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A look at the item system

Discussion in 'Articles' started by Mister Wu, Apr 18, 2015.

  1. Mister Wu

    Mister Wu

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    Although the official PRIMA Mario Kart 8 guide states that Mario Kart 8's item system is position-based[1], many players soon found that the item system is distance-based[2]. Here an investigation of such peculiarity is presented.

    MARIO KART 8 VERSION
    These distributions of frequency were obtained with Mario Kart 8 version 3.0

    METHOD
    A 2-player versus Race was started. The following combinations and controllers were used:

    1st player: Wii U GamePad with classic (non-motion based) controls; Ludwig + Pipe Frame + Blue Standard Tires + Bowser Kite
    2nd player: Wii Remote with classic controls; Iggy + Pipe Frame + Cyber Slick Tires + Bowser Kite

    150cc mode was selected and no CPU players were used. The item distribution tested is the standard (All Items) one.
    Mario Kart Stadium was used as track. After collecting 10 coins with both player, the 2nd player was moved in the position indicated in the description of each case while the 1st player obtained items from the first row of item met after the starting line, except for the frontrunning cases which will be described in the appendix. If the time ran out or if a player accidentaly losed coins or an item which inevitably lead to losing coin was picked (e.g. Spiny Shell or Lightning) the race was restarted and the procedure mentioned before was repeated. 500 items were collected for each tested case.

    THE CASES AND THE OBSERVED DISTRIBUTIONS

    CASE 1
    This distribution of frequency is similar to the frontrunning distributions. it is obtained when the 2nd player is on the first border between the dark and strip and the bright strip after the first row of item boxes:
    1_map.jpg
    The observed distribution is the following:

    Coins: 215/500 = 43%
    Green Shells: 112/500 = 22.4%
    Bananas: 134/500 = 26.8%
    Red Shells: 13/500 = 2.6%
    Super Horns: 26/500 = 5.2%

    CASE 2
    This case has the 2nd player at the border before the beginning of the three sectioned-turn:
    2.jpg
    The observed distribution is the following:

    Coins: 47/500 = 9.4%
    Green Shells: 56/500 = 11.2%
    Bananas: 42/500 = 8.4%
    Red Shells: 104/500 = 20.8%
    Super Horns: 24/500 = 4.8%
    Triple Green Shells: 21/500 = 4.2%
    Triple Red Shells: 24/500 = 4.8%
    Triple Bananas: 24/500 = 4.8%
    Bob-ombs: 26/500 = 5.2%
    Fire Flowers: 28/500 = 5.6%
    Boomerang Flowers: 14/500 = 2.8%
    Piranha Plants: 27/500 = 5.4%
    Dash Mushrooms: 46/500 = 9.2%
    Triple Dash Mushrooms: 17/ 500 = 3.4%

    CASE 2B
    In this case the 2nd player is near the lamp before the one at the center of the three sectioned turn, with the back wheels near the screws:
    2B.jpg
    The observed distribution is the following:

    Coins: 11/500 = 2.2%
    Green Shells: 42/500 = 8.4%
    Bananas: 9/500 = 1.8%
    Red Shells: 84/500 = 16.8%
    Super Horns: 13/500 = 2.6%
    Triple Green Shells: 31/500 = 6.2%
    Triple Red Shells: 28/500 = 5.6%
    Triple Bananas. 24/500 = 4.8%
    Bob-ombs: 25/500 = 5%
    Fire Flowers: 22/500 = 4.4%
    Boomerang Flowers: 24/500 = 4.8%
    Piranha Plants: 30/500 = 6%
    Dash Mushrooms: 76/500 = 15.2%
    Triple Dash Mushrooms: 66/500 = 13.2%
    Crazy Eights: 15/500 = 3%

    CASE 3
    In this case the 2nd player is near the lamp at the center of the three sectioned turn, with the back wheels near the screws:
    3.jpg
    The observed distribution is the following:

    Coins: 2/500 = 0.4%
    Green Shells: 33/500 = 6.6%
    Bananas: 2/500 = 0.4%
    Super Horns: 1/500 = 0.2%
    Red Shells: 40/500 = 8%
    Triple Green Shells: 28/500 = 5.6%
    Triple Red Shells. 25/500 = 5%
    Triple Bananas: 1/500 = 0.2%
    Bob-ombs: 4/500 = 0.8%
    Fire Flowers: 11/500 = 2.2%
    Boomerang Flowers: 17/500 = 3.4%
    Piranha Plants: 1/500 = 0.2%
    Dash Mushrooms: 127/500 = 25.4%
    Triple Dash Mushrooms: 161/500 = 32.2%
    Super Stars: 23/500 = 4.6%
    Spiny Shells: 6/500 = 1.2%
    Crazy Eights: 7/500 = 1.4%
    Bloopers: 11/500 = 2.2%

