I have a P938 that I shoot weekly. It is a fine little pistol. I have a question. What is the purpose of the little hardened steel ball that comes in contact with the hammer when the slide is withdrawn to chamber a round?

Are you referring to the back of the firing pin ? as there is no steel ball part...

No. If you remove the slide and turn it upside down, you will see a hardened ball attached to the underside of the slide. It rubs on the top cartridge in the magazine. I suspect its purpose is to slightly move the top cartridge forward if a loaded magazine is inserted in the pistol with the slide closed. When you work the slide, the ball pushes the cartridge down then shoves it forward a wee bit as the slide closes.

The ball also touches the base of the hammer and slightly moves it rearward as the slide retracts. Why does this happen? What is the purpose of the slight hammer movement?

Aha. I believe it is to control the angle of the top round as it heads toward the barrel feed ramp. The square end of the slide pawl at the breech drives the cartridge off the magazine between its lips. https://www.dropbox.com/s/dh4i...lh/IMG_2817.jpg?dl=0

So is the fact that it slightly moves the hammer rearward is an unintended consequence?