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A visual inference on the effect of speed value on Dash Mushroom's boost

Discussion in 'Articles' started by Mister Wu, Jan 4, 2015.

  1. Mister Wu

    Mister Wu

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    A VISUAL INFERENCE ON THE EFFECT OF SPEED VALUE ON DASH MUSHROOM'S BOOST

    Mister Wu[1]


    [1]Passons, Italy


    ABSTRACT
    The influence of speed value on the Dash Mushroom's boost in Mario Kart 8 was evaluated through the use of screenshots, revealing that this influence is indeed present.

    INTRODUCTION

    It is well known that in Mario Kart Wii the maximum speed that can be obtained during a Dash Mushroom's boost is affected by the maximum speed the combination can reach[1]. Therefore a test of whether this is also true in Mario Kart 8 would be recommended. Here such a test is performed empirically through the use of the Wii U built-in screenshot function.

    MATERIALS AND METHODS

    MARIO KART 8 VERSION
    Mario Kart 8 version 3.0 was used.

    CONTROLLER USED
    The Wii U GamePad in normal (with the gyroscope disabled) mode was used.

    COMBINATION TESTED
    The following combinations were tested:

    SPEED VALUE DEPENDENCE:
    1.0 combination: Lemmy + Mr. Scooty + Roller Tires + Bowser Kite
    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
    5.75 combination: Morton + Circuit Special + Slick tires + Bowser Kite

    SAME SPEED COMBINATIONS:
    Kart combination: Iggy + Standard Kart + Standard Tires + Bowser Kite
    Bike combination: Iggy + Standard Bike + Standard Tires + Bowser Kite
    Sports Bike combination: Iggy + Sports Bike + Standard Tires + Bowser Kite
    ATV combination: Iggy + Standard ATV + Standard Tires + Bowser Kite

    METHOD
    Time Trial mode without ghost was used. Mario Kart Stadium was chosen as track. After the beginning of the time trial, the "ZL" button was pushed once in order to use a single mushroom. When the vehicle completely stopped, the "HOME" button was pushed to take a screenshot which was sent through e-mail service. The starting point of the measurement is therefore the starting point of the time trial.

    RESULTS

    DEPENDENCE ON SPEED

    The first evaluation was focused on the dependence on speed value of the mushroom boost. The results are the following:

    1.0 combination:
    MKS_1.jpg

    2.0 combination:

    MKS_2.jpg

    3.0 combination:

    MKS_3.jpg

    4.0 combination:

    MKS_4.jpg

    5.0 combination:

    MKS_5.jpg

    5.75 combination:

    MKS_5_75.jpg

    Since a dependence on the speed value of the Dash Mushroom's boost was apparent, several combination having the same speed value (3.75) were tested. The results were:

    Kart combination:

    MKS_SK.jpg

    Bike combination:

    MKS_SB.jpg

    Sports Bike combination:

    MKS_SPB.jpg

    ATV combination:

    MKS_SATV.jpg

    DISCUSSION

    From the screenshot taken in exam it seems that the speed value affects where the ending point is in this experimental design. Interestingly enough, the use of different combinations suggests that having the same speed value results in the same distance driven. Some differences in the data above can be seen, when watching at the position of the rear wheels, however the use of a different camera angle (see the supplementary materials) indicates that these differences are likely due to the different length of the vehicles and the particular posture the driver is forced to have while driving.
    Since not only speed value, but also coins affect the maximum speed of the combination, a test was devised to reveal whether coins affect the mushroom boost (see the supplementary materials). The results of this test, although less reliable than these data, support this hypothesis.

    CONCLUSION

    The screenshots taken in this study suggest that in Mario kart 8 the Dash Mushroom's boost is indeed affected by the speed value of the combination, and it is likely that this dependence is actually a dependence on maximum speed as determined both by speed value and coins.

    COMPETING INTERESTS

    The author declares no competing interests.


    REFERENCES

    [1]see for example the thread "speeds of the "Big 3" in km/h" by thondam at GameFAQs (http://www.gamefaqs.com/boards/942008-mario-kart-wii/51159501)

    ACKNOWLEDGEMENTS

    The help of MKBoards' users Ade and Dragmirejr in suggesting proper formatting, Ade in suggesting the acquisition of quantitative data, Shito Ryu in obtaining the "mushrooms and coins without sterring in N64 Toad's Turnpike" method and Nefos in inspiring the aforementioned method is acknowledged.

