In order to produce my playoff seed projections for the NFL, I had to do some rather tedious coding of the tiebreaker rules. For example, here are the divisional tiebreaker rules when two teams have the same win-loss-tie record:
1. Head-to-head (best won-lost-tied percentage in games between the clubs).
2. Best won-lost-tied percentage in games played within the division.
3. Best won-lost-tied percentage in common games.
4. Best won-lost-tied percentage in games played within the conference.
5. Strength of victory.
6. Strength of schedule.
7. Best combined ranking among conference teams in points scored and points allowed.
8. Best combined ranking among all teams in points scored and points allowed.
9. Best net points in common games.
10. Best net points in all games.
11. Best net touchdowns in all games.
12. Coin toss
Most casual fans are aware of the implications head-to-head, divisional records, and conference records have for playoff seeding. But things get pretty esoteric as you move further down the list. I had to look up what "Strength of Victory" meant (it's the combined winning percentage of the opponents you beat), and frankly had to make a bit of a guess as to what "combined ranking" meant for #7 and #8. At the very bottom of the list is "Coin Toss", which I even went through the trouble of simulating with a random number generator.

But could the "Coin Toss" scenario ever come in to play? (doubtful) Would ESPN televise it? (probably) Should they have replaced "Coin Toss" with "Dance Off"? (definitely)

Thanks to my borderline-OCD determination to code each tiebreaker scenario, I can attempt to answer the first question. My playoff projections are based on a 10,000 run Monte Carlo simulation, so it was easy enough to output how frequently each tiebreaker was actually used. The table below summarizes the frequency (per simulated season) of each tiebreaker rule.

tiebreakerfrequency
conference record3.1433
common games1.3530
division record1.2119
strength of victory0.7248
strength of schedule0.0375
points rank (conf)0.0030
points rank0.0001
net points in common games0.0000
net points0.0000
net touchdowns0.0000
coin toss0.0000

Not too surprisingly, head to head was the most commonly applied tiebreaker. In 10,000 simulated seasons, the "Combined ranking among all teams in points scored and allowed" tiebreaker was only needed once. And the remaining three (net points in common game, net points, and net touchdowns) were never used, making it highly unlikely that a playoff seed would ever come down to a coin toss; unless, of course, the NFL manages to stick around for the next 100,000 years. Not that I'd put it past them.