rivalry game going back to 2010 (looking at the 4 years Utah has won). You could make the argument that Utah gets up for the rivalry game and then under-performs for the games before and after, and you could make the opposite argument for BYU. BYU plays more like who they really are in the games before and after, and then lets down in the rivalry game. But I think you are missing a pretty large piece of the puzzle. Who BYU and Utah are playing before and after the rivalry game. Here is what I found.

BYU went 3-1 in 3 home and 1 away game before the rivalry game against teams that had a combined win pct. for the season of 0.388. Here they are for each year:

2010 W at Home vs New Mexico (1-11)
2011 L away vs Texas (8-5)
2012 W at Home vs Weber (2-9)
2013 W at Home vs Texas (8-5)

Utah went 1-3 in 1 home and 3 away games before the rivalry game against teams that had a combined win pct. for the season of 0.725. Again here they are:

2010 W away vs SDSU (9-4)
2011 L away vs USC (10-2)
2012 L away vs USU (11-2)
2013 L at Home vs OSU (7-6)

BYU went 3-1 in 2 home and 1 away game plus a bowl game after the rivalry game against teams with a combined win pct. for the season of 0.588. Here they are:

2010 W Bowl vs UTEP (6-7)
2011 W at Home vs UCF (5-7)
2012 L away vs Boise St. (11-2)
2013 W at Home vs MTSU (8-5)

Utah went 0-4 in 2 home and 1 away game plus a bowl game after the rivalry game against teams with a combined win pct. for the season of 0.711. They are:

2010 L Bowl vs Boise St. (12-1)
2011 L at Home vs Washington (7-6)
2012 L away vs ASU (8-5)
2013 L at Home vs UCLA (10-3)