Almost Kicking Away a Chance at the Playoffs - Green Bay at Chicago - December 29, 2013

With the NFC North title on the line, the Green Bay Packers came back from a 28-20 deficit against the rival Chicago Bears.  Quarterback Aaron Rodgers, in his first game back from a fractured collarbone, drove the Packers from their own 13 yard line for the winning touchdown to receiver Randall Cobb, also back from injury.  A thrilling finish, one which I watched alongside many Packers fans in a bar in Wisconsin.  (Also at the same time, the Chargers were completing their own comeback, also for a playoff spot)

The Packers comeback almost didn't happen.   Coach Mike McCarthy almost prevented his own team from this comeback by sending out the punt team on a 4th-and-1 situation in their own half of the field. His offense had to talk him out of punting and go for it.  The linked nfl.com article calls it a gamble.  Many others in the bar thought it was an obvious play.

So was it a gamble, the right call, or could it go either way?

The Situation

Losing by 1 point, 28-27, with 4:41 to go in the game, the Packers face a 4th-and-1 at their own 22 yard line. This game is basically a playoff game, with the winner earning a spot in the playoffs as NFC North Champions, and the loser going home.  What should the Packers do in this spot?  To figure this out, we need to see what the Win Probability (WP) of each decision, to punt or to go for it.  We need to look at several factors to see what the right decision is.

The Factors

Coaches and fans can talk about "trusting their defense" or "pinning the other team back", but it basically comes down to several probabilities:

1. The probability of success on this 4th down and 1.
2. The probability of winning the game, given a conversion on this 4th and 1.
3. The probability of winning the game, given a punt to the Bears.

While we might not be completely accurate with these numbers, we can put in some estimates and see which decision gives the best chance of the Packers winning.  To get some ballpark figures, we will once again go to our friends at Advanced NFL Stats.

When NOT to score - Pittsburgh at Green Bay - December 22, 2013

Outside of sportsmanship purposes, is it ever right to NOT go for the most expected points?  Should there be a time when you tell your team to NOT score a touchdown?  If that's true, then wouldn't the defensive team WANT you to score a touchdown?  This scenario came up again in Week 16 of 2013 with the Pittsburgh Steelers visiting the Green Bay Packers at Lambeau Field.

The Situation

Pittsburgh and Green Bay are tied up, 31-31 in the 4th quarter.  On the first play after the 2 minute warning, Steelers safety Troy Polamalu forces a Matt Flynn fumble, recovered by Brett Keisel who returns it to the Packers' 17 yard line.  

The Steelers now have the ball with 1:51 left in the game.  The Packers have all 3 timeouts remaining.  Knowing that a score is highly likely, the Packers proceed to use their timeouts in an attempt to get more time on the clock for a comeback once the Steelers score.

The situation is a favorable one, as they force a 4th and 3 at the 10 yard line with 1:35 left in the game and the field goal team trots out to attempt a 28 yard field goal.  A field goal here would give the Packers over a minute left to tie or win the game and the Packers still have 1 timeout left.  However, an encroachment penalty gives the Steelers an automatic 1st down at the 5 yard line.

At this point, the question is: Should the Steelers intentionally not score until the last second, so they prevent any chance at a Packers comeback?  If this it true, then should the Packers intentionally allow the Steelers to score?  Remember, what's bad for my opponent must be good for me.

What should the Steelers do in this case?

Jamaal Charles Passes to Himself - Real or Fake?

There's a video of Kansas City Chief running back Jamaal Charles in Pumas catching his own 45 yard pass. 

This is a pretty awesome feat for anyone, including NFL players.  Charles is one of the best backs in the NFL and (as a former track star) a very fast guy, but since we never saw the ball actually leave his hand, nor did we see it in flight until he catches it, could it have been faked?  Is it actually possible for him to have caught his own pass 45 yards down the field?  This isn't a feat made to look obviously fake, like Michael Vick throwing a ball out of the stadium, but is something that is in the realm of possibility.  Let’s look at the physics behind what he did.

There are two factors to look at in determining whether this feat is possible or not.  Can Charles realistically run that fast and can Charles throw that ball that high and far?

Let's see if our analysis can help determine if this is possible or not.  Warning, lots of math ahead!

Going for Two. Washington at Atlanta December 15, 2013

Washington coach Mike Shanahan gets the opportunity go for the win in regulation and takes it, going for a 2 point conversion instead of electing to take a PAT and take his chances in Overtime.  QB Kirk Cousins misses the pass and Washington loses to the Atlanta Falcons 26-27.  Regardless of the result, was this the right decision?