    CONTACTS

    If more information or clarifications are needed, or if suggestions or complaints have to be made about this study, the user Mister Wu of MKBoards may be contacted.
     
    Last edited: Jan 7, 2015
    Horse likes this.
  2. Mister Wu

    Mister Wu

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    THE ASSESSMENT OF COINS' EFFECT ON DASH MUSHROOM’S BOOST

    MATERIALS AND METHODS

    THE “MUSHROOMS AND COINS WITHOUT STEERING IN N64 TOAD’S TURNPIKE” (MCTT) METHOD

    This method is useful to obtain Dash Mushrooms and coins in N64 Toad’s Turnpike without having to steer. Two controllers are needed. It works as follows:

    · Select the multiplayer match race.

    · Use 2 players. The first one can use any combination, while the second one will use the combination to be studied.

    · Don’t use CPU opponents and, if needed, select 150cc as engine class. Tracks must be selectable.

    · Select N64 Toad’s Turnpike as track

    · When the race begins, drive the first player to a location far from the second player.

    · Use the brake and acceleration buttons on the second player controller to reach item boxes in the lane on the right of that player when they pass. The same buttons can be used to avoid or collect coins wandering above the dashed lines.

    · The valid items that can be had from the item boxes are

    o Dash Mushroom

    o Triple Dash Mushrooms

    o Golden Dash Mushroom

    o Crazy Eight

    · If a different item is obtained, it must be discarded and a new item box must be reached. If a Bullet Bill is obtained, the method must be started over.

    MEASUREMENT OF THE EFFECT OF COINS ON DASH MUSHROOM’S BOOST

    The MCTT method was used with the following combinations:

    First player: Larry + Standard Kart + Standard Tires + Super Glider

    Second Player: Lemmy + Mr. Scooty + Roller Tires + Bowser Kite

    150cc engine class was chosen. The controller for the first player was the Wii U GamePad, the controller for the second player was the Classic Controller. The first player was left under the first bridge in the middle of the track, while the second player collected triple dash mushrooms which were used for the assessment. First, the following starting point was reached:
    r_TT_0C_starting_point.jpg
    Then the “L” button was pushed once to use a mushroom and, after the vehicle stopped, a screenshot was taken. 10 coins were collected without steering and the following starting point was reached:
    r_TT_10C_starting_point.jpg
    The “L” button was pushed once to use another mushroom and after the vehicle stopped a second screenshot was taken.

    RESULTS

    The results of the method are presented here:

    Without coins:
    r_TT_0C.jpg
    With 10 coins:
    r_TT_10C.jpg
    Even though there may be a slight difference in the starting positions, the results shown here are likely due to the effect of the coins on maximum speed.

    THE EVALUATION OF COMBINATIONS HAVING THE SAME SPEED

    MATERIALS AND METHODS

    The same method presented in the article was used, but when evaluating combinations having the same speed, after taking each screenshot presented there, the “X” button was used to activate the rear view and another screenshot was taken.

    RESULTS

    The results of this method are the following:

    Kart combination:
    MKS_SK_rear.jpg
    Bike combination:
    MKS_SB_rear.jpg
    Sports Bike combination:
    MKS_SPB_rear.jpg
    ATV combination:
    MKS_SATV_rear.jpg
    Viewed from this camera angle, the only apparent difference is the angle of the camera which is different for bikes. There doesn’t seem to be a difference in the position of the driver and his vehicle.
     
  3. Mister Wu

    Mister Wu

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    As you noticed, this article is less about number and more about empirical observations. I will "publish" a few of these article, which might be interesting to you but are surely useful for me to find new methods (such as the MCTT presented here) and they will be more frequent since less time is needed to prepare them. Just don't expect from me an article per week! Now I am on holidays and I had time to prepare this, but for the next one I will have less time, and some studies require much more time!
     
