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An inference on the contribution of coins and land speed value to maximum land speed

Discussion in 'Articles' started by Mister Wu, Feb 16, 2015.

  1. Mister Wu

    Mister Wu

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    AN INFERENCE ON THE CONTRIBUTION OF COINS AND LAND SPEED VALUE TO MAXIMUM LAND SPEED

    Mister Wu[1]

    [1]Passons, Italy

    ABSTRACT

    To better understand the effect of land speed value and coins on maximum land speed in Mario Kart 8, a method was devised and used to test the assumptions published previously by MKBoards' user Nefos[1]. The data collected support both these assumptions.

    INTRODUCTION


    It is known from official sources that maximum land speed is influenced both by land speed value and coins[2]. First experiments about the exact contribution of both to maximum land speed were done by the MKBoards' user Nefos, resulting in two interesting hypotheses:
    1. coins contribute to maximum speed independently from land speed value
    2. the contribution of each coin is likely to be equal to the contribution of a 0.5 increment in land speed value
    A new method is presented here to systematically evaluate the contribution of both coins and land speed value to maximum land speed. This method is then applied to test both final hypotheses.

    MATERIALS AND METHOD

    EVALUATION OF THE CONTRIBUTION OF COINS AND LAND SPEED VALUE

    A modified version of the "mushrooms in Toad's Turnpike" method was used. A two-player 150cc match race was begun without CPU opponents and using only mushrooms as items. N64 Toad's turnpike was chosen as track. To maximize the chance of getting a mushroom, the first player reached after the beginning a point which was distant enough from the point of measurement (in this case in the second emergency area with coins), after this happened the second player used the acceleration and brake button to reach item boxes as they passsed on the right lane and obtain dash mushrooms and to collect or avoid coins. When the right number of coins was obtained, the ending part of the first non-straight white segment behind the starting line was reached using the acceleration and brake buttons:
    coins_mushroom_point.jpg The Item button was pushed to use a mushroom (if a golden dash mushroom was obtained, it was used only once) and the acceleration button was pressed and kept pressed immediately after to maintain maximum speed after the effect of the mushroom until the ending point of the measurement was passed. If needed and possible, after the run coins were collected using only the acceleration and brake buttons and a new run was performed in the same way. When it was longer possible to perform new runs, the race was finished normally and its highlights were watched through Mario Kart Television. The highlights settings were changed to watch the second player for the entire race. Each run was observed in slow-motion by holding the "B" button on the GamePad. The starting point of the measurement was the starting line:
    coins_starting_point.jpg
    Slow motion was started before this point and kept until after the ending point was passed. When the starting point was passed, the stopwatch was started. The ending point of the measurement, where the stopwatch was stopped, is the end of the first white segment met after the change in camera angle:
    coins_ending_point.jpg
    After a measurement with the stopwatch was performed, the highlights were rewinded until the start of the run and another measurement was repeated. For each run 4 measurements were performed.

    MARIO KART 8 VERSION

    Mario Kart 8 version 3.0 was used.

    CONTROLLERS USED

    The first player used a Wii U GamePad, the second player used a Classic Controller.

    COMBINATIONS USED

    The following combination were used

    First player: Iggy + Pipe Frame + Standard Tires + Bowser Kite
    1.0 Speed: Lemmy + Mr. Scooty + Roller tires + Bowser kite
    2.0 Speed: Wendy + Biddybuggy + Standard Tires + Bowser Kite
    3.0 Speed: Larry + Sport Bike + Slim Tires + Bowser Kite
    4.0 Speed: Ludwig + Standard Bike + Slim Tires + Bowser Kite
    5.0 Speed: Roy + Mach 8 + Slim Tires + Bowser Kite
    5.75 Speed: Morton + Circuit Special + Slick Tires + Bowser Kite

    STOPWATCH USED

    The iOS 7 clock application in stopwatch mode was used.

