So, I wanted to see if the chances of getting a 4* ascension mat from a roll was indeed increasing with the loot tier, or if it was a fixed 3% like we see floating around, with variations due to limited sample.
A bit of math: I took the number of each 4* mat appearing in this great data collection and estimated the uncertainty by taking the square root of the number of mats divided by the total number of rolls. That’s the curve below with the bars representing uncertainty. The bars are much larger when there is just a few mats drawn.
I then fitted the points with a linear curve, taking for each points the inverse square root of the relative uncertainty as weights, and looked at the 95% confidence interval on the slope of this curve. There are more rigorous methods of determining this, but this seems good enough for me.
The results is that the slope of this curve is calculated to 0.27 % more mats per loot tier, with a 95% confidence interval between 0.15 %/tier and 0.39 %/tier. A constant chance of getting a 4* mat irrespective of the loot tier would give a slope of 0 %/tier, which is way out of the confidence interval. We can thus be quite sure that the chances are indeed increasing.
To try to retro-engineer the formula used by SG, I tried more round values: a starting chance of 1% at loot tier 8, and an increase of 0.3% per tier. This gives 4% chance for 4* mats at the maximum loot tier of 18. This curve is drawn in red on the graph and looks very good in my opinion. The formula would be (loot tier-8)*0.3%+1%
TCDU Math on this great data collection says the chance per roll of getting 4* mats is definitely increasing, and a plausible formula is a linear increase from 1% at tier 8 to 4% at tier 18.