There is an adage in baseball that "sinkerball pitchers improve as the game goes", that in particular the sink improves - so sinkerball pitchers tend to give up a lot of fly balls in the first few innings but then get more sinking action later on, leading to sinkers actually sinking and yielding ground balls (or swing-and-miss). (I can't immediately find this online, but it's a common adage from sportscasters; Steve Stone just mentioned it during the White Sox - Twins game on 7/7/2021).
If this is true - and I'm open to statistics otherwise - why? If it's because being tired helps, why don't they just throw a few dozen extra pitches during warmup at full speed? If it's something else... what?