You can break a players value into possessions used and efficiency per possession. Some players are generating value largely from the former, so when they transition from a team where they are the star to a team where they are second (or third) fiddle their value drops.
Look at what happened to the Heat:
TS% | Shots | WP48 | |
James | -0.031 | -3.35 | -0.117 |
Wade | 0.011 | -2.85 | 0.008 |
Bosh | -0.028 | -3.8 | -0.102 |
In the Heat's case part of the WP48 decline is a small decrease in efficiency. The bigger part of it is a decrease in the number of shots attempted by over 10% each. For James and Bosh though, I suspect, that most of the WP48 drop is accounted for by declines in rebounded, steals, etc.
This picture tells the story about the Big Three:
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