Davis has a UZR of -5.0 this year, which means he is 5 runs worse than an average ML outfielder defensively. You say that's merely a product of his arm and that his speed gets him to more balls than the average defender? Wrong. His range (RngR on Fangraphs) is -2.4 (2.4 runs worse than average) while his arm (Arm rating on fangraphs) is -2.0. So actually his arm is 'less bad' than his range. We all know he isn't slow, so his poor range comes from getting bad reads on balls and/or taking poor routes on fly balls. Keep in mind, these range stats are from all three OF positions. If we only considered his stats in CF (-7.8 UZR, -3.4 Arm, -3.5 RngR) he would actually look much worse.
Well, he must make up a ton of runs with his speed on the bases right? Wrong again. Davis has a -1.47 WPA this year, meaning he has cost the A's about 1.5 wins... Just on the offensive side of the ball. His positive contributions on the basepaths (34 SB - 7 Times Caught) comes out to a WPA of only 0.392. Let's also not forget the fact that his K/BB ratio is 3.17 (54/17 when I checked) and his OBP is only .319. Compare this to speedster Carl Crawford who has a WPA of 1.66 and a UZR of 15.8 even with a -1.4 Arm and things look even worse for Davis. The stats say Rajai is a really fast guy with very poor baseball skills. The one good thing Davis does have going for him is that he appears to be able to take a base whenever he wants, even if it is a big situation.