Sunday, July 23, 2017

GOING FOR TWO---A PRACTICAL GUIDE FOR NFL COACHES



INTRODUCTION---THE BASICS

From 2001 to 2016, the two-point conversion rate in regular-season NFL games was 47.2% (481/1018).  The conversion rate for one-point conversions approached 99% during this period, but the NFL then pushed back the line of scrimmage to the 15 yard line, for extra-point kicks, in the 2015 season.  This dropped the success rate on one-point conversions to 94%, which is almost exactly double the success rate of two-point conversions.  Thus, the result of this rule change is that the “expected points” to be gained from either type of conversion are now the same.  It’s either 94% of 1 or 47% of two---in either case, the expectation is .94 points.

This has changed everything.

If the goal is to maximize the points you will score, there is now no difference between kicking or going for two.  Over the course of a season, a team that goes for two after every touchdown can expect to score the same number of points as it would by kicking.  Thus, the only reason to prefer one over the other is tactical, and a coach cannot properly be criticized for choosing one or the other, except in those situations where tactical considerations prevail.  If you’re down eight and you score a TD with three seconds left in the fourth quarter, you must go for two or you will be fired.  If it happens with three seconds left in the first quarter, do what you like.  Nobody will care, or at least nobody should care.  In the first quarter, kicking an extra point is never a mistake, and neither is going for two.

Another fundamental reality underlying the one-or-two-point conversion decision is the dominance of the home team in overtime games.  For the period from 2007 to 2016, in the regular season, home teams won 1467 of 2556 games (57.4%).  We all know there is a home-field advantage, of course, but what is little understood is that the advantage persists even when the two teams end the first sixty minutes in a tie.  The home team still wins 56.5% of these games (87 of 154).

Why is this home-team dominance in OT significant in the conversion decision?  The best illustration comes in the classic go-for-two scenario.  The Jets, on the road, trail the Raiders by 7 and score on the last play of regulation.   Do they kick the point and take their chances in OT or do they go for two to win it (or lose it), in regulation?  The home/away OT stats suggest that a road team should normally go for two in this situation since they have a 47% chance of making the two-point conversion but only a 43.5% chance of winning in OT.

Other factors can affect this particular end-of-game decision, of course.  Any coach, either at home or away, may identify factors at that moment that must be considered in deciding whether to go for two.  If the Raiders are reduced to their emergency quarterback, or have their all-pro shutdown corner nursing a bad knee, it might be wiser for the Jets to try the kick and head for OT.  If there are key Jets injured, it may be best to take the one shot at winning.  Win or lose, they will get to go home without sustaining more damage.

In the course of this guide, the inherent edge of the home team in overtime will appear again and again.  OT is no bargain for a road team and should be avoided if at all possible, even if it means increasing the chance of losing in regulation. 

Coaches faced with a one-or-two decision will make the wrong choice for many reasons.  (Trying to get to OT when they should really be trying to win the game is just one of them.)  Perhaps the biggest reason a coach will get this wrong is that he is routinely brutalized by the sports media whenever he makes a binary decision that leads immediately to a bad result.

If a coach punts on 4th-and-1 with three minutes left and loses, he was “too conservative.”  If he runs a play in the same situation, fails to make a first down, and loses the game, he “took a big chance.”  A coach will never be criticized for kicking an extra point with a minute left in the game in order to get to overtime, but if he goes for two and misses, somebody in the media will demand he be fired.  I have never seen a reasoned analysis of one of these decisions in the Monday sports section.  Never.  Thus, many decisions by coaches are made with a view to avoiding criticism from the press and the mass of football fans who don’t understand this stuff either.

Yet another reason coaches muff the conversion decision is that making them is a tiny fraction of a very difficult job, and the considerations involved have little in common with the rest of their duties.  NFL coaches are primarily managers and not “game players.”  Most do not actually play a lot of games like poker or backgammon or scrabble or chess.  (Pardon the generalization.) They are more like military leaders whose job it is to lead men into battle.  It is difficult to harness the energy, intelligence and aggression of fifty large men who enjoy violence and have few manners, but that is an essential task of an NFL coach.  “Gosh, I wonder if I should kick or go for two” is just not a priority.

Then, once he has performed his management tasks, gotten all his players “on the same page,” and adjusted their testosterone levels to workable parameters, his other near-impossible job is to make instantaneous decisions in the fast-moving and ever-changing environment that is a football game.

In a particular game situation, for a particular play, the decision on whether to run a cover-3 pass defense or a man-to-man scheme is a judgment call that must be made in seconds.  There are no charts to tell the coach what to do.   And while he and his assistant coaches may review these decisions when the game is over, there is no alternative, in the moment, to “going with his gut” because there is no time to assess the alternatives in some methodical and logical fashion.  His “gut” is what his twenty years of football experience tells him to do in that moment, with that down and yardage, with that time remaining in the half or the game, against that opponent on that day.  These are what I would call “football decisions” because the knowledge that goes into making them is specific to the game of football.