    RESULTS

    RAW DATA

    1.0 SPEED
    0 coins: 33.96 s, 33.96 s, 33.83 s, 33.88 s
    2 coins: 33.19 s, 33.25 s, 33.29 s, 33.24 s
    4 coins: 33.08 s, 33.19 s, 32.95 s, 33.05 s
    6 coins: 32.49 s, 32.61 s, 32.59 s, 32.58 s
    8 coins: 32.18 s, 32.15 s, 32.14 s, 32.18 s
    10 coins: 31.47 s, 31.44 s, 31.50 s, 31.62 s

    2.0 SPEED
    0 coins: 33.34 s, 33.09 s, 33.31 s, 33.14 s
    2 coins: 32.50 s, 32.68 s, 32.64 s, 32.52 s
    4 coins: 32.37 s, 32.50 s, 32.44 s, 32.39 s
    6 coins: 32.08 s, 31.99 s, 32.02 s, 31.97 s
    8 coins: 31.67 s, 31.85 s, 31.60 s, 31.59 s
    10 coins: 31.07 s, 31.08 s, 30.95 s, 31.09 s

    3.0 SPEED
    0 coins: 32.92 s, 32.81 s, 32.70 s, 32.80 s
    2 coins: 32.20 s, 32.55 s, 32.29 s, 32.06 s
    4 coins: 32.20 s, 31.98 s, 32.12 s, 32.15 s
    6 coins: 31.75 s, 31.81 s, 31.57 s, 31.82 s
    8 coins: 31.20 s, 31.54 s, 31.36 s, 31.41 s
    10 coins: 30.92 s, 30.84 s, 30.86 s, 30.96 s

    4.0 SPEED
    0 coins: 32.35 s, 32.39 s, 32.34 s, 32.29 s
    2 coins: 31.91 s, 31.92 s, 31.97 s, 31.92 s
    4 coins: 31.47 s, 31.43 s, 31.41 s, 31.44 s
    6 coins: 30.95 s, 31.10 s, 31.08 s, 30.83 s
    8 coins: 30.85 s, 30.90 s, 30.88 s, 30.77 s
    10 coins: 30.48 s, 30.63 s, 30.45 s, 30.49 s

    5.0 SPEED
    0 coins: 31.94 s, 32.04 s, 31.90 s, 31.94 s
    2 coins: 31.51 s, 31.48 s, 31.44 s, 31.47 s
    4 coins: 30.85 s, 30.88 s, 30.94 s, 30.92 s
    6 coins: 30.58 s, 30.75 s, 30.54 s, 30.67 s
    8 coins: 30.33 s, 30.46 s, 30.40 s, 30.48 s
    10 coins: 29.77 s, 29.84 s, 29.86 s, 29.83 s

    5.75 SPEED
    0 coins: 31.66 s, 31.58 s, 31.72 s, 31.59 s
    2 coins: 31.24 s, 31.47 s, 31.22 s, 31.25 s
    4 coins: 30.79 s, 30.92 s, 30.78 s, 30.80 s
    6 coins: 30.58 s, 30.63 s, 30.56 s, 30.53 s
    8 coins: 29.86 s, 29.92 s, 29.96 s, 29.84 s
    10 coins: 29.80 s, 29.84 s, 29.79 s, 29.72 s

    MEAN ± STANDARD DEVIATION

    1.0 SPEED
    0 coins: 33.91 s ± 0.06
    2 coins: 33.24 s ± 0.04
    4 coins: 33.07 s ± 0.10
    6 coins: 32.57 s ± 0.05
    8 coins: 32.16 s ± 0.02
    10 coins: 31.51 s ± 0.08

    2.0 SPEED
    0 coins: 33.22 s ± 0.12
    2 coins: 32.59 s ± 0.09
    4 coins: 32.43 s ± 0.06
    6 coins: 32.02 s ± 0.05
    8 coins:31.68 s ± 0.12
    10 coins: 31.05 s ± 0.07

    3.0 SPEED
    0 coins: 32.81 s ± 0.09
    2 coins: 32.28 s ± 0.21
    4 coins: 32.11 s ± 0.09
    6 coins: 31.74 s ± 0.12
    8 coins: 31.38 s ± 0.14
    10 coins: 30.90 s ± 0.06

    4.0 SPEED
    0 coins: 32.34 s ± 0.04
    2 coins: 31.93 s ± 0.03
    4 coins: 31.44 s ± 0.02
    6 coins: 30.99 s ± 0.13
    8 coins: 30.85 s ± 0.06
    10 coins: 30.51 s ± 0.08

    5.0 SPEED
    0 coins: 31.96 s ± 0.06
    2 coins: 31.48 s ± 0.03
    4 coins: 30.90 s ± 0.04
    6 coins: 30.64 s ± 0.09
    8 coins: 30.42 s ± 0.07
    10 coins: 29.83 s ± 0.04

