by Ben Zauzmer. Ben is a junior majoring in Applied Math at Harvard University and is a member of the Harvard Sports Analysis Collective. This article was originally published at harvardsportsanalysis.org.
In 2012, the NFL created new overtime rules designed to make the game fairer. The league switched from a sudden death setup to an arrangement that allows both teams to have a chance at scoring, unless the first team to receive scores a touchdown. Even with this change, it would seem that a coach should still always elect to receive if he wins the coin toss at the start of overtime, since an opening touchdown drive wins the game.
However, earlier this year, for the first time under the new rules, a coach made exactly the opposite decision. Bill Belichick, the three-time Super Bowl-winning coach of the New England Patriots, made the gutsy call to kick at the start of overtime. Many considered the main factor behind this decision to be the heavy winds at Gillette Stadium (if a team defers the choice of kicking or receiving, it may choose which direction to face). However, kicking first may also give a team better field position on offense and may actually benefit teams with strong defenses.
To calculate which strategy coaches should prefer, we will model NFL overtime as a Markov Chain. We will define our states as the set of possible point differentials, from the perspective of the team that receives the opening kickoff, in overtime: -6, -3, -2, 0, 2, 3, 6. This model inherently assumes that state-to-state probabilities are not conditional, and that the probability of the score differential being 5 or 9 – both technically possible under the new rules – is negligible.
We will let be the transition matrix for the receiving team’s first offensive possession, be the receiving team’s first defensive possession, be every subsequent receiving team offensive drive, and be every subsequent receiving team defensive drive. The first row/column of each matrix represents the receiving team at a -6 scoring difference, and so on until the last row/column is the receiving team at a +6 scoring difference.
The matrices have the following forms:
NFL Overtime Modeled as a Markov Chain
Chargers Courageous Call & Playoff-Clinching Drive
Despite the controversy surrounding an illegal defense on the Chiefs' missed field goal at the end of regulation, the San Diego Chargers defied odds and clinched a postseason berth on Sunday. In overtime, Philip Rivers orchestrated a 17-play, nine-and-a-half minute field goal drive to start the extra quarter that ultimately sealed their win. The length of the drive, in this case, is just as important as the outcome as San Diego could advance with either a win or a tie.
Using our Markov model, let's take a look at the drive. Keep in mind, the model is best used for a standard drive when time and score differential would not greatly affect decision-making or play-calling. Since this was the opening drive of overtime, those standards will predominantly hold true, although not perfectly given the leverage of the situation.
Overtime Field Goal Gaffes Galore
The Vikings ended up in overtime for the second consecutive week, this time against the Chicago Bears. After a quick Bears' three-and-out, the Vikings drove down field to the Bears 21-yard line. The game is now in sudden death format, so a field goal wins it. Unfortunately, in the NFL there is the myth of field goal range. The summation of that article is in bold at the bottom: "Closer is always better."
I first want to mention that field goal kicking has improved dramatically over the last few years, and the two kickers involved in this game (Robbie Gould and Blair Walsh) are among the very best in the league. The Vikings, facing a 3rd-and-10 from the Bears 21, opted to attempt a 39-yarder rather than try to get closer. For Blair Walsh, this is seen as a gimme. In today's NFL, that is about an 87% proposition. Very likely, although still more than a 1-in-10 chance he misses.
The New Overtime Format Is a Complicated Mess--Here's How to Fix It
Dear Competition Committee:
The ostensible purpose of NFL overtime is, first and foremost, to declare a winner and avoid a tie, and second, to do so quickly. If ties were acceptable, I assume the league would not bother to even have overtime.
In recent years, as offenses gradually gained an ever stronger upper hand over defenses, it became clear that the former sudden death format gave too much advantage to the winner of a trivial coin flip. We saw time and time again as a team won the coin toss, got a decent return, earned a couple first downs, and kicked a long field goal without even a whimper from the unlucky loser of the coin flipping contest. Something needed to be done.
And, unfortunately, "something" was done. The current format is a mess because its effects are contrary to both stated purposes of overtime. It increases the chances of a tie while a prolonging the overtime period.
The new rules are complex and non-traditional. In the event the team with first possession scores a field goal, the opponent now has a drive opportunity with all four downs and no pressure of time to respond. And the rules still favor the team that wins the coin toss.
Here is what I think is a much better and far more elegant solution, which is fair, traditional, avoids ties, and leads to much quicker resolutions:
Jets 'Push' Their Luck
After forcing overtime, the Jets stopped the Patriots on their first drive, reverting to the old OT format - sudden death. Geno Smith and the Jets moved downfield before being stopped for a 4th-and-7 from the New England 38. Rex Ryan had three viable options here, keeping in mind that the next score wins: Kick a low-probability (40% league-wide) 55-yard field goal, attempt to convert a low-probability (42% league-wide) 4th-and-7, or punt the ball deep and risk Tom Brady leading a game-winning drive.
The Jets elected to attempt the field goal. Nick Folk missed wide left, but in a crazy turn of events, New England was penalized 15-yards for an unsportsmanlike conduct "pushing" penalty. Before we get to the penalty, let's talk about the decision. While I almost always advocate going for it in no-man's land, in this situation, I was leaning toward the punt.
For this analysis, I used a combination of my Markov probabilities as well as Brian's overtime win probabilities.
Markov Model of Overtime
Last week, Brian offered analysis on the new overtime format, particularly on fourth down decisions. The new OT format is inherently state based, as he mentions, and therefore can be modeled adequately by a Markov chain (thanks to some of the commenters for the idea). The Markov property, which essentially states that we only need the most recent event to predict future events, holds true. If we are in a sudden death state, we don't need to know whether both teams kicked field goals or who even received the opening kick in order to make a prediction about who will win the game.The Set Up
In Brian's post, he discusses three distinct states: Opening of Overtime, The "Matching Field Goal" Drive (where teams get a chance to match or beat after a field goal), and Sudden Death. These will be referred to as Opening, Mid OT, and Sudden Death (SD) respectively from here on. In this Markov model, there will be 10 total states:
Slate: Onside Kicks in the New Overtime Format
I've got an article in Slate today that takes a look at how the new overtime rules might affect the likelihood of onside kicks. My thanks to Josh Levin who had the idea for the article and who jazzed up the prose quite a bit.
The New Overtime Format
The NFL finally admitted its overtime format was broken when it revised the rules to allow a team a possession to match or beat a first-drive field goal. Although I have been shouting from the rooftops that OT was broken, I was not strongly in favor of any particular fix. I thought that adjustments such as returning the kickoff line to the 35 from the 30 would do a lot to reduce or eliminate the advantage the coin-flip winner had, but if the NFL wanted to keep it's sudden death format, there weren't many other good options.
The solution the NFL settled on strikes me as too complicated, and it only partially addresses half of the problem. I'm reminded of my favorite non-sequitur (all too common in politics and public policy):
We have a really big problem. We must do something.
This is something, so we must do this.
Well, the NFL has certainly done something.
New Proposed Overtime Rules
The NFL announced it is considering new overtime rules. The new rules will be considered by the competition committee and, if approved, would be implemented for future playoff games only. I've heard two versions of the proposal, and in this article I'll analyze both.
The version I heard goes like this: the team that loses the coin flip is always guaranteed at least one possession. If the coin-flip winner (which I'll refer to as the 'first team') scores and the second team matches the score, then the game reverts to the sudden death format. If the first team fails to score and the second team does, the second team wins. If the first team scores a field goal, and the second team scores a touchdown, the second team wins.