A site was loading slowly and kept dropping offline. The client was preparing to change hosting to fix it.
The caching plugin wasn't doing anything, because the server lacked the software it needed, so I replaced it and worked through the front end. While deploying I watched the server fall over as the cache cleared, which turned out to be the cause of the outages.
PageSpeed went from 32 to around 90, and three times faster on throttled mobile.
The score moves with server response time and has touched 95. The outages had been put down to hosting, but they were the cache preloading every page at once against a box that could not absorb it, so switching that off stopped them. The move is still going ahead in February, now for a reason somebody has actually established rather than as a guess.