> And now I'm just confused. How do we know that fast thinkers aren't using "slow thinking" or anything else when they play at slower time controls? Maybe good fast thinking is correlated with good slow thinking, but this doesn't mean it is the dominant factor!

I believe that the author is just restating the NH, which is the hypothesis that slowing down time controls will make the dominant player more dominant (or at least maintain the advantage). The alternate hypothesis is stated afterwards

> AH: NHC is false. On average, given some rating difference \(x\), if \(A\) beats \(B\) at the quick time control with a probability \(p\), then \(A\) beats \(B\) at the slower time control with probability \(p' < p\).