__What happened to the curve?__

The curve was a good fit, indeed the R^2 value (which measures how good a line fits a set of data) was better for the curve than the 5 straight line theory. However:

1) This could be due to over parameterisation.

2) The curve rarely predicted 52,43,19,8 gain and loss correctly (I.E. where the barriers of each straight line are). The data points just bent too fast for any curve that I'm familiar with to keep up. This isn't to say that it couldn't be a curve, but the curve wouldn't have a nice and easy equation to work with.

3) The 5 straight line theory just worked too well:

- We know how the gain/loss works from 18-42 with the only errors due to rounding.
- The 43-52 and 8-19 lines were within error of having the same gradient.
- The gradient of the 43-52 and 8-19 lines were within error of being 10 times smaller than the 18-42 gradient.
- The 0-8, 52-60 lines were within error of having the same gradient.
- The gradient of the 0-8, 52-60 lines were within error of being 10 times smaller than the 43-52 and 8-19 lines (which in turn makes them 100 times smaller than the 19-42 line).

__What are the gaps in the Predicted gain line?__

Were we don't know exactly where the corners in the graph are due to rounding. The 128ish trophy difference is a well measured corner however could be 126, could be 130. The 1100ish barrier is not so well documented. I used the value of 1128 when performing the trophy analysis but mathematically the value of 1408 crops up.

- Trophy gain loss within the old 18,42 limits has not been changed. It still follows the same rules (+/-30 trophies for matching trophy counts with an additional trophy gained/lost for every 10ish trophies difference between each player).
- This same rule is not followed outside of these limits (Otherwise at differences of 330+ trophies it would become possible to lose a match and gain trophies or win a match and lose trophies).
- Data so far implies that this is not just 3 straight lines broken by the old 18, 42 limit. Instead outside of the 18,42 limits the trophy gain/loss bends (google Sigmoid function if you want a general idea of what this looks like).
- This is not a traditional Elo system. The curve bends too fast after the approximately straight line middle bit.
- So far I have not received any trophy match ups that surpass an 8/52 limit

- AdvancingElk (Librarian)