Chiefs Crawling Drive, Come Away With Nothing

The Chiefs lost to the Broncos 24-17 on Sunday and had a chance to at least tie the game at the very end. Kansas City kept Peyton Manning off the field for an enormous chunk of the second half. The Broncos offense had only two drives after halftime (not including the final kneel down), one for a punt, one for a field goal, totaling just 8:51 in possession. The longest drive came from the Chiefs at the very start of the second half, where they ran 23 plays, taking 10 minutes off the clock... and ultimately missed a field goal. This got me thinking, how does drive length (in minutes) affect the probability of a team scoring?

First, here's a look at the ridiculous drive using our Markov model:

NFL Overtime Modeled as a Markov Chain

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:

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.

Philly Finishes Strong

Up 27-13, the Eagles stopped Green Bay on a 4th-and-4 from the PHI 7-yard line - a huge stop, keeping it a two-score game. But, with a full 9:32 remaining in the 4th quarter, the Packers still had plenty of time to get back in it... or so they thought. The Eagles took over on downs, deep in their own territory. What followed was a masterfully orchestrated, 16-play, 70-yard drive that drained the entire contents of the game clock.

Here we can see the development of the drive using our Markov model:

Packers' Perfect Third Quarter

After a grown-man run from Adrian Peterson to end the first half, the Green Bay Packers opened up the second half up only a touchdown to the dismal Vikings, 24-17. Aaron Rodgers led the Pack on a 16-play, 80-yard touchdown drive that lasted over eight minutes. During the march, Green Bay converted on three third downs and a fourth down. Let's look at the progression of the drive using our Markov model:

Bengals' Big Time Drive

A week after losing to the Cleveland Browns, the Cincinnati Bengals were tasked with taking down the undefeated New England Patriots in Week 5. The game was not enjoyable to watch and had a baseball score of 6-3 heading into the fourth quarter. Needing to separate themselves from the Patriots, the Bengals put together a 15-play, 93-yard, nearly eight minute drive, ultimately scoring a touchdown to go up two scores, 13-3.

Using our Markov model, we can look at the evolution of the drive:

What Are You Doing, Chip?

Cards on the table, I'm a huge Eagles fan. As an NFL stats nerd, I could not have been more excited for Chip Kelly to make the transition to the big leagues. While I did not expect him to immediately institute his Oregon trademarks, I did expect to see him going for it more often on fourth down, especially in situations where the numbers called for it -- and generally, making decisions to maximize the Eagles win probability.

It's four weeks into the season, and too many times I've asked my TV, "What are you doing, Chip?" Today against the Broncos, there were a couple of questionable decisions. Down 14-3, the Eagles were moving the ball very well to start the game. Vick and company strung together a 15-play drive that ended up with a 4th-and-4 from the Broncos 7-yard line. Using our Markov model, we can look at the progression of the drive:

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:

Niners Nine-Minute Drive

Up 28-21 with the ball nearing the end of the third quarter, the Niners had a 78% of winning the game over the streaking Saints. That 78% does not account for the prolific Saints offense, though. What followed was a nine-and-a-half minute drive, lasting deep into the fourth quarter, draining precious time that Drew Brees would need in order to make a comeback. Any Saints fan -- or someone whose fantasy team depends on the Saints offense like myself -- could not have been more frustrated watching the Niners rumble down the field over the course of 17 plays and 85 yards.

Let's take a look at the evolution of the drive using our Markov model:

First Falcons Drive & Botched Bears Field Goal

Andy Reid had never lost coming off a bye week in his head-coaching career. Matt Ryan did not care. Leading the Falcons on a 8 minute 44 second opening drive, Ryan and company marched 80 yards down the field over 18 plays before hitting Drew Davis on a 15-yard touchdown. Up 7-0, the Falcons were 72% favorites to win the game and that probability would never dip below that the rest of the day.

Here is a quick look at Matty Ice's first drive -- on which he went 6 for 7 for 62 yards -- using our Markov model:

Reid's "Gutsy" Call Goes Unnoticed

Down six to the Steelers on the road, Michael Vick and the Eagles took the field near the start of the fourth quarter. After three short gains, the Eagles faced a 4th-and-1 from their own 30-yard line. In today's NFL, this is an easy decision for coaches: Teams punt the ball over 90% of the time. Since there was still significant time remaining in a one score game, it's safe to assume that the Eagles should have performed similarly to a score and time-agnostic situation (although obviously it had some factor in Reid's decision).

Reid was feeling some extra confidence from his tufty moustache, so he decided to go for it. I mentioned it was an easy decision for coaches to punt, but is it the right decision?

Vikings Open & Cardinals Close

On a crazy Sunday with upsets out the wazoo, the most surprising win had to be Christian Ponder and his lowly Vikings taking down the San Francisco 49ers. Minnesota outplayed the Niners from the very start of the game; their opening drive lasted 7 minutes and 40 seconds and went 82 yards over 16 plays for the first score of the game.

The Cardinals dominated the Eagles all game long, but after back-to-back field goals to bring the game within 18 points (why do teams still kick field goals down 21 in the third or fourth quarter?), Arizona needed to seal the win. They did so with a 13-play, six-and-a-half minute drive (including two Eagles timeouts), which resulted in a field goal.

Using our Markov model, let's look at these two game-changing drives.

