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A systematic evaluation of top land speed without coins as a function of the Land Speed value

Discussion in 'Articles' started by Mister Wu, Dec 31, 2015.

  1. Mister Wu

    Mister Wu

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    A SYSTEMATIC EVALUATION OF TOP LAND SPEED WITHOUT COINS AS A FUNCTION OF THE LAND SPEED VALUE

    Mister Wu[1]

    [1]Passons, Italy

    ABSTRACT

    The top land speed without coins was systematically evaluated for all possible values of Land Speed, showing no particular evidence for tiering.

    INTRODUCTION

    Although other studies already attempted to measure how top land speed without coins changes as a function of the Land Speed value [1][2][3], a systematic study was never made. Such a study is presented here.

    MATERIAL AND METHODS

    CAPTURE DEVICE

    An Elgato Game Capture HD was used to record an incoming 720p stream from the Wii U console through HDMI.

    MARIO KART 8 VERSION

    Mario Kart 8 version 4.1 was used.

    CONTROLLER USED

    The Wii U GamePad in normal (non-gyroscopic) mode was used.

    COMBINATIONS USED

    The following combinations were used to obtain the respective Land Speed values:

    1.00: Lemmy + Landship + Button Tires + Bowser Kite
    1.25: Lemmy + Landship + Wood Tires + Bowser Kite
    1.50: Larry + Landship + Button Tires + Bowser Kite
    1.75: Larry + Landship + Wood Tires + Bowser Kite
    2.00: Wendy + Landship + Off-Road Tires + Bowser Kite
    2.25: Wendy + Landship + Slim Tires + Bowser Kite
    2.50: Ludwig + Landship + Button Tires + Bowser Kite
    2.75: Ludwig + Landship + Wood Tires + Bowser Kite
    3.00: Roy + Landship + Button Tires + Bowser Kite
    3.25: Roy + Landship + Wood Tires + Bowser Kite
    3.50: Morton + Landship + Button Tires + Bowser Kite
    3.75: Morton + Landship + Wood Tires + Bowser Kite
    4.00: Ludwig + Standard Bike + Slim Tires + Bowser Kite
    4.25: Ludwig + Standard Bike + Slick Tires + Bowser Kite
    4.50: Roy + Standard Bike + Slim Tires + Bowser Kite
    4.75: Roy + Standard Bike + Slick Tires + Bowser Kite
    5.00: Morton + Standard Bike + Slim Tires + Bowser Kite
    5.25: Morton + Standard Bike + Slick Tires + Bowser Kite
    5.50: Morton + Gold Standard + Gold Tires + Bowser Kite
    5.75: Morton + Gold Standard + Slick Tires + Bowser Kite

    METHOD

    A Time Trial without ghost was started in Toad Harbor. Using only the "B" and "A" buttons, the mushroom release point was reached.
    Shroom.jpg
    The first mushroom release point.

    After reaching it, the "ZL" button was pressed to use a Dash Mushroom and soon after the "A" button was held until near the end of the straight section. Then, "A" was released, the "B" button was pressed to brake and the mushroom release point was reached again. Three iterations were made for each Land Speed value. The time was measured by subtracting the number of the first frame where the starting line disappeared from the number of the frame where the first non-straight line met at the end of the straight section disappeared.
    Start.jpg
    The point where the first measurement started.

    End.jpg
    The point where the first measurement ended.



    The following times in frames have been measured:

    1.00: 214, 215, 215
    1.25: 214, 214, 214
    1.50: 213, 213, 213
    1.75: 212, 212, 212
    2.00: 212, 211, 211
    2.25: 211, 211, 211
    2.50: 209, 209, 210
    2.75: 208, 209, 209
    3.00: 208, 208, 208
    3.25: 207, 207, 207
    3.50: 207, 207, 206
    3.75: 206, 206, 206
    4.00: 205, 206, 206
    4.25: 205, 205, 204
    4.50: 204, 204, 204
    4.75: 203, 203, 203
    5.00: 202, 202, 202
    5.25: 201, 202, 201
    5.50: 201, 201, 201
    5.75: 200, 200, 201

    RESULTS

    The following speeds relative to the slowest speed have been measured:

    1.00: 1
    1.25: 1.003 ± 0.003
    1.50: 1.008 ± 0.003
    1.75: 1.013 ± 0.003
    2.00: 1.016 ± 0.005
    2.25: 1.017 ± 0.003
    2.50: 1.025 ± 0.003
    2.75: 1.029 ± 0.000
    3.00: 1.032 ± 0.003
    3.25: 1.037 ± 0.003
    3.50: 1.039 ± 0.005
    3.75: 1.042 ± 0.003
    4.00: 1.044 ± 0.000
    4.25: 1.049 ± 0.005
    4.50: 1.052 ± 0.003
    4.75: 1.057 ± 0.003
    5.00: 1.063 ± 0.003
    5.25: 1.066 ± 0.003
    5.50: 1.068 ± 0.003
    5.75: 1.072 ± 0.003

    DISCUSSION

    The results are more easily interpreted when looking at them in a scatter plot:
    Speed.png
    The results appears to be mostly linear, even though some values are either higher or lower than expected. Some lower than expected values might be due to the loss of speed after a Mushroom Boost, which requires a few second to fully recover from at the lowest acceleraion tiers[4], likely meaning that in the first frames of the measurement the top speed is not yet reached. Unfortunately, the lack of a tachometer doesn't allow a perfect evaluation of when top speed is reached, so this uncertainty cannot be ruled out. The intrinsic uncertainty due to the low number of iterations and the reduced range of the durations of the tests (that goes from around 200 frames to around 215 frames) can also be a significant confounding factor.
    Nonetheless, no sign of tiering can be observed.
    The equation for the linear fitting shown above is:

    TLS = 0.9855 + 0.0151 X LSV

    Where TLS is the Top Land Speed, while LSV is the Land Speed Value. It's R² value is 0.9964.