  4. Dragmirejr

    Dragmirejr Always keep an open mind! World Cup Staff

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    Keep up the good work :)

    I love numbers, so hopefully you'll do more of those in the future. The layout still seems kinda, idk, off. But I think that is because it feels like the pictures areinterupting the text. Maybe you should put pictures in a spoiler, since it may give this a more professional look ^^
     
  5. Mister Wu

    Mister Wu

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    Well, numbers require much more time than these articles, so more articles about numbers will be present (after all coins, acceleration and mini-turbos have to be evaluated!), but they will also be less frequent. Sorry for that...

    I am too wondering whether it is better if pictures stay in spoilers, but could you please specify in what way pictures are not in the correct place? In my pc they seem to be fine, but maybe on other devices they are not. And by the way, is there a way for them to be shown as full images even for users not logged in?
     
    Dragmirejr likes this.
  6. Zinthos

    Zinthos

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    It's better to provide qualitative and quantitative data in your research. The slightest change is still a change, so putting down the exact data is necessary. Other than that, good stuff.
     
  7. Dartanian

    Dartanian rWS Connoisseur WL Staff

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    All this maths is giving me a headache x_x

    Nice findings btw mate! Keep up with the good work. :)
     
  8. Mister Wu

    Mister Wu

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    Challenge accepted! But you will have to wait a little...
     
  9. Mister Wu

    Mister Wu

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    AN ESTIMATION OF DISTANCE DRIVEN DUE TO DASH MUSHROOM BOOST BASED ON QUANTITATIVE DATA

    MATERIALS AND METHODS

    MEASUREMENT OF QUANTITATIVE DATA AND INFERENCE ON THE DISTANCE DRIVEN
    The same method described in the article was used, but instead of taking the screenshot, the number of full squares between the rear wheels of the vehicle and the starting line was counted. The measurement was repeated four times. If a measurement didn't have the right number of squares (even or odd) based on the position of the first square observed, the measurement was discarded and a new measurement was done. Since reliable measurement were obtained only for the first two drivers, the full squares between the rear wheels of the vehicle until the first square not completely under the tunnel on the side of the starting line (which was not counted) were counted and the real number of squares between the rear wheels and the starting line was inferred. To have a more reliable estimation, the length of the starting line and the vehicle must be added. The vehicle is approximately 3 squares long, as can be seen for the 1.0 combination and the 5.75 combination:

    1.0 combination:
    1_vehicle.jpg

    5.75 combination:
    5_75_vehicle.jpg

    (the difference due to different shapes and length of the various vehicles will be added as error on the measures), the metal part of the starting line can be approximated with a single square, while the big squares can be approximated with 4 squares. So a total of 3 + 2 + 12 = 17 squares are added in order to have a slightly more accurate inference on the actual length driven due to the Dash Mushroom's boost. The error is estiimated as follows: 1 square of error is due to not counting the partial square behind the rear wheels,1 square of error is due to the differences in the shape and length of the vehicles, 1 square of error is considered to be due to the approximation of the starting line. Therefore the final error, reported as standard deviation of the measurement, is approximated as:

    √3 = 1.732050808 ≈ 2

    DETERMINATION OF THE LACK OF DEPENDENCE OF THE DISTANCE DRIVEN ON HITBOX CLASS

    COMBINATIONS USED
    The following combinations having a speed value of 4.75 were used:

    Medium hitbox combination: Ludwig + Circuit Special + Slick Tires + Bowser Kite
    Large hitbox combination: Morton + Standard Kart + Standard Tires + Bowser Kite

    METHOD

    The method was the same used for the determination of differences in combinations having the same speed value.

