It wasn't Swoopes that lead Texas to go 13-20 on 3rd down.

Texas' 3rd Downs vs OU:
1st Drive:
3rd & 7 - 10 yd pass from McCoy to Shipley
3rd & 13 - 22 yd pass from McCoy to Sanders
3rd & 2 - 4 yd run from Brown
3rd & 3 - -2 yd pass from McCoy to Shipley

2nd Drive:
3rd 2 - 5 yd run from Gray
3rd & 7 - 21 yd pass from McCoy to Shipley

3rd Drive:
3rd & 9 - 38 yd run from Gray
3rd & 3 - 1 yd run from Gray

4th Drive:
3rd & 1 - 5 yd run from Gray
3rd & 6 - false start
3rd & 11 - 59 yd TD pass from McCoy to Johnson

5th Drive:
3rd & 7 - 12 yd pass from McCoy to Shipley
3rd & 5 - inc pass from McCoy

6th Drive:
3rd & 4 - kicked 43-yd FG to end half

7th Drive:
3rd & 8 - OU Pass Interference
3rd & 13 - 2 yd pass from McCoy to Gray

8th Drive:
3rd & 1 - 1 yd run by Gray
3rd & 6 - 7 yd pass from McCoy to Sanders

9th Drive:
3rd & 3 - 0 yd run by Gray

10th Drive:
3rd & 7 - INT by McCoy

11th Drive:
3rd & 5 - -3 yd run by Gray

12th Drive:
3rd & 1 - 2 yd run by Brown
3rd & 2 - 4 yd run by Brown

All tolled McCoy was 8 for 10 for 131 yds 1 TD and 1 INT on 3rd Down. He threw on 11 of those 20 3rd Downs (counting the PI). I think the Texas QB is very relevant when talking about how Texas beat Oklahoma last year.

Malcolm Brown is a SR this year and he had 3 carries for 10 yards. Jonathan Gray had 7 carries for 47 yards. Both of them are back this year.