But there are other kinds of decisions as well.  In almost every game, including football, there are some decisions to be made that have a correct and an incorrect answer.  Let’s call these “game decisions” since by their nature, they are not unique to football or Parcheesi or bridge.  If your blackjack hand totals 20, you stand.  If you have 13 and the dealer is showing a king, you hit.  By making these plays, you maximize your chances of winning.  To do otherwise is demonstrably wrong; in the game context, you reduce your chance of winning.

No one can dispute there are such moments in football.  If you trail by 8 points and you score a touchdown on the last play of regulation, you may kick an extra point, but you would be wrong to do so since it would ensure your defeat.  There are many other situations in football, however, where the answer (and the math), is just as clear, but coaches don’t know what to do. 

After a game, a coach will often be asked why, in a particular spot, he chose to punt, or kick a field goal, or try a two-point conversion.  To this, many coaches (e.g., Mike Tomlin) will reply, “I went with my gut.”  This is the uniform response for those who 1) know a lot about football, 2) know nothing about math, and 3) do not know how to think logically about “game decisions.” 

The problem is that these game decisions arise regularly, and they are often important.  There are always binary decisions to be made that have a correct and an incorrect answer, and if you “going with your gut,” you will often get them wrong.  On 4th down, do you punt or try to retain possession by running a play?  Do you kick a field goal or try for a first down?  There is usually a right answer to these questions, and even where there is an element of judgment involved, the judgment component is typically much smaller than coaches want to believe.

For coaches, the attraction of “I went with my gut” is that it can never be second-guessed.  If how you feel at the moment is the correct basis for a decision, then nobody can call you an idiot later on.  The problem is that it doesn’t matter what your gut tells you when the question is what two and two add up to.

But not every coach “goes by his gut” in every situation.  Recognizing (in a general way), that there are right and wrong decisions about these questions, and also recognizing that the pressure of the moment may make it difficult to think clearly or remember the right move, many coaches carry a chart telling them whether to go for one or two in various situations (i.e, up two points, down four points, etc.).  The original of these charts, which is still in use by some coaches, was created by Dick Vermeil when he was offensive coordinator for Tommy Prothro at UCLA in 1970. 


LEAD BY
TRAIL BY
1 point
Go for 2
1 point
Go for 2
2 points
Go for 1
2 points
Go for 2
3 points
Go for 1
3 points
Go for 1
4 points
Go for 2
4 points
Decision
5 points
Go for 2
5 points
Go for 2
6 points
Go for 1
6 points
Go for 1
7 points
Go for 1
7 points
Go for 1
8 points
Go for 1
8 points
Go for 1
9 points
Go for 1
9 points
Go for 2
10 points
Go for 1
10 points
Go for 1
11 points
Go for 1
11 points
Go for 2
12 points
Go for 2
12 points
Go for 2
13 points
Go for 1
13 points
Go for 1
14 points
Go for 1
14 points
Go for 1
15 points
Go for 2
15 points
Go for 1
16 points
Go for 1
16 points
Go for 2
17 points
Go for 1
17 points
Go for 1
18 points
Go for 1
18 points
Go for 1
19 points
Go for 2
19 points
Go for 2
20 points
Go for 1
20 points
Go for 1

































To read the chart, a coach finds the point margin that exists once a touchdown is scored, but before the conversion is attempted.  Thus, if you are losing 3 – 0 and score a touchdown, you now lead 6 – 3.  Next to the box for “LEAD BY 3 points,” you are instructed to “Go for 1.”

(Note the “TRAIL BY 4 points,” where the advice given is “Decision”---i.e., no advice at all.  “Go with your gut” is what you need to do, apparently.  That this is the one situation where Vermeil was uncertain seems a bit odd.  If you are down 10 – 0 and you score a touchdown, you’re down four.  Every coach in America is going to kick the extra point, isn’t he?  Is the possibility of trailing 10 – 8 so very attractive that you would accept the risk of being behind 10 – 6 and needing more than a field goal to tie?

There is, however, an argument for the two-point conversion in certain situations that will be discussed in the Trail by Four section.)

To the best of my knowledge, Dick Vermeil does not have a degree in mathematics or game theory, so I suspect the entries in these boxes are more of a seat-of-the-pants Vermeilian view of conversion possibilities.  In any event, some of them are wrong.  Also, other coaches and football people have changed specific entries on the Vermeil chart, so now there are other, different, charts in use by various teams.

In the rest of this article, I will examine these specific situations (up 2, down 4, etc.), and provide the best analysis I can.  Some of this analysis consists of my own thoughts and calculations, and some of it has been around for decades.  Many of the situations are trivial, of course, and require little discussion.

One further point needs to be made: these are end-of-game situations.  That does not mean that we are only concerned with a touchdown on the last play of the 4th quarter, or with four minutes left or eight minutes left.  This analysis can be important in the third quarter as well.  There is no single bright line on the 60-minute clock where the decision to go for one or two points suddenly becomes critically important.  About the most we can say is that these decisions become more important as we get deeper into the game, simply because there are fewer possessions left in the contest and thus fewer scoring scenarios to be examined.

