There was a statistic analysis that showed that there is no difference for the end result, so why do people feel so strong about it? ...
Where was that? Was it amateur or pros? Because my recollection of the At Large work is that the break does favour the good pros.
Perhaps skor is remembering what Bob Jewett has said on winner breaks vs. alternate break formats, such as this from 2024:
If psychology is not a factor, probability and statistics has a definite and rather surprising answer to this question.
Consider all of the following formats for a race to N games:
Winner breaks
Alternate break
Loser breaks
Winner of the flip says who will break each game but cannot assign more than N breaks to either player
Winner of the flip breaks N times and then the other player breaks N-1 times
The amazing result from probability and statistics is that all of these break formats give the same advantage to the better player.
That means you can choose a format that is good for other reasons without worrying about giving more/less advantage to the better player.