Author Topic: Board Score Distribution  (Read 361 times)

1 Member and 1 Guest are viewing this topic.

Online xelnia

  • Global Moderator
  • Spring Jumper
  • *
  • Posts: 1394
  • Stop using 0.106
    • Twitch
Board Score Distribution
« on: November 13, 2017, 09:44:36 PM »
Players often ask (or are asked): what does it take to reach 1,000,000? 1,100,000? The world record? A slightly different way to ask that question is: how are 1,000,000 players scoring those points? 1,100,000 players? World record holders?

To hopefully answer that question, I've analyzed data from 305 games by 82 players, a total of 25,713 individual boards. I've broken the data down into four categories:

-Below 1M
-1M to 1.1M
-1.1M to 1.16M
-Above 1.16M

To separate players into these categories, regardless of their final scores and distance, I first analyzed their average points per board from Levels 5 through 21. Players generally stick to a certain play style or philosophy in the meat of the game, while Starts and death points can vary wildly. While not a perfect method, the per board average (PBA) system works well enough to separate players (or games) into general categories:

-Below 1M: <8,400 PBA
-1M to 1.1M: 8,400<>9,400 PBA
-1.1M to 1.16M: 9,400<>10,000 PBA
-Above 1.16M: >10,000 PBA

Unfortunately, I don't have data on whether a particular barrel board is top hammer vs. double hammer, or if a pie factory is a free pass or not, or if a spring is a 2-prize vs. 3-prize, or if a rivet is a weave vs. star, etc., etc. Someday I might go back and add that information...someday.

Anyway, after separating games into these categories, I graphed the resulting individual board scores for every board:

Barrel Score Distribution


Pie Score Distribution


Spring Score Distribution


Rivet Score Distribution


There's a lot to unpack here. I'll just make a few observations with my limited math skills:

1) There's obviously a clear increase in score on barrels and springs among the different categories. This makes sense, as point-pressing barrels is necessary for high scores and better players are better at springs.

2) Barrels and rivets are pretty close to a normal distribution. Interestingly, the distribution of rivet scores among ALL players are bunched up pretty closely. Is this mathematical confirmation that luck plays a larger role in this board than skill?

3) Springs appear to be slightly left/negatively-skewed in distribution. This means one would expect to see more spring scores fall below the mean than above it. This also makes sense, as there isn't really any room to build your score on the springs. It's a race against time in which you're mostly losing points.

4) Although I don't have data on how pie scores are achieved, it seems pretty clear that the "free pass" is the most popular technique among players of all tiers. Scores between 8,100 and 8,500 account for 43.78% of all pie scores. The lower tier of pie scores have a stronger left/negative skew than the higher tiers. This is likely due to playing for survival vs. playing for score.
"Do not criticize, question, suggest or opine anything about an upcoming CAG event, no matter how constructive or positive your intent may be. You will find nothing but pain and frustration, trust me. Just go, or don't go, and :-X either way!" -ChrisP, 3/29/15
Twitch TV  Streamer DKF Blogger DK Killscreener Crazy Kong Killscreener

Offline Barra

  • Spring Jumper
  • *
  • Posts: 919
  • Pie Kicker
Re: Board Score Distribution
« Reply #1 on: November 13, 2017, 11:26:55 PM »
So many jrycharts Kreygasm <3
First player to get both highest and lowest score during a Kong-Off <Kuh>
Twitch TV  Streamer DKF Blogger DK Killscreener Crazy Kong Killscreener DK 1 Million Point Scorer DK Jr. Killscreener DK3 Repetitive Blue Screen

Offline Kibbey93

  • Jr. Member
  • *
  • Posts: 42
  • Soon to be #1 in Aus...
    • My Twitch!
Re: Board Score Distribution
« Reply #2 on: November 14, 2017, 01:45:27 AM »
Nice graphs sir
Twitch TV  Streamer DKF Blogger Crazy Kong Killscreener DK Killscreener

Offline Svavar

  • Senior Member
  • *
  • Posts: 161
Re: Board Score Distribution
« Reply #3 on: November 14, 2017, 04:24:18 AM »
Really cool to see this visual representation. Great job
Twitch TV  Streamer DK Killscreener DK 1 Million Point Scorer Crazy Kong Killscreener

Offline hooch66

  • Full Member
  • *
  • Posts: 82
    • Personal Blog
Re: Board Score Distribution
« Reply #4 on: November 14, 2017, 07:02:27 AM »
This is great!

