figure to do something

[ostap77]

" Their first-rounder, former Texas defensive tackle Casey Hampton, figures to play in the league for 10 years."

Does it mean he's been playing for 10 years or he's probably going to do so?

[emsr2d2]

His plan is to play in the league for ten years. He thinks (figures) he will do so.

[Barb_D]

The rest of the sentence, in case you care, means that he was picked in the first round of the draft (that means he's a very good player) and that he went to the University of Texas.

[SoothingDave]

So, he is in his first year of playing professionally and has plans to play for 10 years.