I took a look at May stats just now. Top candidates to turn the page to June--Vázquez (.446 OPS), Kepler (.548), MAT (.552), Buck (.645). Pitchers--Jax 1-4 5.56 ERA, JLópez 0-2 9.00 ERA
Incidentally, the Twins were 12-15 despite outscoring their opponents by 20 runs in May.