Once upon a time I wrote a post about unintended consequences of ACKS' stat generation system. One of those consequences is that replacement characters will tend to be less-good than first generation characters. The logic goes something like this:
When everyone is first rolling characters, you have a total of 5 stat-lines per player, and the best wizard will be the stat line with the best Int of 20-25 3d6 rolls, which for 4 players tends to be around 16.
When that wizard bites it, you go to roll a new PC but you have a wizard-shaped hole in the party and a desperate need for some sleep support. But you roll five sets and your best Int will be the best of 5 3d6 rolls, which is only about 14. So sure, you can bring in another wizard, but he will probably be worse than the wizard you lost, beyond just lower XP.
I mentioned this in discord and someone pointed out that when PCs get killed, often it is several PCs at once. If a bunch of PCs die at once, then you might be rolling 10 or 15 sets instead of just 5, as each of the other players with a dead PC rolls up a new one too. If you do this, then the gap between first-generation PCs and later-generation PCs should be much smaller. If you lost a fighter, a wizard, and a thief, you no longer have the constraint that the player who was playing the wizard has to be the new wizard, so you're free to take the best wizard statblock from among those 15 sets, which should be much closer to the best wizard statblock from among 20 sets.
So then the question became, how often do PCs die in groups in practice? So I looked back over my notes from the first summer of my first ACKS campaign and found 7 "PC death events", 5 in which only 1 PC died, 1 in which 2 PCs died, and 1 in which (all) 3 PCs died. So half of PCs who died didn't die alone. The other fellow I was discussing this with in discord went and checked his session logs and found an even heavier-tailed distribution, something closer to 60% of PCs dying at the same time as at least one other PC.
So if this is true, then we should expect first-generation supremacy to not be as serious a problem in practice as I had thought it was theoretically. And I suppose the correct advice for players who are worried about first-generation characters being better is "you can solve this problem by TPKing more often. Leave no-one behind, make valiant last stands, play heroically and all die together." Which is weird, counter-intuitive advice, but heroic last stands are one of the finest parts of D&D in any case.
(Another objection worth noting to the theory is that first-generation supremacy problems probably apply under almost any random ability score generation scheme, not just ACKS')