How much is an extra card worth in MTG?
The concept is messy because Wizards knows the cost is high and that's why they keep trying to mitigate the effect with the mulligan rules, but going off the data collected from 17lands.com Resources on MTGA, it's about 12% after the London mulligan. It was previously 16% with the Vancouver mulligan. For context, the best players tend to be in the 60% for win rates, the best decks tend to be in the mid 50% range. So without mitigating the card disadvantage, you are basically turning an average player on an average deck into one of the best players on one of the best decks.
Now please don't waste people's time pointing out irrelevant details like the difference between limited and Vintage. That's not the point. The point is an extra card has a huge effect on a deck's win percentage and the Companions were trying to mitigate that advantage solely by their deck building restrictions. Or they could have made the cards week, like a basically vanilla 5/5 or 4/5 (and those still see competitive play). Lurrus's deckbulding restriction is not very significant in the context of Vintage and the card is pushed relative to other three drops if you've ever tried to play it maindeck in any format. Lurrus compounds the advantages of the extra card by being a strong card in it's own right. The 11% advantage that we calculated from our data set is likely an accurate representation of the cards power despite the fact that the format is completely warping around itself with up to 75% of decks running it.
I don't know how to spell it out any clearer.
This analysis is incomplete and I think somewhat incompatible. It measures win rates against an opponent with a 7 card hand size, but does not account for the diminishing returns as you go down the scale. For instance the 12% you refer to is in reference to a 6 card hand vs a 7 card hand, but that same statistic would likely not hold up when measuring a 4 card hand vs a 5 card hand. the ratios are undoubtable a curve that suffers from some sort of diminishing returns as you go down the scale and your hand starts to become less important than what you top deck, and I imagine as players start getting into the very low numbers the difference starts to flatten.
Likewise, we have no precedent for an 8 card hand size until just now, sorta. Companion has its own wrinkles that do not make it really an 8 card hand size, but for the sake of simplicity let's roll with it. I would imagine that the win ratios here are theoretically a bell curve of sorts, where the higher up the chain you go the more if eventually flattens. Take it to a more extreme level like what does a 19 card hand look like vs an 20 card hand, and I imagine it is not nearly as sharp a decline as a 6 vs 7.
Potentially throw in some combo cards, like Necropotence and Flash, and we may be able to get back to a 3-deck format.
The format is already a multideck format, Lurrus is not a deck type any more than decks running force of will are a deck type.