    CASE 4
    In this case the 2nd player is at the left of the lamp after the lamp of the previous case, with the back wheels near the screws:
    4.jpg
    The observed distribution is the following:

    Green Shells: 34/500 = 6.8%
    Red Shells: 48/500 = 9.6%
    Triple Green Shells: 25/500 = 5%
    Triple Red Shells: 24/500 = 4.8%
    Fire Flowers: 11/500 = 2.2%
    Boomerang Flowers: 16/500 = 3.2%
    Dash Mushrooms: 114/500 = 22.8%
    Triple Dash Mushrooms: 182/500 = 36.4%
    Super Stars: 19/500 = 3.8%
    Spiny Shells: 6/500 = 1.2%
    Crazy Eights: 8/500 = 1.6%
    Bloopers: 13/500 = 2.6%

    CASE 5
    In this case the 2nd player is at the border at the end of the three-sectioned turn:
    5.jpg
    The observed distribution is the following:
    Dash Mushrooms: 62/500 = 12.4%
    Triple Dash Mushrooms: 209/500 = 41.8%
    Golden Dash Mushrooms: 68/500 = 13.6%
    Super Stars: 77/500 = 15.4%
    Bullet Bills: 40/500 = 8%
    Spiny Shells: 11/500 = 2.2%
    Lightnings: 3/500 = 0.6%
    Crazy Eights: 11/500 = 2.2%
    Bloopers: 19/500 = 3.8%

    CASE 6
    In this case the 2nd player is at the left of a lamp immediately after the 2nd row of items:
    6.jpg
    The observed distribution is the following:

    Dash Mushrooms: 26/500 = 5.2%
    Triple Dash Mushrooms: 162/500 = 32.4%
    Golden Dash Mushrooms: 96/500 = 19.2%
    Super Stars: 102/500 = 20.4%
    Bullet Bills: 82/500 = 16.4%
    Spiny Shells: 8/500 = 1.6%
    Lightnings: 13/500 = 2.6%
    Crazy Eights: 11/500 = 2.2%

    CASE 7
    in this case the 2nd player is in a position slightly behind the position of case 1, since now the front wheels rather than the rear part of the kart are over the border, but he has lapped the 1st:
    7.jpg
    The observed distribution is the following:

    Triple Dash Mushrooms: 44/500 = 8.8%
    Golden Dash Mushrooms: 152/500 = 30.4%
    Super Stars: 61/500 = 12.2%
    Bullet Bills: 224/500 = 44.8%
    Lightnings: 19/500 = 3.8%

    CONCLUSIONS
    A partial evaluation of the distance-dependence of the item system was performed, revealing that this distance-dependence is indeed present.

    REFERENCES
    [1]Official PRIMA Mario Kart 8 guide, section How to Drive/Items
    [2]See for example, the "The way the new item distribution in Mario Kart 8 works" on IGN.com forums, section Boards>Gaming>Nintendo>Nintendo Wii & Wii U Lobby (http://www.ign.com/boards/threads/the-way-the-new-item-distribution-in-mario-kart-8-works.454019197/), the "Items are based on DISTANCE not POSITION" thread on GameFaqs forums, section Wii U>Racing>Arcade>Automobile (http://www.gamefaqs.com/boards/700050-mario-kart-8/69442052), the "Mario Kart 8 item distribution balance" thread on GameSpot forums, section GameSpot>forums>Nintendo Discussion (http://www.gamespot.com/forums/nintendo-discussion-1000001/mario-kart-8-item-distribution-balance-31532845/), the "Why I don't mind Mario Kart 8's item balance " thread on MARIOKARTWII.COM forums, section Forums>Modern Mario Karts>MK8 General (http://www.mariokartwii.com/threads/139350-Why-I-don-t-mind-Mario-Kart-8-s-item-balance).