Colts Win On Minnesota's Miscues

Andrew Luck got his first of what will likely be many career wins on Sunday, with the Colts taking down the Minnesota Vikings on a game-clinching field goal with eight seconds to play. Luck played extremely well throwing for 224 yards on 31 attempts and adding two scores; he notched a formidable +12.9 EPA and +0.67 WPA. What killed the Vikings, however, was not just Luck's play, but penalties. They were penalized 11 times for 105 yards, which may not sound terrible, but they continuously allowed the Colts to continue drives. The biggest of these follies came on the Colts first drive of the second half.

Up 17-6, the Colts took the ball from their own 20 and would ultimately kick a 45-yard field goal. Below we can see the development of the drive using our Markov model.

1-Play Touchdown Probability

In Week 1 last year, Tom Brady connected with Wes Welker for a 99-yard touchdown against the Dolphins. In an effort to determine whether teams actually protect the ball better as they approach the goal line, we recently looked at 1-play fumble and interception probabilities (also known as transition probabilities from our Markov model). Out of all our absorption probabilities, only fumble, interception and touchdown really make sense to examine on a 1-play basis across downs. Punts and field goals almost always occur on 4th down (turnover on downs always occur on 4th down) and while a safety can occur on any down, they occur extremely infrequently.

In 2011, 37.7% of all offensive touchdowns occurred on 1st down, 33.0% on 2nd down, 25.0% on 3rd down and 4.3% on 4th down. This makes logical sense as there will be more 1st downs than 2nd downs, more 2nd downs than 3rd downs, and so on. But, how does down affect the probability of scoring a touchdown on the next play? Do teams take (and successfully convert) more shots downfield on 1st down than later in the drive?

Absorptions Over Expectation

Another thing we can look using our updated Markov model is how teams were expected to perform based on where they took over on the field. In other words, based on starting field position, how many touchdowns was a team expected to score on the year? And further, how many touchdowns did they actually score.

Not surprisingly, New Orleans, Green Bay and New England were the top three offenses in terms of touchdowns scored above expectation. Drew Brees and the Saints scored just shy of 26 additional touchdowns above expectation at the start of their drives. That's a whopping 182 points. By comparison, the St. Louis Rams scored 193 points total in 2011.

Click here to see the full table of expected number of each drive-ending state based on starting field position over the course of 2011 for each team.

San Francisco was given the most advantageous starts, which should have resulted in about 31 field goals and 47 touchdowns on average. Akers kicked a record 44 field goals but SF scored a miserable 32 offensive TDs. Other notable expectations are the Broncos' expected 104 punts and Giants' expected 102 punts, the most and second-most in the league.

Modifying The Markov Model

Last season, we revealed our Markov model of a football drive outlined here. 

All of the same math and logic still apply, but this offseason we updated the model to reflect some previous weaknesses.

Check out the Markov Calculator Tool and model results here.

More Falcons' 4th-Down Decisions

Earlier this year, the Falcons were criticized for going for it on 4th down and failing to convert against the Saints in OT.  Mike Smith was crucified for his "incorrect" decision.  But, as Brian wrote, his decision was correct.  A decision cannot be evaluated based on the outcome, but rather the theoretical expectation of the choice itself.  This week against the Giants, Mike Smith was faced with several 4th-down decision throughout the course of the game.  The first came at the end of a 14-play, 66-yard drive at the start of the 2nd quarter.  Using our Markov model, we can look at how the drive developed:

Jets Lose on Dolphins' Epic Drive

The Dolphins, with nothing to play for but respect, eliminated their division rival Jets from playoff contention on Sunday.  Miami was down 10-6 with 7:56 left in the 3rd when they went on an epic 94-yard, 21-play, 12+ minute go-ahead drive.  Yes, a 21-play drive, tiring out Rex Ryan's prized defense.  Highlighted by six 3rd down conversions, there was a 73% chance of the drive ending in a punt and only 6% chance of a TD on 3rd-and-9 from their own 7-yardline (Play 3).  Using our Markov model, we can see the progression of the drive - and the progression of the Jets' demise.

Chiefs' Conflicting 4th Down Decisions

In this tumultuous Week 15, we saw the winless Colts beat the Titans, the seemingly unstoppable Packers lose to a floundering Chiefs team, and his holiness, Tim Tebow, lose for the first time in 7 games.  Kansas City jumped out to a 6-0 lead with two early field goals, but just as importantly, kept the ball out of Aaron Rodgers' hands by sustaining long drives.  The Chiefs' first three drives totaled 38 plays consuming over 19 minutes of game clock.  Newly anointed interim head coach Romeo Crennel was also faced with a few early 4th-down decisions.  Using our Markov model, we can see how these drives developed.

The Chiefs received the opening kickoff and proceeded to drive 79 yards on 14 plays, not letting the Packers offense take the field until six minutes had already run off the clock.  Here is a look at how the probabilities developed throughout the drive:

Lions Take The Field Goal

Despite all the Tebow-madness, there were quite a few other games decided in the waning seconds.  With 0:26 left in the game, Joe Webb and the Vikings were faced with a 4th-and-6 from the Detroit 12, down 6.  If the Vikings were only down 3, this is a no brainer: Kicking the field goal results in a win probability of 43% versus only 33% if they go for it.  Detroit, however, had tacked on a field goal early in the 4th quarter and their defense came up huge, stopping Webb at the goal line (ignoring any questionably missed face mask calls on the last play of the game).  Let's take a look at Detroits' last scoring drive.

With 4:21 left in the 3rd, Matthew Stafford led a 7-minute procession that began on his own 10-yardline.  The Lions converted on three separate 3rd-downs to keep the drive alive, the biggest of which was a 25-yard completion to Titus Young on 3rd-and-1 from their own 19.  Using our Markov model, we can see how the drive developed: