Here is how each QB played over their final winning starts:
Young (won final 11 starts):
309 of 434 for 3,908 yards with 33 TDs & 14 INTs, 165.48 Passer Rating, 71.2% complete. BYU averaged 42.6 points and gave up 18.8. Opponents combined record was 64-63 (.504). He also ran for 289 yards & 7 TDs

Sarkisian (won final 12 starts):
227 of 338 for 3,307 yards with 23 TDs & 10 INTs, 165.88 Passer Rating, 67.2% complete. BYU averaged 39.5 points and gave up 16.8. Opponents combined record was 64-73 (.467). He also ran for -36 yards & 1 TD.

Beck (won final nine starts):
206 of 399 for 2,913 yards with 26 TDs & 6 INTs, 175.42 Passer Rating, 68.9% complete. BYU averaged 39.8 points and gave up 13.6. Opponents combined record was 51-61 (.455). He also ran for 26 yards & 5 TDs.