While the multiplicative nature of the data might have tripped someone up who just put the data into a tool that assumed additivity, it wasn’t hard to see that it wasn’t; in my case I looked at an x-y chart of performance vs Murphy’s Constant and immediately assumed that at least Murphy’s Constant likely had a multiplicative effect; additivity wasn’t something I recall consciously considering even to reject it.

I did have fun, though I would have preferred for there to be something more of relevance to the answer than more multiplicative effects. My greatest disappointment, however, is that you called one of the variables the “Local Value of Pi” and gave it no angular or trigonometric effects whatsoever. Finding some subtle relation with the angular coordinates would have been quite pleasing.

I see that I correctly guessed the exact formulas for the effects of Murphy’s Constant and Local Value of Pi; on the other hand, I did guess at some constant multipliers possibly being exact and was wrong, and not even that close (I had been moving to doubting their exactness and wasn’t assuming exactness in my modeling, but didn’t correct my comment edit about it).

The lowest hanging fruit that I missed seems to me to be checking the distribution of the (multiplicative) residuals; I had been wondering if there was some high-frequency angle effect, perhaps with a mix of the provided angular coordinates or involving the local value of pi, to account for most of the residuals, but seeing a normal-ish distribution would have cast doubt on that.* (It might not be entirely normal—I recall seeing a bit of extra spread for high Murphy’s Constant and think now that it might have been due to rounding effects, though I didn’t consider that at the time).

*edit: on second thought, even if I found normal residuals, I might still have possibly dismissed this as potentially due to smearing from multiple small errors in different parameters.

Thanks abstractapplic.

Retrospective:

While the multiplicative nature of the data might have tripped someone up who just put the data into a tool that assumed additivity, it wasn’t hard to see that it wasn’t; in my case I looked at an x-y chart of performance vs Murphy’s Constant and immediately assumed that at least Murphy’s Constant likely had a multiplicative effect; additivity wasn’t something I recall consciously considering even to reject it.

I did have fun, though I would have preferred for there to be something more of relevance to the answer than more multiplicative effects. My greatest disappointment, however, is that you called one of the variables the “Local Value of Pi” and gave it no angular or trigonometric effects whatsoever. Finding some subtle relation with the angular coordinates would have been quite pleasing.

I see that I correctly guessed the exact formulas for the effects of Murphy’s Constant and Local Value of Pi; on the other hand, I did guess at some constant multipliers possibly being exact and was wrong, and not even that close (I had been moving to doubting their exactness and wasn’t assuming exactness in my modeling, but didn’t correct my comment edit about it).

The lowest hanging fruit that I missed seems to me to be checking the distribution of the (multiplicative) residuals; I had been wondering if there was some high-frequency angle effect, perhaps with a mix of the provided angular coordinates or involving the local value of pi, to account for most of the residuals, but seeing a normal-ish distribution would have cast doubt on that.* (It might not be entirely normal—I recall seeing a bit of extra spread for high Murphy’s Constant and think now that it might have been due to rounding effects, though I didn’t consider that at the time).

*edit: on second thought, even if I found normal residuals, I might still have possibly dismissed this as potentially due to smearing from multiple small errors in different parameters.