The above tells what special skill to expect, depending on chosen leveling method, at the final level.
Not included in the above table, but hopefully obvious:
So, if I am reading this correctly 1* same color methods are the best leveling methods. One at a time for best odds or up to 10 at a time to save food. Is that about right?
Yes, at least if you care more about the special skill than food. 
The simple though a bit imprecise answer is that one at a time or ten at a time doesn’t matter.
Still, it says there in the 3.50 column 68% vs. 65% and 52% vs. 50% when comparing 10 heroes at a time vs. 1 at a time and those are not errors. The reason is that while 1 at a time and 10 at a time will result in the same average number of increases over many attempts, we have an upper limit of 8 and one at a time results in higher variance than 10 at a time. 1 at a time has higher odds for both a very high number of increases and a very low number of increases (if unconstrained by the 8/8 skill limit), while 10 at a time will keep the number of increases closer to the expected average.
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)?
I don’t think you interpreted it correctly. The numbers in each cell are exclusive. The way to read 0/2/6/11/15/65 is: if you’re leveling a 3* hero from 1.1 to 3.50 using the method on the left then you should expect the special skill at 3.50 to be: 3/8 with 0% chance, 4/8 with 2% chance, 5/8 with 6% chance, 6/8 with 11% chance, 7/8 with 15% chance and 8/8 with 65% chance. All the numbers are rounded, which is why the numbers in each cell won’t always add up to 100 (and that 0% can’t be exactly 0, it just means <0.5% chance).
Thank you @kahree for that clarification.
That rounded number for 0 for 3/8 at 50 just might have explain what happened to @Rook 's Gunnar! She loves it when we talk about her legendary 3/8 3^50 Gunnar.
I’m eating that Gunnar… grumble grumble 
That makes a lot of sense. Hmm…
You know that Gunnar holds a special place in your heart, er Roster… Whenever you are about to feed that Gunnar to some other hero, you’ll probably still hesitate…
Besides, it’s a good tool to show other players who complain about their specials not increasing that their luck really isn’t that bad.
A must read to all.
Can’t believe I didn’t know of this before. Thanks @kahree for the thread.
With the introduction of Emblems a few versions back, the special level ups would become less of a frustrating mess once max XP levels are reached (5X at 3^50 for a 3*). Although 3* should become much less of a headache to get the specials up, I can see the data could still be relevant to some extent for newer players because they may be lacking in higher tiered heroes and only have 3* and below to work with before acquiring better heroes.
Although less likely to happen, there has been a few instances in which 4* and possibly 5* do not have the special leveled before reaching their final ascensions (being limited by the lack of non-farmable ascension materials), the annoying thing is that you are unable to work on those heroes’ special skills until you ascend them. Example, I had a 4* Wilbur stuck at 3^60 with specials at 6/8 and I did not have the Fine Gloves to ascend him. So I had to go work on other red heroes and come back to him when I do have the Gloves that pushed him to 7/8 on the ascension, and then wouldn’t you know it, 2 or 3 more levels later he was 8/8.
