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Well here's one analysis that suggests very strongly that nothing to play for teams so indeed have a performance drop. http://harvardsportsanalysis.org/2018/03/do-midtable-premier-league-teams-perform-worse-at-the-end-of-the-season/ The other conjectures I'll look for.

There's always the end of season factor where a team still desperately fighting comes up against those with nothing left to play for, or cup and European games to rest for, and the of odd top player who coasts a little those last few games because they have an eye on upcoming internationals...