In my opinion, the Magic Wand tool is about the worst method for extracting a background in 95% of all use cases. Unfortunately, I realize it is the "go to" method for many users. However, it's not often the "best" method, in fact it's among the worst. The Magic Wand method can work for hard edged objects without any cast shadows. But beyond that it's pretty horrible.
Use Channels
Channels are often easier and faster than any other selection technique if the subject is already isolated on white. Channels allow you to retain shadows and subtle drop offs in many instances.
So, to use channels...
Find a channel with decent high contrast... in this case I've chosen the Blue channel..

- Duplicate that channel in the Channels Panel.
- Use Levels or Curves to boost the contrast on the copy.

Command/Ctrl-click the duplicate channel thumbnail in the Channels Panel to load it as a selection.
Go back and highlight your Layer in the Layers Panel.
Hold down the Option/Alt and click the New Mask
button (
) at the bottom of the Layers Panel.


From here you may need to go in with a brush and manually refine the mask in a few places.
For images such as this one with pronounced cast shadows....

You may need to extract the shadows to a separate layer to better control their appearance.
So I duplicate the masked layer twice...
On the first duplicate I go in with a brush and manually mask the shadows...

On the second duplicate I go in with a brush and manually mask everything except the shadows...

This gives me a separate layer to control the cast shadows.
With both these duplicate layers visible, you can alter the blending mode and/or opacity of the shadows to better the overall appearance.

Both these image took roughly 30 seconds each to mask. The second image took maybe 1 or 2 minutes to refine the mask for shadows, but it could use a bit more time.