    RESULTS

    MEASUREMENT OF QUANTITATIVE DATA AND INFERENCE ON THE DISTANCE DRIVEN

    The measurement of the distance between the rear wheels and the starting line gave the following results:

    1.0 combination: 159 squares, 159 squares, 159 squares, 159 squares
    2.0 combination: 160 squares, 160 squares, 160 squares, 160 squares
    3.0 combination: 161 squares, 161 squares, 161 squares, 151 squares
    4.0 combination: 163 squares, 165 squares, 165 squares, 163 squares
    5.0 combination: 167 squares, 165 squares, 165 squares, 165 squares
    5.75 combination: 166 squares, 170 squares, 166 squares, 166 squares

    There are inconsistencies in these measurements. The error of the 3.0 combination is typical of italian people and is due to the fact that sixty ("sessanta") and seventy ("settanta") are pronounced in a similar way. On the other hand, the errors on the highest speed value combinations are clear errors in counting and in the case of the 4.0 combination, it is impossible to infer the correct value. Therefore, the distance between the rear wheels of the vehicle and the first square that is not completely in the tunnel was measured. The results are:

    1.0 combination: 52 squares, 52 squares, 52 squares, 52 squares
    2.0 combination: 53 squares, 53 squares, 53 squares, 53 squares
    3.0 combination: 54 squares, 54 squares, 54 squares, 54 squares
    4.0 combination: 56 squares, 56 squares, 56 squares, 56 squares
    5.0 combination: 58 squares, 58 squares, 58 squares, 58 squares
    5.75 combination: 59 squares, 59 squares, 59 squares, 59 squares

    The results are now completely consistent, if we assume that the first two combinations were measured correctly, we would obtain this results for the distance between the rear wheels and the starting line:

    1.0 combination: 159 sqaures
    2.0 combiantion. 160 squares
    3.0 combination: 161 squares
    4.0 combination: 163 squares
    5.0 combination: 165 squares
    5.75 combination: 166 squares

    Since each of these values was counted more than once in the first count, these distances were considered correct.
    There seems to be a greater increase in distance when the hitbox class is changed. To test this hypothesis, two combinations having the same speed value but different hitbox classes (i.e.: medium and large) were observed. the results were:

    Medium hitbox combination:
    MKS_medium_hitbox_rear.jpg

    Large hitbox combination:
    MKS_large_hitbox_rear.jpg

    This hypothesis can clearly be discarded.
    The reconstructed distance between the starting point and the ending point of the measurement are:

    1.0 combination: 176 squares ± 2
    2.0 combination: 177 squares ± 2
    3.0 combination: 178 squares ± 2
    4.0 combination: 180 squares ± 2
    5.0 combination: 182 squares ± 2
    5.75 combination: 183 squares ± 2

    The increase in distance driven is therefore:

    1.0 combination: 0 %
    2.0 combination: 0.57 % ± 1.40
    3.0 combination: 1.14 % ± 1.40
    4.0 combination: 2.27 % ± 1.41
    5.0 combination: 3.41 % ± 1.42
    5.75 combination: 3.98 % ± 1.42

    This quantitative model is not precise enough to correctly represent most of the visual inferences that were made, which are on the other hand perfectly reproducible, the data can still be fitted to find a very approximate description of the increase of distance driven after the use of a Dash Mushroom:

    Increase_in_distance.png


    Despite the apparently high R^2 value, this equation has to be taken with a grain of salt.
     
  10. Mister Wu

    Mister Wu

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    So yeah, not very good results... and man, I can't really count!
     
  11. Mister Wu

    Mister Wu

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    To be clear, I measured a difference by counting, and the errors while counting are always in defect, because I was not counting part of squares and the fact that the vehicles was longer in the case of the biggest ones (Roy on Mach 8, Morton on Circuit Special) and the rear wheels started behind the rear wheels of the small combinations, on the other hand the error on the estimation of the starting line could be either way, and what is interesting is also the difference between two measurements, so in the end I preferred putting the error in both directions, this way the statistical evaluation is also easier. Anyway independent checks done from other people are always welcome!
     
    Last edited: Jan 6, 2015
  12. Mister Wu

    Mister Wu

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    Wait! Maybe I found a slightly more precise method to measure this difference and also the length of the starting line, I will try it this evening!
     
