Club Face Angle

It's awesome that we now have angle of attack and club path angle, but is there a way to calculate club face angle at impact from those metrics? It's great to see how far in/out;out/in my club is as well as how steep or shallow I'm coming into the ball, but without knowing the degree of open/close of the club path, it's hard to determine the full extent of why a shot went the way that it did. You can deduce that if you have an in/out angle, the ball will go right to left but if your club face is completely shut, you're gonna get a massive duck hook. It would be cool to see club face angle too.