    CONCLUSIONS

    The top land speed without coins as a function of Land Speed value was measured, showing a mostly linear behavior without significant signs of tiering.

    COMPETING INTERESTS

    The author declares no competing interests.

    REFERENCES

    [1]post #14 of MKBoards' user Nefos in the "Coin Count and Performance" thread of the "Mario Kart 8- General Discussion" section of MKBoards (http://www.mkboards.com/forums/threads/coin-count-and-performance.8777/#post-189057)
    [2]"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 (http://www.mkboards.com/forums/thre...d-minimum-speed-possible-without-coins.11162/)
    [3]"An inference on the contribution of coins and land speed value to maximum land speed" thread in the "Mario Kart 8 - General Discussion - Articles" section of MKBoards' forum (http://www.mkboards.com/forums/thre...land-speed-value-to-maximum-land-speed.12619/)
    [4]post #6 in the "A video investigation of the speed loss after various kinds of boosts" thread in the "Mario Kart 8 - General Discussion" section of MKBoards' forum (http://mkboards.com/forums/threads/...er-various-kinds-of-boosts.20164/#post-441774)

    ACKNOWLEDGEMENTS

    The author would like to thank the MKBoards' community for the interests shown for his studies and, regarding this study, in particular the user @Nefos for proposing an appropriate method, the user @Nick. for suggesting a proper formatting of the articles and the user @Shito Ryu for suggesting proper tests.

    CONTACTS

    MKBoards's user @Mister Wu can be contacted for corrections, suggestions or clarifications.
     
    Last edited: Dec 31, 2015
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  2. Mister Wu

    Mister Wu

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    A year ago I joined these forums and started "publishing" an article about top land speed, so now I'm doing the same! Thanks for this year!

    Of course, I also wants to thank @Jake, @flc, @Dragmirejr, @Nicola, @Rookie, @λsuna, @RRD_mindscarp, @aleroh, @Luigi_Fan2, @Sarantis, @Luso, @Domenico, @Sayn, @Harmonia, @Savannah, @Teeples, @Ryan's and all the other people in these forums that I should thank but that I don't remember at the moment because I am a bad person...

    Anyway, regardless that you are in this incomplete list or not, I want to wish you a great new year and a merry Christmas period!

    EDITS: 1 it was tachometer, not odometer... 31/12/2015
     
    Last edited: Dec 31, 2015
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  3. Dragmirejr

    Dragmirejr Always keep an open mind! World Cup Staff

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    I too wish you and everyone else a merry christmas and a happy new year @Mister Wu
     
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  4. Nizer

    Nizer Defiant Hero

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    Thank you for this study. Getting more data may seem boring and uninteresting to some, but I think it's good to have this kind of info around for people who value it highly.

    I know it's a lot of work to compile data like this, so thanks for the efforts you put in.
     
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  5. Mister Wu

    Mister Wu

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    Thanks for appreciating this work, even though it might not be something particularly interesting in that it adds few new information! A merry Christmas and a great 2016 to you too, by the way!
     
  6. Sarantis

    Sarantis

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    Heheh, thanks to you too! I tried my best to find these results I did! I too wish for everyone a Happy New Year! Let's hope 2016 gets EVEN better :D (We always say at the end of each year that the next year will be better, don't we? o_O JUST LOOK AT FRANCE. PARIS GOT ATTACKED BY THOSE PEOPLE WHO ARE EITHER JEALOUS OF US OR HAVE A DIFFERENT RELIGION. THAT WAS A HORRIBLE YEAR FOR THEM.)
     
  7. Luigi_Fan2

    Luigi_Fan2

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    Thanks for this, and happy new year! Even though I don't always comment, I find your articles interesting. :)
     
  8. Mister Wu

    Mister Wu

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    Ok, now a little inference based on the famous MK8 speedometer video:

    I'll consider the gliding sections because when drifting more tightly (moving the stick/pressing the direction towars the turn) there is a loss of speed.
    We can see that while gliding, the speed gets rounded at most to 86 km/h. Now, this is 5.5 Air Speed, but let's consider this simple model, where 1.0 speed with 10 coins has a maximum speed of 80 km/h and each 0.25 speed increment is 0.31 km/h. We would have maximum speed of 85.58 km/h with 5.5 speed (which can get rounded to 86 km/h only when you are very near to max speed) and maximum speed of 85.89 km/h with 5.75 speed. The ratio between 5.75 and 1.0 would then be 1.073625, consistent with these results. So a decent approximation of the max speed with 10 coins is:

    MS = 80 km/h + 0.31 x (pSV -1)

    Where pSV is the speed value in points as reported in the PRIMA guide. If you want it converted in UI units, the formula is:

    MS = 80 km/h + 1.24 x (SV -1)

    Of course, I am not expecting the game to use these exact values, they are just a simple way to bring together my results with the speedometer video.
     

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