Assume 700 PA's
So far in the majors Belt has walked about 8% of his at bats.
In the minors he walked about 17% of the time which translates to a major league line of about 7%.
Let's be optimistic and say that in Belt's prime he can draw a walk 10% of the time. That's 70 walks
So far in the majors Belt has stuck out about 24% of the time.
In the minors he struck out about 18% of the time which translates to a major league line of about 21%.
Let's be optimistic and say that in Belt's prime he can strike out about 20% of the time. That's 126 strikeouts.
That gives belt about 504 balls in play (less home runs, which we'll deal with later).
So far in the majors Belt has the following batted ball profile:
22% line drives, 39% ground balls, 37% fly balls-of which 6% were infield flies, and 9% HR/FB.
In the minors his lines were
Let's be optimistic and say that in Belt's prime he can hit 25% line drives, 37% ground balls, 38% fly balls of which 5% are infield flies with a 15% HR/FB rate.
So, on Belt's 504 BIP we'll expect (.25*504) 126 line drives, (.37*504) 186 ground balls and (.38*504) 192 fly balls of which (.05*504) 25 are infield fly balls.
Of Belt's 192 fly balls 15% of them will go for home runs, that's (.15*192) 29 HR's.
That leaves Belt with (504-29) 475 balls in play.
Using league average BABIPs for each batted ball type we'd expect the following amount of hits
Line drives: .740 BABIP * 126 line drives = 93 hits
Ground balls: .240 BABIP * 186 ground balls = 45 hits
Fly balls: .140 BABIP * 164 fly balls (192 fly balls - 28 home runs) = 23 hits
That's a total of (93+45+23+28) 189 hits.
700 PA's - 70 walks leaves Belt with 630 at bats.
189/730 = .300 batting average.
So, using some projections that I'd consider optimistic, I get Belt-in his prime-hitting .300 with 28 home runs.
Unlikely that he'll get to Roy's .280 with 24 home runs this season.
Feel free to adjust the numbers as you see fit.