The Situation

Down 20-27, Washington QB Kirk Cousins completes a TD pass to WR Santana Moss, pulling the team within 1 point.  There are 18 seconds left in the game, so whatever happens here is highly likely to be the final outcome of regulation.  Coach Shanahan decides to go for a 2 point conversion.  Was this the right move?

This is a relatively simple situation to analyze since there are only a couple of possibilities.

If Washington goes for the PAT, they will go to overtime 98% of the time historically.  That's close enough to 100% for our purposes.  In overtime, there is nominally a 50/50 chance of winning the game.

If Washington goes for the 2PAT, they will convert and win the game x% of the time and lose the game 100-x% of the time.  What is x actually?

Taking the Points, Part II - Miami vs. New England, December 15, 2013

The Miami Dolphins once again faced a "close" 4th down decision nearing halftime of the New England @ Miami tilt in week 15.  Down, 0-3, Miami decided to attempt a field goal, as color announcer Phil Simms said, "It looks like it's a whole yard short ... it's a good decision by the Dolphins [to go for the field goal].  Get on the scoreboard, Jim [Nantz], there nothing worse for a QB or coach to look up at that scoreboard and see that 0."

Was Simms right?  Is it better to kick the field goal here?

The Situation

After the 3rd down pass to Michael Egnew falls short of the line to gain, the Dolphins face 4th down and a long yard (one closer to 2 yards than 0 yards) on the New England 24 yard line with 3:34 left in the first half.  Out trots the FG team and Simms claims it's good to get the points on the board rather than to walk away with nothing.  However, the game of football doesn't care if you score points, you need to out score the opponent, and in this situation, you should maximize the number of Expected Points you're going to get.

So how do we calculate whether it was the right decision to kick the field goal or not?

The Factors

We have to look at several factors to determine whether or not attempting a field goal is the right move here.  Of course, we are simplifying some of these percentages, but if there is an obvious decision, that won't change with fine tuning of these numbers.

1) What is the chance kicker Caleb Sturgis will make the 42 yard field goal attempt?

2) What is the chance Miami will convert this 4th and 1 attempt?

3) If Miami makes the 4th and 1, what are the expected number of points they can expect from this drive?

4) When New England recovers the ball, either after a failed FG try, failed 4th down try, or after a kickoff following a Miami TD, what is their chances of scoring?

Taking the Points - Less Likely to Win? Miami at Pittsburgh December 8, 2013

Conventional Wisdom says to take the points, especially when taking "gimme" points makes your lead go from 3 points to 6 points and forces your opponent to score a touchdown to win the game, rather than being able to tie the game with a field goal.  Depending on the situation, is this always right?  Should you be taking the "gimme" points in this situation at all times?

The Situation

Miami has the ball and is leading Pittsburgh 31-28.  It's 4th and goal on the Pittsburgh 9 yard line and 1:12 left to go in the game.  The obvious play is to kick the field goal, which they do, and they now lead 34-28.  However, on 4th down, with 3 seconds left, the Steelers complete a near miracle 5-lateral play to score a touchdown.  However, Antonio Brown stepped out of bounds on his way to the end zone, ending the game and allowing Miami to escape with a win.

Antonio Brown steps out of bounds before finding paydirt

The fact that Miami won overlooks the 4th and 9 decision a minute before.  Was it the right decision?

The decision comes down to whether the Dolphins should kick the field goal, or run a play on 4th down.

The Factors

There are several factors which can help us decide the right course of action, some are more relevant than others depending on the decision made.  We will look at all probabilities from the Dolphin's point of view.

• What is the probability of making the field goal?
• Given the field goal is made, what is the probability you will win the game?
• If the field goal is not made, what is the probability you will still win the game?
• What is the probability of scoring a touchdown?
• What is the probability of winning the game if you score a touchdown?
• What is the probability of winning the game if you don't score a touchdown?

All factors can be boiled down into one of the preceding factors.  For example, how well your defense is playing or how well the opposing kickoff return unit is playing, all can be taken into account with the above factors.

The Calculations

To determine the best course of action, we need to calculate the total win probability for each action, then figure out which decision is more likely to win the game.  With the game nearly over, the important metric is Win Probability (WP), not Expected Points (EP).  Expected Points is something coaches should be looking to maximize early in the game as it's highly correlated with WP, but by the end of the game, EP and WP can diverge quite a bit.  

