After reading the chart and some of your replies, I am a little confused with the way your numbers appear.
So say for a 3* maxed at level 50 - Say it somehow sat at 3/8. By the numbers you posted same color 1* only, 1 hero at a time. 0/2/6/13/15/65. If I am interpreting the graph correctly, obviously there is 0% you are going to upgrade to 3 because you are already at 3/8.
The next one is 2% that it will go from 3 to 4 on a 1* same color 1 at a time feed
6% to go from 4 to 5
13% to go from 5 to 6
15% to go from 6 to 7
65% to go from 7 to 8
Did I interpret your graph correctly? If so, and you saying 1 at a time vs. 10 at a time doesn’t matter much, it sounds more like the each hero regardless of matter which * level, has equal chance of getting a special upgraded, and each represents a single pull (like a single summon) and 10x heroes is like 10 single pulls each time not affecting the other (like a 10x summon). So a 1* done 10 separate times has very similar chance vs 1* done 10 times together. But what about the percentage displayed (2% is 1* same color), (20% is 1* same color x 10 at a time)?