    5.75 SPEED
    0 coins: 31.64 s ± 0.07
    2 coins: 31.30 s ± 0.12
    4 coins: 30.82 s ± 0.07
    6 coins: 30.58 s ± 0.04
    8 coins: 29.90 s ± 0.06
    10 coins: 29.79 s ± 0.05

    PERCENT INCREASE IN MAXIMUM LAND SPEED RELATIVE TO THE CASE WITHOUT COINS

    1.0 SPEED
    0 coins: 0 %
    2 coins: 2.0 % ± 0.3
    4 coins: 2.5 % ± 0.2
    6 coins: 4.1 % ± 0.3
    8 coins: 5.4 % ± 0.2
    10 coins: 7.6 % ± 0.4

    2.0 SPEED
    0 coins: 0 %
    2 coins: 1.9 % ± 0.5
    4 coins: 2.5 % ± 0.5
    6 coins: 3.8 % ± 0.3
    8 coins: 4.9 % ± 0.7
    10 coins: 7.0 % ± 0.6

    3.0 SPEED
    0 coins: 0 %
    2 coins: 1.6 % ± 0.7
    4 coins: 2.2 % ± 0.3
    6 coins: 3.4 % ± 0.3
    8 coins: 4.6 % ± 0.7
    10 coins: 6.2 % ± 0.3

    4.0 SPEED
    0 coins: 0 %
    2 coins: 1.3 % ± 0.2
    4 coins: 2.9 % ± 0.2
    6 coins: 4.4 % ± 0.3
    8 coins: 4.8 % ± 0.1
    10 coins: 6.0 % ± 0.2

    5.0 SPEED
    0 coins: 0 %
    2 coins: 1.5 % ± 0.2
    4 coins: 3.4 % ± 0.3
    6 coins: 4.3 % ± 0.2
    8 coins: 5.1 % ± 0.2
    10 coins: 7.1 % ± 0.2

    5.75 SPEED
    0 coins: 0 %
    2 coins: 1.1 % ± 0.5
    4 coins: 2.6 % ± 0.4
    6 coins: 3.5 % ± 0.3
    8 coins: 5.8 % ± 0.2
    10 coins: 6.2 % ± 0.3

    PERCENT INCREASE IN MAXIMUM LAND SPEED RELATIVE TO THE 1.0 SPEED COMBINATION WITHOUT COINS

    1.0 SPEED
    0 coins: 0 %
    2 coins: 2.0 % ± 0.3
    4 coins: 2.5 % ± 0.2
    6 coins: 4.1 % ± 0.3
    8 coins: 5.4 % ± 0.2
    10 coins: 7.6 % ± 0.4

    2.0 SPEED
    0 coins: 2.1 % ± 0.5
    2 coins: 4.1 % ± 0.4
    4 coins: 4.6 % ± 0.3
    6 coins: 5.9 % ± 0.2
    8 coins: 7.0 % ± 0.3
    10 coins: 9.2 % ± 0.2

    3.0 SPEED
    0 coins: 3.4 % ± 0.2
    2 coins: 5.1 % ± 0.6
    4 coins: 5.6 % ± 0.4
    6 coins: 6.8 % ± 0.3
    8 coins: 8.1 % ± 0.5
    10 coins: 9.8 % ± 0.3

    4.0 SPEED
    0 coins: 4.8 % ± 0.2
    2 coins: 6.2 % ± 0.3
    4 coins: 7.9 % ± 0.2
    6 coins: 9.4 % ± 0.5
    8 coins: 9.9 % ± 0.3
    10 coins: 11.1 % ± 0.2

    5.0 SPEED
    0 coins: 6.1 % ± 0.1
    2 coins: 7.7 % ± 0.1
    4 coins: 9.7 % ± 0.3
    6 coins: 10.7 % ± 0.3
    8 coins: 11.5 % ± 0.4
    10 coins: 13.7 % ± 0.3

    5.75 SPEED
    0 coins: 7.2 % ± 0.4
    2 coins: 8.3 % ± 0.3
    4 coins: 10.0 % ± 0.2
    6 coins: 10.9 % ± 0.2
    8 coins: 13.4 % ± 0.4
    10 coins: 13.8 % ± 0.2

