For Compression in general, there’s not really a strong evidence base in support of it, especially from a sport perspective (some in terms of clot prevention for bedridden patients). In terms of the compression boots, the evidence is even sparser, most of it being studies conducted with funding (or in kind contribution) of the manufacturer’s themselves, so I would be skeptical of most of that. That being said, anecdotally I see plenty of people using them, that swear by them, but there’s no evidence to suggest that’s much more than a really expensive placebo effect. (for the boots it’s really hard to study definitively, since essentially you would need to create a sham boot for your control arm in order to mitigate for possible placebo effects).