I've been reading through this thread - fascinating stuff by the way - and there's lots of detailed analysis, but could someone paint an overall picture of what it really means.
I know from my own experience this is not easy to do until you have all the data, complete the analysis and then say - ah this is how it works, and publish your results. However, it all looks so interesting and yet I feel when reading through this that I cannot see the wood for the trees.
For example, there are graphs which show (if I understand correctly) TT value of a skill increment of 1 plotted against skill level. This centres around zero, so some skill increments are negative. This makes no sense to me, as it would imply that at some skill levels the TT would pay you to accept a skill increase of 1 point.
Probably I've misunderstood what the graph is plotting, but this sine wave idea seems very weird. Why have a value that oscillates. I know TT value is all code-generated, and not natural phenomena, but is it possible there's another explanation for the perceived sine-wave based variation. Like rounding at an early stage in the calculation inside the servers because the programmer used an integer variable by mistake?
I think I understand the objective here - to be able to predict the TT value of any skill level (is it just an assumption that this is the same for all skills?). But if there is a lot of variation outside of rounding factors, doesn't this mean something else is also affecting the TT values being observed? I mean here that if the formula was say TT = skill delta * X (it's not I know - this is for illstration) then you could find a value for X +/- some error due to rounding issues. But if more than a couple of data points (which could be put down to measurement error) were outside the rounding error range, then the formula is wrong. Because code is perfect. If the skill valuation code in the game has a formula of whatever, this will always give the same answer. If it doesn't, it's not going to be power surges on the server - the code will have been written to bring in the other factors.
So I guess what I'm saying here is could someone summarise the tentative theories which you're hoping to prove/disprove with the data.
I'm keen to see the outcome of this exercise - a fascinating project