    DISCUSSION

    The more interesting results, which are those regarding the increase in maximum land speed relative to the 1.0 speed combination without coins, can more clearly be visualized by doing a scatter plot:
    Mk8coins.png
    Linear regressions were performed for each combination used and the results are reported in the plot using the appropriate color coding. Although the R² of the regressions are relatively high, some nonlinear phenomena can be observed. It is however likely that these are due to the measurement system which is not accurate nor precise enough since it's heavily dependent on the operator. In this case, a frame by frame analysis of recorded MKTV footage in slow motion is likely needed to collect meaningful quantitative data and to verify the existence of nonlinear phenomena. However, the data collected in this study can still be used to test the hypotheses made by Nefos. For this reason, a least-squares regression of these data was performed. The model used was:

    %MSI = a + b x SV + c x C

    where %MSI is the percent increase in maximum land speed, SV is the land speed value and C is the number of collected coins.

    The result of the regression were the following values:

    a = -1.112512111 ± 0.199114881
    b = 1.485508541 ± 0.043977918
    c = 0.67092955 ± 0.021223021

    Although the errors in the measurements lead to values for a and b which are not equal in term of absolute value, the r² of this model is still 0.984816332, therefore if there is a dependence between the contribution of the coins and the contribution of land speed value, this is likely to be very small. For this reason, the first assumption of user Nefos is supported by these data. The second assumption can be tested by comparing what maximum land speed would be had for an hypothetical 6.0 land speed value combination and a 1.0 land speed value combination with 10 coins.
    In the first case the relative maximum land speed would be:

    %MSI = -1.112512111 + 6 x 1.485508541 ≈ 7.800539136 % ± 0.330564364

    In the second case the relative maximum land speed would be:

    % MSI = -1.112512111 + 1 x 1.485508541 + 10 x 0.67092955 ≈ 7.082291928 % ± 0.291012711

    In the simplified assumption that both values follow a normal distribution, they are not significantly different (p-value = 0.102919992). Therefore, these data also support Nefos' second hypothesis.

    CONCLUSIONS

    While the method proved to be viable, the measurement device used led to significant measurements errors. Despite this, these data give even stronger support to the two hypotheses made by MKBoards' user Nefos, which lead to the following model in which maximum land speed depends on the actual land speed value that follows the following formula:

    ALSV = LSV + 0.5 x C

    where ALSV is the actual land speed value, LSV is the land speed value of the combination and C is the number of coins held at the moment. Current data suggest that this formula leads to a good approximation of the actual maximum land speed calculated in-game.

    COMPETING INTERESTS

    The author declares no competing interests.

    ACKNOWLEDGEMENTS

    The author acknowledges the aid of MKBoards' user Nefos in suggesting the track to be used for the method and in the creation of a method to determine the contribution of land speed value and coins to maximum land speed on which this method was based. The aid of user Ade in suggesting a proper formatting and of user Shito Ryu in suggesting the use of linear regressions is furthermore acknowledged.

    CONTACTS

    If more information is needed or complaints, comments or suggestion have to be made, MKBoards' user Mister Wu may be contacted.

    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] Mario Kart 8 UK manual. It must be noted that in the manual it is only written that coins increase speed. The contribution of land speed value is not mentioned but the name is self-explanatory.
     
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  2. Don D

    Don D

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    Great article! Thx for posting.
     
  3. Jayden

    Jayden Guest

    damn you sure are on point, keep these great articles going man.
     
  4. Mister Wu

    Mister Wu

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    Corrected the title of the thread.

    @Don D and @Jayden: Thanks for your comments!
     
    Last edited: Feb 22, 2015
  5. Rookie

    Rookie

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    You've done it again, Mister Wu.

    If you haven't studied the item system I think you should try doing that to give the community a better understanding on how distance based items work.
     
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  6. Mister Wu

    Mister Wu

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    Well, it's one of the experiments I am planning to do, both from the frontrunner point of view and from the 2nd place point of view! I would like to have the results of the experiments before version 4.0 (because it's likely Nintendo will make some undocumented changes as this is apparently what happened with version 3.0). But first I'm going to post results about another experiment which you will see next week or the week after that if all goes well!
     
  7. Rookie

    Rookie

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    That brings up another potential one to do, doing a significance test to try to see if they make any changes after a new update since some people feel they have a little.
     
  8. Don D

    Don D

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    Is there a way to test for the hidden stats of blue falcon? afaik they are still unknown. since the bf is becoming more and more the "standart" online (next to pf), it would be very useful information to settle the discussion bf VS pf in online races.
     
