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Sweet Q16

Mister Death
RJ: McFlono McFloninoo

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Joined: Feb 6, 2012
I was fiddling with the R&D side of my spreadsheet and I noticed something funny happening...

Research cost goes up exponentially, by a factor of 1.2 every level.
Research time is proportional to the cube of the level.

So, the research cost *rate* does something very curious. Here's the math for you nerds:

R = k * 1.2^L / L^3
dR/dL = k * 1.2^L / L^4 * (ln(1.2)*L - 3)

Research cost rate has a critical point at 3/ln(1.2) = 16.45. Below Q17, it actually gets *cheaper* per unit time to research your items as quality goes up!

This unfortunate problem creates a disincentive to research new products, and/or a big hurdle for new players to overcome as they have to spend a lot of money quickly to get over the Q16 hump. (Even established players - at least 2/3 of my product base has research levels below 17.)

The only ways to fix this would be to change the cost or time formulae for research. Until a decision is made, "Math of R&D, Part Two" is on hold (-:

(As a side note, in the bad old days when time was proportional to the square and the factor was 1.1, the critical point was at Q21!)

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