    SUPPLEMENTARY INFORMATION

    VERSION 4.1 ITEM DISTRIBUTIONS

    150cc

    CASE 1
    The observed distribution is the following:

    Coins: 202/500 = 40.4%
    Green Shells: 109/500 = 21.8%
    Bananas: 163/500 = 32.6%
    Red Shells: 16/500 = 3.2%
    Super Horns: 10/500 = 2%
     
    Last edited: May 29, 2015
  2. Mister Wu

    Mister Wu

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    APPENDIX
    THE FRONTRUNNING DISTRIBUTIONS

    CASE F1
    In this case the 2nd player is at the border between the bright and the dark strip behinf the first row of item boxes:
    F1.jpg
    The observed distribution is the following:

    Coins: 215/500 = 43%
    Green Shells: 112/500 = 22.4%
    Bananas: 134/500 = 26.8%
    Red Shells: 13/500 = 2.6%
    Super Horns: 26/500 = 5.2%

    CASE F2
    In this case the 2nd player is in the same place as in case F1, while the 1st player is getting items from the 2nd row of item boxes:
    F2.jpg
    The observed distribution is the following:

    Coins: 211/500 = 42.2%
    Green Shells: 115/500 = 23%
    Bananas: 144/500 = 28.8%
    Red Shells: 17/500 = 3.4%
    Super Horns: 13/500 = 2.6%

    CASE F3
    In this case the positions of the players are the same as in case F1, but the 1st player has completed a lap:
    F3.jpg
    The observed distribution is the following:

    Coins: 180/500 = 36%
    Green Shells: 139/500 = 27.8%
    Bananas: 148/500 = 29.6%
    Red Shells: 24/500 = 4.8%
    Super Horns: 9/500 = 1.8%

    THE EFFECT OF CANNONS ON DISTRIBUTION
    This test was performed in Sweet Sweet Canyon. In both cases the first player gets the items from the first row of item boxes after the starting line.
    CASE BC
    In this case the second player is before the cannon, with the front wheels at around a square of the central line of distance:
    BC.jpg
    The observed distribution is the following:
    Green Shells: 39/500 =
    7.8%
    Red Shells: 41/500 = 8.2%
    Triple Green Shells: 26/500 = 5.2%
    Triple Red Shells: 28/500 = 5.6%
    Fire Flowers: 8/500 = 1.6%
    Boomerang Flowers: 12/500 = 2.4%
    Dash Mushrooms: 130/500 = 26%
    Triple Dash Mushrooms: 152/500 = 30.4%
    Super Stars: 26/500 = 5.2%
    Spiny Shells: 9/500 = 1.8%
    Crazy Eights: 17/500 = 3.4%
    Bloopers: 12/500 = 2.4%

    CASE AC
    In this case the second player is in the section after the cannon, with the back wheels on the border at the beginning of this section:
    AC.jpg
    The observed distribution is the following:
    Dash Mushrooms: 28/500 = 5.6%
    Triple Dash Mushrooms: 151/500 = 30.2%
    Golden Dash Mushrooms: 113/500 = 22.6%
    Super Stars: 94/500 = 18.8%
    Bullet Bills: 67/500 = 13.4%
    Spiny Shells: 17/500 = 3.4%
    Lightnings: 13/500 = 2.6%
    Crazy Eights: 17/500 = 3.4%
     
    Last edited: Apr 23, 2015
    Luso, CanadianWifier, Horse and 12 others like this.
  3. Mister Wu

    Mister Wu

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    Sorry, I have still much work to do (e.g. not all the images have the map, plus I would like to reference this forum!), the first and second post will be updated quite frequently!
     
  4. Mister Wu

    Mister Wu

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    Fisrt edit: proper formatting!
    Fourth edit: fixed the description of the position of case 7!
    Fifth edit: added the case 2B, fixed the name of Bob-ombs and correct some formatting inconsistencies. 19/4/2014
    Sixth edit: added the cases related to the test of the cannon on Sweet Sweet Canyon. 23/4/2015
    Seventh edit: added the version 4.1 150cc class' distribution of case 1 and added an image with the map to case 1 22/5/2015
    Eighth edit: fixed a typo 29/5/2015
     
    Last edited: May 29, 2015
  5. Mister Wu

    Mister Wu

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    Second edit: the appendix!
    Third edit: a typo!
     
    Last edited: Apr 18, 2015
  6. inviso

    inviso

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    If one can figure out how the game calculates distance then, in theory, a formula can be developed to show what % chance you have a getting an item from a particular distance from the person in front of you.

    It appears number of players makes some difference, but I think it's less relevant than it was in MKW.

    Discovering how distance is measured, and the formula for attaining items isn't enough though...you'd also need to test to see at what distances can items be attained, and that will likely be a nightmare :p
     
  7. Mister Wu

    Mister Wu

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    I was going to post it, but the reality appears to be much simpler: the observed distributions are similar to combinations of the distributions of the PRIMA guide! In particular:
    CASE 1, F1, F2, F3: distribution 1
    CASE 2: distribution 2
    CASE 2B: distribution 3
    CASE 3: distributions 3 and 4
    CASE 4: distribution 4
    CASE 5: distributions 5 and 6
    CASE 6: distribution 6
    CASE 7: distribution 8

    Edit: added case 2B
     
    Last edited: Apr 19, 2015
  8. luke

    luke vision of excellence

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    for CoD every distance is measured in "units". The game code doesnt use metres/cm/mm or what have you. We know how many "units" a shipping container is in length from the code, so we know exact distances. (eg 800 units= 3 shipping containers long etc)

    If bean/chadderz/somebody could find something like that, profit?
     
