iOS 7 clock app! I would be very happy to compare my results to yours and to cite you, because the aim is just inspecting this game, not my "glory"!
     
  23. Domenico

    Domenico

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    Fantastic work, finally someone other than Nefos worked on this. o:
    You should try with ghost, for look at the acceleration too.
    Wait, are you Italian?
     
  24. Sayn

    Sayn

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    you should write a book about mk8 m8
     
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  25. Mister Wu

    Mister Wu

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    In realtà sì! Riguardo all'accelerazione, ho in mente un metodo e probabilmente ci saranno due articoli: uno preparatorio e non riguardante in realtà l'accelerazione forse esce la prossima settimana, a seconda di quanto tempo mi servirà a fare le prove e a scrivere (ok, MOLTO più di una settimana probabilmente), quello vero e proprio non so, anche perché sono terribile nelle misurazioni con cronometro e i fantasmi contro cui gareggi non compaiono sulla MKTV (avrei avuto in mente altrimenti un metodo simpatico già utilizzato in modalità due giocatori per scoprire che quando il fumo scompare non si è ancora raggiunta la massima velocità)...
    Yes I am!
    Regarding acceleration, I am probably using a method involving an aspect I may discuss in an article next week (but probably I will end up posting the article much later), but if and when I will "publish" the results about acceleration I really don't know, I'll have to see if I manage to properly use the stopwatch (I had in mind a method similar to the one already used in 2P mode to establish that when the smoke disappears the vehicle still hasn't reached full speed, but unfortunately ghosts against whom you are racing don't appear in MKTV)...
     
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