Note: You may have already read some of this in my contribution to Peter King's Monday Morning Quarterback column this morning. You can hear Dan Patrick and Peter King talk about the topic at this link (about 25 min into the 40-minute clip).
First, some facts.
Over the past decade, there were 158 OT games, including playoff games. There were 2 ties, and there was 1 game in which the coin flip winner chose to defend a side of the field rather than choosing to receive. (They lost.)
In 96 of the 158 OTs, or 61%, the coin flip winner won the game.
In 58 of the 158 OTs, or 37%, the coin flip winner won on their first possession while the loser never touched the ball. This includes 2 of the last 3 OT games in the playoffs.
Don’t be fooled by other numbers. In 2009 there happened to be only 13 OT games, and the coin flip winner won 7 (54%). In 6 of the 13 (46%), the loser never touched the ball. The sample size for any single year is too small for a reasonable estimate of the true numbers.
Also, don’t be tricked by people that say “only 61%.” If we agree 50% would be the fairest rate, you might think 61% isn’t very far from 50%. But that’s not the right way to look at it. As I wrote in my recent NY Times post, the correct comparison is 61% vs. 39%, the respective winning percentages of the coin flip winner and loser. That’s a big advantage--over 3:2. Another way to think of it is that the coin flip winner will win half again more often than the coin flip loser.
I've written previously that I favor a simple solution, which I first heard from economist David Romer: Return the kickoff line to the 35 for the OT kickoff. This is a modest change that will greatly increase touchbacks, forcing offenses to start at the 20. And in OT, a 1st down on the 20 yd-line (and not the 15 as previously thought) appears to be the break-even point between where the team on offense and the team on defense are equally likely to score next. I'd guess that teams may tend to play "tighter" in OT than in regulation, and this is why the break-even point becomes the 20.
The graph below plots OT Win Probability (WP) by 1st down field position. In OT, with the rare exception of the final meaningful possession in an eventual tie, time is not a significant factor.
The data is a little noisy, but the unscientific fat red crayon technique makes it fairly clear that the 0.50 WP line intersects at a team's own 20 or so. The 0.61 WP line, which represents the current expected winning percentage of the coin flip winner, intercepts the red line at about the 33-yard line, which is where the average return ends up (including penalties and TD returns).
Moving the kickoff line back to the 35, where it was when the current OT format was instituted, might go a long way toward equalizing the chances of the coin flip winner and loser. Unfortunately, that's only half the problem. Over one third of OT games result in one team losing the game without ever touching the ball. I think that's the bigger issue to many people.
Moving the kickoff line would reduce the likelihood that one team would never get the ball, but only slightly. I don't think we can solve that part of the problem without a rule requiring an even number of possessions. But such a solution causes a whole new problem.
However the specifics of the even-possession rule would work, the team with the second possession would have an even bigger advantage than the coin-flip winner has now. Knowing whether or not it needs a TD, FG, or can afford to punt, the second team can adjust its strategy accordingly, using its 4th downs to move the ball when necessary. The current college OT format has this problem, which is mitigated to some degree because teams alternate 'going first' on successive rounds. Even baseball's extra innings format has the same problem to a lesser extent, but it's accepted because it's no different than the advantage the home team enjoys in a tied 9th inning. It's simply considered part of home field advantage in baseball.
There is no perfect solution for NFL's overtime problem, but perhaps baseball's system illuminates the best path. Maybe the best we could hope for is to keep the current sudden death format, but award the first OT possession to the home team.
With this arrangement in the playoffs, it would be easier to accept what happened to a visiting team like the Vikings. We would say, "Yeah, it stinks their offense didn't get a chance. But hey, the Saints did earn the right to the first possession by winning home field during the season." Better that a team earns a break than has it bestowed by the flip of a coin.