Trusting your Kicker - Part 2 - Trestman defends his decision, again with binary thinking

Marc Trestman defended his decision to have Robbie Gould try the 47 yard field goal.  Again, as pointed out in yesterday's entry, he's falling victim to binary thinking.

If you are in the habit of evaluating 72% chances (as Gould's history of making those kicks are) as 100% chance, there's a pretty bad process of thinking going on.

Trusting your Kicker - Levels of Probability - CHI at MIN December 1, 2013

The Situation

In Sudden Death Overtime, Chicago has the ball and is driving after a Minnesota missed field goal (well, kicker Blair Walsh actually made one attempt, but was called back due to a stupid face mask penalty).  

On 2nd down and 7 at the Minnesota 29 yard line, coach Marc Trestman elects to have kicker Robbie Gould try a game winning 47 yard field goal.  Was this the right move?

On CBS, former Ravens coach and current color commentator Brian Billick agreed with Trestman, saying something to the effect of deciding what yard line your kicker can make the kick from, get it there, center the ball, then trust your kicker to make the kick.  Billick basically means the 30 yard line is a plenty good position to kick from, so instead of trying to get more yards, try to kick the FG now and now have anything bad happen.

Why would he say that?

Binary Thinking

Once the offense is in "field goal range," especially in a sudden death situation, most coaches go ultra conservative, making sure the ball isn't turned over.  These coaches decide what "field goal range" is for their kicker, then once they cross that line, worry more about keeping possession, centering the ball and the time on the clock rather than the distance to be kicked.  This is an example of binary thinking, where the kick can be made at one distance, but missed at another distance.  In reality, kickers make shorter kicks with more frequency than longer kicks (duh).  So, why are coaches thinking this way?

The reason coaches engaging in binary thinking decide to kick "too early", is because giving up possession on a potential game winning drive is a disaster.  They decide to turtle up and take the long field goal try, rather than trying to get closer.  Coaches in this situation also typically kick on 3rd down instead of 4th, just in case there's a bad snap or botched hold.

A broad analysis of field goals at the 45-49 yard distance shows a 68.6% chance of making the kick. Since 68.6 is more than 50%, surely it's the right move, right?

Given this number, why would any coach try to move the ball down the field further?  What are the benefits and costs of trying to move the ball down the field further, particularly in this sudden death situation?  

Third Quarter Decisions. One good, one bad

Week 13

Tennessee losing to Indianapolis 7-12 in the 3rd quarter 8:04 left to go.  They've been stuffed up to this point and are now at 4th and goal on the 1/2 yard line.  Play call is bootleg - pass, Touchdown and now they're up 14-12 (though as you know, I would have gone for two there)

NY Jets losing to Miami at home 0-13 in the 3rd quarter, 4:30 left to go.  4th down and 1.  Rex Ryan opts to kick the Field Goal here.  Sure, let's not have any faith in your offense.  Game over.

Edit: Miami goes down and scores a TD to make it 20-3 now.

Who Should be Calling Timeouts? A Simplified Bayes Theorem problem - PIT @ BAL, Thursday November 28, 2013

In an individual game, football is a zero-sum game.  Whatever is good for me is bad for my opponent, and whatever is bad for me is good for my opponent.  So, if I should call a timeout, my opponent definitely shouldn't, right?  What do the announcers think?

Down by 8 points with under 4 minutes to go, the Pittsburgh Steelers need to score a Touchdown and convert a 2 point conversion (2PAT) just to tie it up and potentially send the game to overtime.

The Situation

Pittsburgh is behind Baltimore 14-22 with under 2 minutes left to go in the game.  They need a touchdown and a 2PAT just to tie and potentially send the game to overtime.  Steelers QB Ben Roethlisberger threw an apparent touchdown pass to Heath Miller at 1:52 left, but the replay official rules he was down at the 1/2 yard line.  Announcer Cris Collinsworth remarks that it's a good thing the Steelers haven't scored yet since it allows them to burn some more time off the clock, presumably so if they score, the Ravens can't come back and win the game.  When he said that, the message board I was following at the time blew up and said how wrong he was in case the Steelers don't convert the 2PAT.

After a run for no gain, Baltimore takes its last timeout with 1:32 left.  Should they have taken that timeout?  If not, should the Steelers have done so with 2 timeouts remaining?

