cooling down properly, turns out it matters

Right so I've been really good about warming up lately, proper proud of myself tbh, but I realised the other day that I basically just... stop. Session ends, I grab my water, I'm done. No cool-down. Nothing. Had a run on Tuesday and my legs were genuinely horrible for two days after. Not like good-sore either, just stiff and grumpy. Started wondering if that's been the missing bit all along because I've never really taken it seriously. I mean I do a decent warm-up now, bit of dynamic stuff, get the blood moving, all of that — but the end of a session I just abandon my body apparently. Anyone else do this or is it just me being daft.