What's a tie worth in the NFL?

Play for the tie at home, go for the victory on the road.

The Book of Unwritten Baseball Rules, Baseball Digest (1986)

Due to relatively recent rule changes, ties have become a more frequent occurrence in the NFL. From 1974 to 2011, there were 494 overtime games, 17 of which ended in a tie (a rate of 3.4%). From 2012-2016, after the rule change that prevented a team from winning on a first-possession field goal, there were 83 games that went to overtime, and 5 (6.0%) ended in a tie. In 2017, the NFL shortened the overtime period from 15 minutes to 10 minutes. Since 2017, 56 games have gone to overtime, with 4 (7.1%) ending in a tie.

As the game approaches the end of overtime, the team with possession is often faced with a choice:

1. Play for the win: Continue to play aggressively on offense and try to win the game
2. Play for a tie: Burn clock and try to leave your opponent little to no time left to score

When making this decision, I imagine most coaches rough mental math (to the extent there is any) values a tie as a 50/50 split between a win and a loss. 

But is that the correct way to value a tie?

We know it's not correct towards the end of the season, when we start enumerating the various, byzantine playoff scenarios for each team (e.g. "The Cleveland Browns are in the playoffs with a win or a tie against Baltimore, or a loss or a tie from the Titans").

But what about when we're in the middle of the season? For that, we can use the concept of "playoff leverage" to properly assess the value of a tie. Typically, playoff leverage is expressed as how a team's playoff chances vary depending on whether they win or lose a given game. For example, according to my simulations, the Cleveland Browns' chances of making the playoffs will be 74% if they win on Sunday, and 53% if they lose - a swing factor of 21%. Note that we're explicitly ignoring the possibility of a tie here.

Most playoff leverage analyses ignore the impact of a tie, likely because it doesn't get simulated enough (if at all) to reach a reasonable sample size. This can be easily remedied though by deliberately simulating ties a sufficient number of times, and then comparing resulting playoff outcomes. For what follows, a tie is simulated 5,000 times separately for each game this Sunday. This puts ties at a roughly equivalent sample size for wins and losses in my simulations.

Here is an enhanced playoff leverage chart, which shows each team's playoff probabilities in the event of a win, loss, or a tie:

Note that for many teams, the tie "dot" often falls closer to the win or loss dot, rather than squarely in between the two. We can visualize this a bit more straightforwardly by charting the relative value of a tie, compared to a win:

For the Bills, a tie is 0.69 as valuable as a win this Sunday, well above the default 0.50. And on the flip side, a tie is almost as bad as a loss for the Washington Football Team, worth only 20% of a win. In general, teams trailing in the standings see less benefit from a tie, while teams ahead see more benefit. Intuitively, this makes sense, as trailing teams need more "good" things to happen in order to improve their chances. A tie's just not going to cut it.

My goal is to re-run this analysis each week for the upcoming Sunday/Monday games, with the second chart above serving as a nice cheat sheet for overtime decision making.