637 is the number of times I had 1 shard left to complete a star level plus the sim to get the shard. Starting at a point of 24/25 or 29/30, 49/50, 64/65 ... 99/100, these all fit under my conditions. Then I did a single sim to try and get the next shard and recorded the attempt.
I plotted the points (22 successfully achieved shards) on a plot (x axis - shard / y axis # of simulations) I printed the plot and brought it to my teacher. I drew my own line of best fit on the plot which I thought would best split the data. I took two points of data on the line to calculate the slope which is the drop rate.
I did Chi Squared with my teacher. Since I had it done might as well share the findings. It wasn’t part of my original discussion we just happen to be learning Chi Squared in class and adapted to it. We tried to write our own predictions to see if you get X many of zeros then you will get a success. The accepted value was 0, 0, 1 as the population value. Our hypothesis were much worse and seemed to explain the data better. We came to our null and hypothesis by changing the bin sizes of our histogram (# of sims till success) and made assumptions about the std dev of the population 33%.
I couldn’t use the rest of my fiends’ data since they didn’t acquire the shards using a single sim. Some did 2 at a time and others did 1 at a time. They only recorded the # of shards and # of sims. It was bad communication on my part for that. We have since then corrected our data recordings. Without points to plot or knowing when success occurred during sims, I could only get the rate which was 18.67%. 472 shards out of 2528 sims.
My conclusion was inconclusive since using only 1 source for data was dramatically different from my other 4 friends. My teacher mentioned that I might have bad luck and it is confirmation bias. But I argued that I was doing this before the hype.