  9. Harm

    Harm Jupiter Drive

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    I think distance in this game is based on checkpoints, which is why RR has magic boxes at the cannon, and dRR seemingly has broken items as well if 1st gets too far ahead.
     
  10. Mister Wu

    Mister Wu

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    What is sure is that absolute distance is not relevant, i.e. the game take in consideration how much of the track the player must pass to reach the 1st, so that case 1 and 7, despite having a similar placement of players, have different distributions.
     
  11. Harm

    Harm Jupiter Drive

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    yeah, so, how many checkpoints a player has to pass to get where 1st place is I'm assuming.

    btw all of this work looks great so far, I'm glad to see someone attempting to break this system down to a science. If it's accurate enough, it could add a whole new level of item strategy.
     
  12. Mister Wu

    Mister Wu

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    What is really interesting is that this system appears to be a repurported position-based system: the distributions are really similar to the distributions of the PRIMA guide, which are based on position, not distance. If this is true, we will just have to check the guide and check at which distance you change from one distribution to the next. I will try to get the 3rd distribution of the PRIMA guide in the next days, before the update, because with it in a few hours you can obtain easily 500 items. If I manage, I will add it to the results
     
  13. Blackjack

    Blackjack Despair...

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    Gotta love the RNG~
     
  14. EvuL Soldier

    EvuL Soldier

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    Nice read. Hopefully you break the item system so it can somewhat be abused for some advantage. The percentages alone from your current data will definitely help a bit.
     
  15. Mewwy :3

    Mewwy :3

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    very interesting stuff, keep it up :cat:
     
  16. POW!

    POW!

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    this is a pic of item probabilities from the prima guide.
     
  17. Teeples

    Teeples http://i.imgur.com/wZdLxlV.jpg

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    I love reading your experiments Wu, keep it up ;)
     
  18. Mister Wu

    Mister Wu

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    I have the eGuide because it's cheaper, anyway I was wondering if it was possible or not to post its distributions due to copyrght issues.
    As I said before, in the next few days I will try to get the 3rd distribution because, as you have seen, it's full of item that are easy to discard and so you can get 500 items quite rapidly. Getting the 5th distribution would be lovely too, assuming case 5 is not a 5th distribution which was patched by Nintendo to have Bullet Bills.
     
  19. flc

    flc Professional Site Breaker

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    fuck sake wu you've outdone yourself

    enjoy your free supporter status
     
  20. POW!

    POW!

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    why would it be illegal? also i think people should host rooms and test out items like you're doing. because they kind of vary with people i think
     
  21. Mister Wu

    Mister Wu

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    Thank you flc, but really it's just a thing of patience, no particular skill was involved!
     
    Last edited: Apr 18, 2015
  22. Mister Wu

    Mister Wu

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    There's always the possibility that other factors (i.e. position) influence the item distribution you will get, for now i will test the distance because it's easier and because so far it allowed me to see many of the PRIMA guide distributions. Remember, however, that you have to get MANY items to have little variability on the percentages. Maybe even 500 is not enough to see if Nintendo changes the item system in version 4.0 (unless they change the position of the distributions, which would be immediately recognizable because different items would appear, at least in the first 4 cases).
     
  23. inviso

    inviso

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    MKW has a distance tracker. I don't remember the stats menu for this game (since it lacked one for most of the time I played), but does it not have a distance tracker?
     
  24. Mister Wu

    Mister Wu

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    Just to clarify: I'm going to sleep now, and tomorrow will be a busy day, so I won't answer your questions timely!
    To clarify what I would like to do before version 4.0:
    1. try to obtain the 3rd distribution by testing the lamp before the central one. If I still get a mixed distribution then it likely means that the distribution at a certain point is a linear combination of the PRIMA guide distributions
    2. it would be super sweet to know if case 5 actually has a distribution based on a patched 5th distribution, because it would be the first clear sign of Nintendo developers tweaking the item system, but I will need to test a place between case 4 and 5 and I don't know if I'll have the time
    See you tomorrow!

    The stats don't talk about distance. Anyway, tests on Baby Park will immediately clarify if the item system is based on relative (fractions of a lap) or non-relative (e.g. meters) units of distance.
     
  25. Zinthos

    Zinthos

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    Good job Mister Wu!
     

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