You’ve suggested this a couple of times, and I guess I’m curious how much “less random” it actually is.
Fair warning: What follows in not intended as an attack on SoS, but is rather speculation about how deterministic it actually is. Frankly, I’m not entirely opposed to SoS, and I think going too far out of our way to create tiebreaker scenarios that limit variance is a bit silly in a card game where RNG inevitably plays a factor at the match level (even one like A:NR where skill plays a larger role than might be typical for card games).
If Contestant A and Contestant B have the same record but B had a tougher SoS, all we really know is that they earned the same prestige but through two different levels of difficulty. This doesn’t mean that A wasn’t capable of earning the same prestige as B if they had played the same lineup – it’s even possible that A could (in some alternate setup) earn that prestige through a harder lineup than B faced. We do know that B has demonstrated a higher minimum skill than A has demonstrated, so in the absence of any other information it is probable that they have a higher actual skill. However, I’m not certain how much “less random” it actually is in practice. If I want to compare the height of two adults and I know A is “at least 4’ (1.219m),” it is probable, strictly speaking, that B is shorter. Given a working knowledge of distribution of human heights, however, the impact of this information is effectively irrelevant to any probabilistic determination.
Consider, for example, an oversimplified Swiss setup where A and B are strong players (70% and 75% to sweep any non-A/B opponent in the field) and a field of players evenly matched against each other (50% to beat any non-A/B player). In any lineup where A doesn’t play B (because SoS wouldn’t be a factor there), we can see that any determination by SoS is essentially equivalent to a coin-flip. B will win on prestige more often than A (with the odds of that increasing the more rounds of Swiss there are), but SoS is almost exactly as random as a coin-flip here. The only deviation from coin-flipping are the odds that they a) play the same opponent C, and b) one defeats C and the other doesn’t. While this does slightly favor B (who has better odds of beating C), it is also unlikely to occur in most scenarios where SoS matters (because if one has lost to C and they are still tied for prestige, A and B are unlikely to still be at the top table).
Of course, in a real-world setting, the other opponents aren’t just flipping coins, so there are diminishing odds each round that someone at the top tables is an underskilled opponent. Likewise, the more information that moves the final SoS away from the initial random seed of the first round – e.g. through more rounds of Swiss, or even input from past tournaments (such as byes, or a hypothetical continuous ELO ranking system that carried over across tournaments to determine initial pairings) – the more likely SoS is to accurately reflect a minimum player skill.
How much “less random” than a coinflip the bubble-cut is at a typical tournament, though, is something of an open question. We could probably model this by simulating a tourney of ranked players (say, 32 players, each with a 3%-per-rank-difference advantage in a given match) and seeing how frequently the SoS of any two players relative to one another on the bubble reflects their assigned ranks.