  9. Mister Wu

    Mister Wu

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    Ok, what can be tested is:
    • water and antigravity speed through "keep only the acceleration button pressed and start by blowing the engine" method in 2 player match race with the 2 players having the same acceleration tier (in Dolphin Shoals and Mute City, respectively, though the second will be difficult because there is not much straight part at the beginning if I remember correctly, I also might try air speed in Electrodome)
    • Mini-Turbo (this is what I'm trying to evaluate, although I don't know if I'll manage to estimate it correctly for reasons you will see)
    • water and antigravity handling by measuring the time needed to start skidding while steering with a D-Pad
    Unfortunately I cannot think of any experiment involving air handling which is really reproducible.
     
  10. Exodaire

    Exodaire Virtual Insanity

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  11. Crazykonga

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    Maaan you're crazy :eek:


    Thank you tho
     
  12. Luigi_Fan2

    Luigi_Fan2

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    I've tested for the hidden speed stats with time trial ghosts, and here are the results I got:

    Blue Falcon: +0.25 antigravity speed, +0.25 air speed, 0 water speed
    Tanooki Buggy: -0.25 antigravity speed, +0.25 air speed, +0.5 water speed
    Master Cycle: -0.25 antigravity speed, +0.5 air speed, +0.5 water speed (Unsure about this water speed. Master Cycle + Standard seemed a bit too quick when I tested.)

    I used this chart for comparisons.

    Note: As far as I can tell, Tanooki Mario, Cat Peach, and the B-Dasher have the same antigravity and air speeds as their non-DLC counterparts. I'm assuming that the other hidden stats are also the same.

    My tests:
    Antigravity Speed: Do a time trial with a ghost on N64 Rainbow Road, get a perfect start boost, and hold A until the glider pad. Compare your speed with the ghost's, keeping land speed the same between tests.

    Gliding Speed: Same test as antigravity speed, but make sure that land speed and antigravity speed are equal. Hold A until you hit the wall at the first turn and compare during the gliding section.

    Water Speed: Go to Dolphin Shoals and go backwards without turning at the start. Keep moving and stop at the edge of the water, using the increased above water friction. Use a mushroom when the timer reaches 20.000 seconds and start holding A. If you're in a similar position with the ghost when the boost ends, compare speeds.


    Definitely would be nice to know the other stats and have others test for better reliability though. :) (It's really sad how so many people just accept the information given. It's honestly really easy to get something slightly off by mistake.) Here are the results for another person's tests. He agreed with me on the Blue Falcon's air speed partway through the thread, but my result for the Master Cycle water speed was different when I tested later.

    Edit: Also, flc seems to have a source with some different results, although I don't know what it is. (Could be his testing, but I don't know.) See post #15 here.
     
  13. Mister Wu

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    It's great that you already did the experiments! May I suggest some other tests to be sure?

    Antigravity speed: the same test you did, but hold the acceleration button to blow up the engine and start at the very same time in both cases, using combinations with the same acceleration tier. The absolute acceleration depends on speed value, so even little speed differences can be seen and you can use the screenshot method I used for the acceleration tiers (it's better to take a screenshot before the beginning so you can compare the both, since there won't be a perfect superposition this time). You can also try Mute city, but your method is likely to be better because the straight section is longer.

    Air Speed: same as above, you can also try the Electrodrome which begins with a glider section.

    Water speed: same as above.

    Of course if you don't have the time or you have something better to do, I can do these experiments by myself, after I will finish the others.
    Thank you again for the tests!
     
  14. Luigi_Fan2

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    The differences are big enough to be seen as the vehicle is moving. :) For the air speed tests, Electrodrome could be used, but the glider section is a lot shorter. You will hit the second floating boost ring with some vehicles in the N64 Rainbow Road gliding section, but it's not really a problem when you just want to see which of two vehicles is faster. (The difference can be seen before you hit the ring, and being able to hit the ring requires a certain speed, so it can help to make the faster vehicle more obvious.) Should note that I did compare combos in the same acceleration tier for the water speed tests. Forgot to mention that!

    (I'm mainly interested in the vehicle stats instead of how big the speed difference is, so I don't really need screenshots. Feel free to check that if you want. I'm done testing for now, but I'll go back and compare specific combos if something doesn't match up. Good luck with your tests!)
     

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