What software did you use to create the graphs?
DKF Blogger

Online xelnia

  • Global Moderator
  • Spring Jumper
  • *
  • Posts: 1394
  • Stop using 0.106
    • Twitch
Re: Board Score Distribution
« Reply #5 on: November 14, 2017, 07:14:09 AM »
This is great!

What software did you use to create the graphs?

Thanks! I used Excel 2013.
"Do not criticize, question, suggest or opine anything about an upcoming CAG event, no matter how constructive or positive your intent may be. You will find nothing but pain and frustration, trust me. Just go, or don't go, and :-X either way!" -ChrisP, 3/29/15
Twitch TV  Streamer DKF Blogger DK Killscreener Crazy Kong Killscreener

Offline danman123456

  • Spring Jumper
  • *
  • Posts: 697
    • Twitch TV Stream
Re: Board Score Distribution
« Reply #6 on: November 14, 2017, 07:55:06 AM »
Awesome sauce here. Yeah luck is a huge factor on the rivet board and now we know cuz SCIENCE!!  8)    Kreygasm
DK High : 1,059,700 (Lvl 22-1 KS!);
DK KS Speedrun : 1 Hr 16 Min 40 Sec - World Record!
DK Lvl 1 - 1: 12,400
Fix-It Felix Jr - 297,000 (World Record)
Fix-IT Felix Jr 1 Hour Limit - 177,000
Fix-It Felix Jr KS Speedrun - 1h33
Twitch TV  Streamer DKF Blogger Crazy Kong Killscreener DK Killscreener DK 1 Million Point Scorer

Offline krehztim

  • Senior Member
  • *
  • Posts: 146
Re: Board Score Distribution
« Reply #7 on: November 14, 2017, 03:55:01 PM »
LOVE the graphs and the stats.  Phenomenal posts lately. 

You have time for all this, but couldn't throw together an IGBY?   Kappa
Twitch TV  Streamer Crazy Kong Killscreener

Online xelnia

  • Global Moderator
  • Spring Jumper
  • *
  • Posts: 1394
  • Stop using 0.106
    • Twitch
Re: Board Score Distribution
« Reply #8 on: November 14, 2017, 04:24:53 PM »
You have time for all this, but couldn't throw together an IGBY?   Kappa

"Do not criticize, question, suggest or opine anything about an upcoming CAG event, no matter how constructive or positive your intent may be. You will find nothing but pain and frustration, trust me. Just go, or don't go, and :-X either way!" -ChrisP, 3/29/15
Twitch TV  Streamer DKF Blogger DK Killscreener Crazy Kong Killscreener

Offline Barra

  • Spring Jumper
  • *
  • Posts: 919
  • Pie Kicker
Re: Board Score Distribution
« Reply #9 on: November 14, 2017, 07:18:32 PM »
A few observations:

Barrels
Its pretty clear there's 4 different clusters of data and we can easily attribute these to gameplay specifics to answer the how/why.
<1m - purely running boards with mostly top hammers
1-1.1m - grabbing the bottom hammer with varying degree of efficiency and limited grouping
1.1-1.16m - bottom hammer, moderate grouping and again varying in efficiency.
1.16m+ - bottom hammer, heavy grouping and efficiency of the highest order. You could say luck plays a factor here too if the fireball climbs or not but the distribution is pretty standard. I guess that makes sense.


Pies
As Jry mentioned pies are played very similarly between all players and is evident in the distribution. This suggests the pies aren't figured out yet in terms of how to score higher points, or that it is too risky and not sustainable for a full-game.
Would be interesting to see Robbie's (?) technique stacked up against this graph.
More research/messing around on this board is required. The negative skew suggests too many points are lost when not a free-pass, and we haven't found a way to combat that.


Springs
Same as barrels regarding clusters.
No prizes, first 2 prizes, all 3 prizes, everything with efficiency + fireball leeching.
More points available (top-shelf and right-side) but again maybe not sustainable for a full-game.


Rivets
No specific grouping to suggest anything other than playing for survival.
It would be interesting to see this split into the different techniques (star, weave, <Allen> etc).

---


Most of this stuff is pretty obvious and in some cases complete generalizations, but its nice to see some math/data behind how we play and aim for a specific goal.

<3 it Jry. Always
First player to get both highest and lowest score during a Kong-Off <Kuh>
Twitch TV  Streamer DKF Blogger DK Killscreener Crazy Kong Killscreener DK 1 Million Point Scorer DK Jr. Killscreener DK3 Repetitive Blue Screen

Offline krehztim

  • Senior Member
  • *
  • Posts: 146
Re: Board Score Distribution
« Reply #10 on: November 15, 2017, 01:11:56 PM »

Pies

More research/messing around on this board is required. The negative skew suggests too many points are lost when not a free-pass, and we haven't found a way to combat that.

<3 it Jry. Always

As much as I suck (PB = 542k), I've been save stating the pies, and I've not seen any obvious way to consistently avoid the point loss, or any way to effectively leech anything whatsoever, and I've tried, believe me.  I'm not good enough to split fireballs every time and consistently survive and/or waste 2,000 on the timer sitting on the bottom.  Tough board to capitalize on.
Twitch TV  Streamer Crazy Kong Killscreener

Offline mrvaya

  • Senior Member
  • *
  • Posts: 149
Re: Board Score Distribution
« Reply #11 on: November 15, 2017, 02:27:42 PM »
I believe thereís a very great deal of skill to be learned in relation to rivet survivability - but of course thereís an increasing luck-dependancy in masters pb-games since you canít affort too many point dropping screens. Same on pies to a certain degree. If we made a survival contest based on enough data the same players would easily win every time imho.
DKF Blogger DK Killscreener

Offline dnickolas

  • New Member
  • *
  • Posts: 22
Re: Board Score Distribution
« Reply #12 on: November 17, 2017, 04:56:23 PM »
The graphs match up with how I play: Max out points on barrel and elevator, and for pie and rivet just try to not die.

Offline hooch66

  • Full Member
  • *
  • Posts: 82
    • Personal Blog
Re: Board Score Distribution
« Reply #13 on: November 18, 2017, 11:09:22 AM »
Where did you get the data to analyze this?
DKF Blogger

Online xelnia

  • Global Moderator
  • Spring Jumper
  • *
  • Posts: 1394
  • Stop using 0.106
    • Twitch
Re: Board Score Distribution
« Reply #14 on: November 18, 2017, 11:39:04 AM »
Where did you get the data to analyze this?


It's all data I've manually collected over the years, either from submissions to the DKF High Score List or games that I simply analyzed for their own sake. While my methods have changed a little over time, my own archive consists of a separate Excel spreadsheet for each and every game (for the most part...older games might be in a different format that I haven't updated yet). As a result of Wes Copeland's hard work, I can enter that data into kongtrac.kr and then export the entire database as one JSON file. That makes it much easier to work with than hundreds of individual spreadsheets.
"Do not criticize, question, suggest or opine anything about an upcoming CAG event, no matter how constructive or positive your intent may be. You will find nothing but pain and frustration, trust me. Just go, or don't go, and :-X either way!" -ChrisP, 3/29/15
Twitch TV  Streamer DKF Blogger DK Killscreener Crazy Kong Killscreener