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Board Score Distribution

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xelnia:
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.

Barra:
So many jrycharts Kreygasm <3

Kibbey93:
Nice graphs sir

Svavar:
Really cool to see this visual representation. Great job

hooch66:
This is great!

What software did you use to create the graphs?

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