There is an obvious advantage to being ahead at the halftime mark. If the status quo stands, your team will win the game. This is not the whole story as anyone who saw the historic win by the New England Patriots over the Atalanta Falcons is well aware of.
The advantage the Patriots had was that while Lady Gaga was wowing the nation with her show, the Patriots were work-shopping and planning how to stop Atlanta's offense and how to defeat their defense. Atlanta could not and did not need to do this--what they had been doing was working and they had no way to know what changes (if any) the Pats had up their jerseys.
The Patriots had a big points deficit to overcome, but with a lot of luck as well as figuring out how to give Brady time to throw and figuring out how to stop Atlanta's formidable offense, they found a way to win.
Some of it was structural: The Pats offense was on the field a lot and the defenders who sacked and knocked down Brady just got tired out. It wasn't the plan, like Mohammad Ali's "rope-a-dope" but it had the same effects. And it's small things: So many game changing passes were missed in the first half, but not by much. In the second half, the passes were caught--including ones that seemed as if God was in the mix: