College Football Overtime Strategy

Upon winning the coin toss for overtime in a college football game, I have never witnessed a team choosing to go on offense first. Every single time I've seen such a game, the team who won the coin toss has elected to go on defense first. The reason for this is it gives them the last chance in the first overtime and through that, provides them with the necessary information on what they will need to do on their possession in order to either win the game or move it to a second overtime. If the opposing team scores a field goal on their possession, the team who elected to go on defense first will then know they'll need a field goal to send the game to a second overtime or a touchdown to win in the first overtime. 

I understand that, but think I would go about things differently if I were a college coach. It depends on location. If my team were playing at home, I would elect to go on defense first. I'd trust that the crowd would add extra pressure on the opponent on their first (and hopefully only) possession in the extra session, and provide my team with a significant advantage due to that. If my team were playing on the road, however, I may opt to go on offense first. I'd want to ease the pressure off my team and place it on the opponent. In a tough road environment, if I elected to go on defense first and my opponent scored a touchdown, it'd be doubly difficult for my team to tie the game and send it to a second overtime. 

It's like in baseball. Is it nice being the home team and if the game is tied in the 9th inning, to be given the final at bats in the game before potentially heading to extra innings? Of course. However, if I had a choice between being up a run going to the bottom of the 9th inning on the road or being down a run going to the bottom of the 9th at home, I'd choose the former over the latter. To all these college football coaches, it's just about numbers in terms of scoring and knowing what they need to win the game or send it to another overtime. From my perspective, it's about numbers in terms of odds and probability of winning. I'd be very curious to see such numbers in overtime games - how teams have fared when playing defense in the first overtime, and if the results differed any on the road versus at home.