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jgraber
If the sequential tasks don’t need to be sequential, then what is the difference from a diversity bonus?
  Thanks for spreadsheet. I’ll get to it soon. 
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ralsobrook
There isn’t one. In my haste to catch myself up and answer all of the questions you posed, I misinterpreted “diversity group” bonus, thinking you were somehow suggesting a bonus for completing multiple arbitrary tasks, not parts of a larger objective. Should have read your questions more carefully. I now realize that what you meant by a “diversity group” bonus is likely very similar to the bonus I described in my third point. And the bonus for “completing a task” would be awarded for the completion of an exceptionally hard SINGLE task (extinguishing all of your flames in Crossfire). I hope that clears it up. Sorry for all the confusion. Next time I’ll read twice and type once.
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jgraber
I have hacked the datasets to scale them to nearly the same slope, and equally spaced apart, and same number of points.    I also hacked the crossfire trend line to match the flat part of the slope, not the curved ends.
My goal was to make it easier to compare the 'shape' of the score trends.
Observations/Analysis:
- top 4-5 teams don't fit the curve well, all games
- Farm game scores sag in the middle; This happens when the slope is steeper toward the top
- Cross fire has a hump in the middle; This happens when the slope slope is shallower at top.
- Paydirt and Farm games has several humps and sags, representing multiple sections of game, each linear.   
 This agrees with Ralsobrook observation from a few posts ago:
 It seemed to me that the scoring system (for Crossfire) loosely followed a curve where the difference in score between any two teams decreases as you ascend the ranks ....

Assuming the shape could be controlled,  what is the best shape?  --JOel

 
souths_best_graph.jpg 
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ralsobrook
Thanks Jgraber,

The shape I like best, personally, is that of Bladerunner. As I see it there is a great deal of close competition between teams on the lower end of the ranks. Rather than being bored and discouraged by the seemingly insurmountable challenge of competing with scores vastly higher than theirs, they spend the day jockeying for position with the other teams on their level. Another thing I like about the Bladerunner graph is the clear delineation between the multiple "levels" of the competition. To me, this indicates that the ranks are mostly determined by strategy, skill, and robots' abilities, and unforeseen circumstances are less likely to result in a team being ranked below another, less able team. This type of graph provides you with a clear winner, and no clear loser. There are teams that are celebrated for soaring above the competition as a result of their efforts, but none that are singled out and humiliated as significantly inferior to the others. For these reasons, I think a Bladerunner style scoring system is the most rewarding across the board.
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jgraber
jg edit fix my previous post: - Paydirt and Bladerunner games has several humps and sags, representing multiple sections of game, each linear. 
r>I think a Bladerunner style scoring system is the most rewarding across the board

I agree; I was going to say that too, but deleted it to await your opinion.  Farming game is somewhat similar also.
When game has layers of different 'levels' (paydirt), 'activities' (bladerunner, or farm), with linear progression at each level.
So for example, with 3-5 levels abcde, and 2-8 linear scoring objects at each level,  what should be the point multiplier between levels?
Represented as a2 b4 c4 d4 e2,   where dozer level a has 2 easy tasks, final level e (hanging the plane) has 2 tasks.
If each of the 4 (b) items is worth twice as much as an (a) item, then score of a2-b0 is same as a0-b1.  As you go up in level capability, and assume that you can get half of all previous levels, then
(a) capable range is (0-2)*1 = 0-2
(b) capable range is 1*1+(1-4)*2=3 to perfect as 10,
(c) capable range is 1*1+2*2+(1-4)*4=9 to perfect as 26,
(d) capable range is 1+2*2+2*4+(1-4)*8=21 to perfect as 58.
(e) capable range is 1+2*2+2*4+2*8+(1-2)*16=1+4+8+16+(16 to 32) = 45 to perfect as 58+32=90
The overlap between b,c,d look good, because equal number of items at each level.
Should the multiplier between levels take into account the number of items?
b4 c4 the multiplier is 2 which is same as (max b score=8)/(number of c items=4) = multiplier of 2
If we use that formula, then d4 to e2 multiplier would be (max d score = 16)/(number of e items=2) = multiplier of 8 
that makes (e) capable range is 1+2*2+2*4+2*8+(1-2)*64=1+4+8+16+(64 or 128 ) = (29+64 =93) to perfect as (58+64=122)
  complicated
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