This leaves the Steelers with potentially conflicting goals.  If they do tie the game, they want to take as much time off the clock.  However, if they fail to do so, they want as much time on the clock as possible if they recover an onside kick to try to win.

The Factors

The most important, and obvious, factor is whether Pittsburgh can score or not.  However, this point is entirely moot.  At the 1 yard line, even with only 1:32 left, the clock is not the enemy.  Also, if the Steelers can't score in 3 more downs, it doesn't matter whether what's left on the clock since the Ravens will be able to run out the clock.

Another factor is the likelihood the Steelers will recover an obvious onside kick.  This number is less than 20% (to be generous).  If the Steelers don't recover the kick, then the clock doesn't matter.

Ben Watson and the Pythagorean Theorem - AFC Divisional Game Patriots vs. Broncos Jan 14, 2006

The 2005 divisional playoff game (January 14, 2006) between the Patriots and the Broncos featured Patriots TE Ben Watson making one of the greatest hustle plays I had ever seen in my life.  Watch below:

 

A great play, though ultimately for naught as Denver maintained possession at the 1 yard line and would ultimately punch it in on a Mike Anderson TD run.  New England would go on to lose the game, snapping Tom Brady's streak of 10 playoff wins without a loss.

How Far Did Ben Watson Run?

Linebacker Tedy Bruschi said, "We saw Ben was on the other side of the field so he basically had to run like 120 yards, even longer than that, to get that."

A great hustle play for sure, but how far did Ben Watson actually run on that play, and how much further did he go than Champ Bailey, one of the fastest players in the NFL?

Positioning of Watson and Bailey at the time of the interception

Playing not to lose in OT? Packers vs. Vikings Nov. 24, 2013

My buddies give me a lot of flack for suggesting to always go for it on 4th down or for a 2 point conversion, so when my instincts said to kick a field goal, but my friend Tony wanted to go for it, I had to take a step back and see if I was wrong. Even though Tony likes trolling, I think he might be onto something.

The situation: 

Green Bay Packers have the ball at 4th down and Goal at the 2 1/2 yard line in overtime.  This is the first possession in OT, so a field goal does not win the game for the Pack outright but gives the Vikings a shot at matching.  Scoring a touchdown ends the game right there for the home team Packers.

The question: What decision gives the Packers the best chance to win the game?  Going for the touchdown, or kicking the field goal?  How do we decide this?

The first question we have to ask is what factors do we have to consider to make this decision?  There are many, many factors that can go into this calculation.  For example, how good is your offense?  How good is the opponent's offense? How good is your kicker?  Do you have momentum on your side?  It would be impossible to evaluate the effect of each of these factors perfectly, but ultimately, they boil down into one of 4 factors:

1) What is the probability of making the field goal?
2) What is the probability of scoring a touchdown?
3) What is the probability of winning the game, if you go for a touchdown and miss?
4) What is the probability of winning the game if you attempt a field goal?

The coaches know (or SHOULD know) this information very, very well.  Even if they can't perfectly quantify it, their gut instinct is usually pretty good at figuring out these percentages.  However, if they're off, then the future calculations might be off as well.

The second part to this decision is how does the math shake out once we figure out what are the relevant factors. Even if one decision is "too risky", is the other decision the better choice, or is it even riskier?  While we won't be able to 100% accurately figure out the percentages, we can at least attempt to decide the best course of action, given the information we have.

Ultimately, we need to look at the chances of winning (or Win Probability, abbreviated WP) of each decision.

if WP(Field Goal) > WP(going for it), then the Packers should have kicked.
if WP(Field Goal) < WP(going for it), then the Packers should have went for it.
if WP(Field Goal) = WP(going for it), then it doesn't really matter either way.

Welcome!

This blog will attempt to simplify NFL mathematics, to see whether or not coaches are making the right decision given many factors.  While it's impossible to accurately estimate all the factors (and their probabilities) involved, we can see how decisions and probabilities can change potential decisions depending on those factors.

From there, we can look at the probabilities of success given the options available.  Of course, even if the right decision is made, an unfavorable outcome may occur.  The opposite is also possible, a team could make an incorrect decision and have a favorable outcome occur.  Certain numbers may be simplified to get a "general idea" of things.

We will also try to take away emotional decisions like "momentum" and "trusting your defense" instead choosing to try to quantify those if possible.

If you're a math or statistics teacher, please feel free to use material from this blog in writing lesson plans or for classroom examples.

Comments are welcome, please keep them civil.