If/OR formula, criteria met on Sheet A, show data from Sheet B onto Sheet A

Sheet A:

A	B	C	D
Hitter	vs Pitcher	Pitcher Throws	Hitter Average vs Hand
Barry Bonds	Randy Johnson	Left Handed	????????

Sheet B:

A	B	C
Hitter	Average vs Left Handed	Average vs Right Handed
Barry Bonds	.310	.365

I am trying to create a formula to display: Sheet A the Hitters Average vs Hand in Column D based on Column C. The data in Column D in Sheet A will either be Column B or C from Sheet B.

So I have been trying to use an IF/OR formula but it is not displaying the data correctly. I am trying to have a more compact "Master" Sheet that only displays the relevant information for that particular day. Today Barry Bonds is against Randy Johnson (Left Handed). I only need to see Barry Bonds average vs Left Handed Pitchers. Tomorrow if Barry Bonds plays against a Right Handed Pitcher, I only need to see his average against Right Handed Pitchers.

Currently my formula:

=IF(C2="Left Handed",(INDEX('Sheet B'!B:B,MATCH(A2,'Sheet B'!A:A),OR(IF(C2="Right Handed",(INDEX('Sheet B'!C:C,MATCH(A2,'Sheet B'!A:A))))))))

If C2 is Left Handed, Match the Hitter Name from Sheet A Column A with the Hitter Name on Sheet B Column A, display Column B from Sheet B

OR

If C2 is Right Handed, Match the Hitter Name from Sheet A Column A with the Hitter Name on Sheet B Column A, display Column C from Sheet B

Hi,

If you are willing to change the titles in sheet2 to "Left Handed" and "Right handed" and omit the "Average vs"
then you can do a double match like that:

=INDEX(Sheet2!$B$2:$C$2,MATCH(Sheet1!A$2,Sheet2!$A$2:$A$70), MATCH(Sheet1!C$2,Sheet2!$B$1:$C$1,0))
(yellow tables in the attachment)

If you want to leave the titles as is, then use this formula:

=IF(Sheet1!C7="Left Handed",INDEX(Sheet2!A6:C6, MATCH(Sheet1!A7,Sheet2!A6:A10,0),2),IF(Sheet1!C7="Right Handed",INDEX(Sheet2!A6:C6, MATCH(Sheet1!A7,Sheet2!A6:A10,0),3)))
(green tables in the attachment).