Power spark/time reduction, math wizards assemble 📈

I’m trying to figure out the formula for power spark/time reduction but it eludes me. I gathered some data, and by plotting it I see the logic, but my math skills aren’t enough to solve it :smiley:

Full Data
Extra Power 0 Power Recipe % of original 400 Power Recipe % of original 1200 Power Recipe % of original
0 40000 100.00% 10000 100.00% 30000 100.00%
100 32812 82.03% 9470 94.70% 28711 95.70%
200 31695 79.24% 8973 89.73% 27617 92.06%
300 30645 76.61% 8508 85.08% 26534 88.45%
400 29611 74.03% 8071 80.71% 25518 85.06%
500 28738 71.85% 7662 76.62% 24566 81.89%
600 27875 69.69% 7279 72.79% 23674 78.91%
700 27069 67.67% 6919 69.19% 22841 76.14%
800 26317 65.79% 6582 65.82% 22061 73.54%
900 25617 64.04% 6404 64.04% 21333 71.11%
1000 24967 62.42% 6242 62.42% 20654 68.85%
1100 24363 60.91% 6091 60.91% 20020 66.73%
1200 23804 59.51% 5951 59.51% 19430 64.77%
1300 23288 58.22% 5822 58.22% 18880 62.93%
1400 22812 57.03% 5703 57.03% 18368 61.23%
1500 22374 55.94% 5593 55.93% 17892 59.64%
1600 21971 54.93% 5493 54.93% 17449 58.16%
1700 21603 54.01% 5401 54.01% 17038 56.79%
1800 21267 53.17% 5317 53.17% 16656 55.52%
1900 20961 52.40% 5240 52.40% 16300 54.33%
2000 20683 51.71% 5171 51.71% 15970 53.23%
2100 20431 51.08% 5108 51.08% 15664 52.21%
2200 20205 50.51% 5051 50.51% 15378 51.26%
2300 20001 50.00% 5000 50.00% 15113 50.38%
2400 19819 49.55% 4955 49.55% 14866 49.55%
2500 19656 49.14% 4914 49.14% 14742 49.14%
2600 19512 48.78% 4878 48.78% 14634 48.78%
2700 19385 48.46% 4846 48.46% 14539 48.46%
2800 19273 48.18% 4818 48.18% 14455 48.18%
2900 19176 47.94% 4794 47.94% 14382 47.94%
3000 19092 47.73% 4773 47.73% 14319 47.73%
3100 19019 47.55% 4755 47.55% 14264 47.55%
3200 18950 47.38% 4739 47.39% 14218 47.39%
3300 18904 47.26% 4726 47.26% 14178 47.26%
3400 18860 47.15% 4715 47.15% 14145 47.15%
3500 18824 47.06% 4706 47.06% 14118 47.06%
3600 18794 46.99% 4699 46.99% 14096 46.99%
3700 18770 46.93% 4692 46.92% 14077 46.92%
3800 18751 46.88% 4688 46.88% 14063 46.88%
3900 18736 46.84% 4684 46.84% 14052 46.84%
4000 18724 46.81% 4681 46.81% 14043 46.81%
4100 18716 46.79% 4679 46.79% 14037 46.79%
4200 18710 46.78% 4678 46.78% 14033 46.78%
4300 18706 46.77% 4676 46.76% 14029 46.76%
4400 18703 46.76% 4676 46.76% 14027 46.76%
4500 18702 46.76% 4675 46.75% 14026 46.75%
4600 18701 46.75% 4675 46.75% 14025 46.75%
4700 18700 46.75% 4675 46.75% 14025 46.75%
4800 18700 46.75% 4675 46.75% 14025 46.75%
4900 18700 46.75% 4675 46.75% 14025 46.75%
5000 18700 46.75% 4675 46.75% 14025 46.75%

Recipes used were Refined Amethyst (0 power), Iron Filigree (400 power) and Titanium Filigree (1200 power)

The curve changes after extra power reaches 2 * recipe power requirement. It seems to be a cubic curve after that, maybe quadratic in the beginning? Somebody intelligent here who’s able to figure it out?

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@MrNiX this sounds right up your alley

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Yeah I can do this.

@Mayumichi shoot me your data…

It’s in the first post, just have to click it open. The “Full Data” section.

Got it. I suspect that discrete conditionals are involved here and that this isn’t purely a continuous curve. Question: for 400 and 1200 power recipes, does the +100 imply 500 and 1300 power respectively?

Are these numbers in ms?

Yes, +100 extra power is 1300 total power for the 1200 recipe. The numbers are the spark costs, they go down with the same multiplier as time.

Oh, yeah, duh, that makes more sense. Fun!

I think i see what this is. Let me brunch and ill try check it

Here goes nothing, @lucadeltodecso any hint about how the spark reduction is calculated from the excess power? I’ve talked about this with multiple people, and nobody has been able to figure it out thus far :sweat_smile:

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