It is an element in loser breaks format as well. It is not explicitly a table size effect. It is about runouts getting too easy. That can happen by some combination of players getting stronger and equipment getting easier. The game is kind of broken at that point when you have too high a fraction of games for which opponent provides no resistance. That’s pool becoming bowling. The race calculator works fine for the vast majority of players/competitions. I think you’d not see any statistically meaningful effect comparing, for example, matches at turning stone (winner breaks) to international open. But you would in a pro level bar box 8-ball tournament.
As Bob mentioned, straight pool is a good example to exaggerate the issue to make it plainly discernible. In straight pool races to 10, the race calculator probably works fine for players under 350 and starts failing sometime after that.
Your initial answer referred to packages, which is only relevant in winner break formats. Otherwise, the other person gets to the table every other game to restart their own (presumably independent) trial.
Bob's example was helpful. It works because each run is its own trial as each shot is not independent--if a person makes a shot (say, they have a 98-99% chance of any one shot) then they are at the table for the next shot. However, I am willing to bet if straight pool were played in some bizarro fashion where each player traded off each shot then the scores would be a lot closer.
Ultimately, your argument that p=.55 but somehow standard deviation changes and break format doesn't matter is unconvincing.
As well, with regards to handicapping, you implied (perhaps just illustratively) that a race to five on a 9' table might be equivalent to a race to seven on a 7' table. Since a lower-rated player would have a better chance of beating a higher ranked player in a shorter race, that means given a fixed race to seven, a worse player would strictly have a better chance on a 7' than a 9'. That means, according to your evaluation of your own system, if one is handicapping two players based on Fargo, that handicapping must depend on table size.
So which table size is Fargo correct for? More likely, Fargo is technically wrong for both since it's an average across all games and all table sizes. The number it's giving us is somewhere in the middle. For example, if Fargo says player A is 60% to win a race to seven against player B, the probabilities are more like (making up numbers here for illustrative purposes) 65% on a 9' table and 56/57% on a barbox.
(I didn't make the difference from 60% uniform under the assumption that for the set of players under 700 Fargo many more games in the system are on barboxes than 9' tables and therefore the given estimate would be closer to the barbox value).
I do appreciate your responses, and your accessibility with discussing your system.