  13. Luso

    Luso mk8 is the superior game

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    holy shit
     
  14. Mister Wu

    Mister Wu

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    A MORE PRECISE MEASUREMENT OF THE DISTANCE DRIVEN

    MATERIALS AND METHODS

    MEASUREMENT OF THE DISTANCE DRIVEN

    The method is the same used before to count full squares until the beginning of the tunnel, but the starting point this time was the starting line reached only using the "A" and "B" buttons of the GamePad. Furthermore, if the determination of whether a square was or not covered by wheels was impossible due to smoke coming from the vehicle or other factors, the measure was discarded. This happened in the third measurement of the 5.75 combination. For reference, the starting point of the first measurement for the 1.0 combination is shown here:

    MKS_Lemmy_1.jpg

    Screenshots of the starting point for all the other measurements have been acquired and are available on request. The error of this method is due to two factor: the error due to the measurement of full squares, which is 1 square, and the error in the starting point, which has been estimated to be half a square. Therefore the final error on the measurement is:

    √(1²+0.5²) = √(1+0.25) = √1.25 ≈ 1.118033989 ≈ 1

    Since with the previous method the first two estimates of the length between the rear wheels and the starting line were consistent, they were used to infer the distance between the beginning of the tunnel and the starting line, which is:

    159 squares - 52 squares = 160 squares - 53 squares = 107 squares

    This distance was added to the measured distance to infer the total distance driven.

    VISUAL EVALUATION OF THE LINEARITY OF THE DISTANCE FUNCTION

    The method is the same used before, but instead of counting the squares, after the vehicle stopped a screenshot was taken. In the case of the 2.0 combination, this method was applied on the second measure of the aforementioned mehod. The starting point of the three experiments were:

    1.0 combination:
    MKS_Lemmy_check.jpg

    2.0 combination:
    MKS_Wendy_2.jpg

    3.0 combination:
    MKS_Larry_check.jpg

    RESULTS

    The measured distances between the rear wheels and the first square that is not completely in the tunnel are:

    1.0 combination: 65 squares, 65 squares, 65 squares, 65 squares
    2.0 combination: 66 squares, 66 squares, 66 squares, 66 squares
    3.0 combination: 66 squares, 66 squares, 66 squares, 66 squares
    4.0 combination: 69 squares, 69 squares, 69 squares, 69 squares
    5.0 combination: 71 squares, 71 squares, 71 squares, 71 squares
    5.75 combination: 73 squares, 73 squares, 73 squares, 73 squares

    These mesurements are all consistent, therefore the inferred distance between the rear wheels and the starting line is:

    1.0 combination: 172 squares ± 1
    2.0 combination: 173 squares ± 1
    3.0 combination: 173 squares ± 1
    4.0 combination: 176 squares ± 1
    5.0 combination: 178 squares ± 1
    5.75 combination: 180 squares ± 1

    Here, the results in the case of the 3.0 combination are surprising, in that the distance between its ending point and the ending point of the 2.0 combination is less than a square. To further investigate this aspect, screenshot of the ending point of the 1.0 combination, the 2.0 combination and the 3.0 combination were taken and are shown here:

    1.0 combination:
    MKS_Lemmy_check_end.jpg

    2.0 combination:
    MKS_Wendy_2_end.jpg

    3.0 combination:
    MKS_Larry_check_end.jpg
    It is clear that the distance between the ending points of the 3.0 combination and the 2.0 combination is less than the distance between the ending points of the 2.0 combiantion and the 1.0 combination. It is unlikely that this difference can be completely attributed to the slight differences in the starting points. Furthermore, after the 3.0 combination the distance between the ending points of consecutive combinations tends to be at least 1 square, suggesting that the distance function is not linear with respect to speed value.

    The inferred percent increase in distance driven with respect to the 1.0 combination is:

    1.0 combination: 0 %
    2.0 combination: 0.58 % ± 0.92
    3.0 combination: 0.58 % ± 0.92
    4.0 combination: 2.33 % ± 0.93
    5.0 combination: 3.49 % ± 0.94
    5.75 combination: 4.65 % ± 0.94

    The results were plotted but, due to the distance function which is probably not linear with respect to speed value, were not fitted with a linear model.

    distance_more_precise.png
    Again, the distance between the ending point of the 1.0 combiantion and the ending points of the 2.0 and 3.0 combination could not be reliably measured.
     
  15. Mister Wu

    Mister Wu

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    So much for a linear function of distance with respect to speed value... and man that took much more time than I expected!
     
  16. Mister Wu

    Mister Wu

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    Revised the formatting of the article, corrected the "affiliations" and added the users who helped improving the article.
     

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