The phrase "straight bat" means to face a difficult situation or argument in a calm and fair manner, without showing any bias or aggression. Full definition
I'm less hopeful than some on Ozil signing though — he's played a very straight bat on his way to a lucrative free transfer exit so far. (goonerholic.com)
Say what you like about the Electoral Commission but it has always played things with a pretty straight bat. (theconversation.com)
Balls put forward an unsettlingly out - of - character straight bat. (politics.co.uk)