Another way to put it is that at the beginning of the game, none of this matters.  If you run back the opening kickoff for a touchdown, for example, you won’t be wrong whether you kick the extra point or go for two.  We have already seen that your (mathematical) “expectation” is .94 points no matter which conversion you choose, so suit yourself.  Indeed, it is hard to make a case that any of this is terribly important until the second half, so I won’t try to.


WHAT TO DO WHEN YOU…

Trail by One

And here we are.  At the very beginning of our inquiry we are presented with the classic go-for-2 conundrum.  You have scored a touchdown on the last play of regulation, and you are down 14 – 13 (or 87 – 86).  Do you take the near-certain one-point conversion and go to OT, where your chance of winning will be somewhere near 50%?  Or do you run a play for two points and try to win right here and right now?

Are you feeling lucky?

As we have seen, there is a 94% chance of kicking the extra point, so if you have a 50% chance of winning in OT, your chance of winning the game if you attempt a one-point conversion is .94 times .5, or 47%.  Since your chance of making a two-point conversion is also 47%, there is no reason to prefer one path over the other.  Are you feeling lucky?

But there is a variable here, buried in the game and everything that has occurred.  Do you have a 50% chance of winning in overtime?  You almost certainly do NOT.  Your chance of winning in OT is a probability that is significantly better than 50% or significantly worse.  If your chance of an overtime victory is more than 50%, you should opt for OT by kicking the conversion.  If it is less than 50%, you should go for two and take your chances now.

So what are your chances of winning in OT?  What factors will move the needle from 50% to a greater or lesser number?

In the NFL, in the ten seasons from 2007 to 2016, the home team won the game 57.4% of the time.  This is not surprising---every sport has a home-field advantage.  What is surprising is that during the same period, home teams won 56.5% (87 of 154) overtime games.  Thus, even if a visitor has battled the home team to a standstill and fought its way into overtime, the home team still maintains a significant advantage.  Road teams win only 43.5% of overtime games.  All other considerations aside, a road team that scores a touchdown on the last play of regulation and is behind by one point should go for two.  A 47% chance of making the two-point conversion is much better than the 43.5% chance of winning in overtime.  As a general rule, road teams should go for two in order to win in regulation; home teams should take the single point and take their chances in overtime.

But there are always other considerations.  There are ebbs and flows in the course of a football game, for example.  If Team A has scored the last seventeen points of the game to draw within one, Team A’s coach may feel that Team B is on the verge of physical or psychological collapse, and that all he has to do is get to overtime in order to win the game.

If instead, Team A is melting down, the wisest course may be to run one play (the two-point conversion).  If Team A is down to its emergency QB, or if one of their other weapons is physically compromised, it may be best to avoid OT.  Even if there are no serious injuries, there may be reasons to decide the issue now.

There is no clear answer on what to do in this situation.  Dick Vermeil’s original chart from 1970 says “go for two.”  A revised edition still in use on NFL sidelines says kick.  My answer is kick at home and go for two on the road, unless there are compelling reasons to do otherwise.


Trail by Two

With ten seconds left in regulation, this is a trivial case, and all the charts tell you to go for two.  However, the more interesting question arises about what to do when the situation arises two minutes into the 3rd quarter, or even in the first half.  You have probably noticed that most coaches down say, 14 – 12, with plenty of time left in the game, will kick the point to make the score 14 – 13.  Their choice is defensible, but I think they are wrong.

Going for two in this common scenario means you will either tie the game or trail by two points.  Tied is good; down two is not so good.  The question is whether the upside is bigger than the downside.  Coaches routinely kick because they have concluded that the downside of going for two and missing is more significant than the upside of tying the score.

What they fear is a subsequent touchdown by their opponent.  If they trail 14 – 12, and the opponent scores seven points, they will trail by 21 – 12 and will be two scores behind.  Trailing 14 – 13, however, seven points for the other side will make it 21 – 13, which the trailing coach views as being “in touch” or “within striking range” because eight points is potentially achievable with just one score and a two-point conversion.

There are several flaws in this reasoning.  First, if the bogeyman you fear is that the other guys will score a TD and force you to score a TD and a 2-point conversion just to tie, well, why put off that day of reckoning?  You have just scored a touchdown to make the score 14 – 12, so why not try your 2-pointer now?  If there is any likelihood you will need a 2-point conversion, it will always be wise to try it sooner rather than later.  Doing it now tells you how many times you need to score to catch or overtake your opponent.  Putting off the decision means you may not discover the answer to the question until you miss your 2-point conversion with 1:50 left in the game, and you suddenly realize, “Oops.  I guess I need to score again.”  If you had gone for two back in the third quarter and missed it, you would have known what you had to do much earlier, and you might have planned your offensive strategy accordingly.

The clich√© you hear from sportscasters is that a team trailing by 8 is “one score down.”  It’s not true.  Seven points is “one score” because we can assume a one-point conversion, but you can never assume you will make a two-point try.  Eight points is really “one score or two scores, but we won’t know until we flip a coin.”  If you’re going to flip that coin, do it now.  Why keep yourself in the dark?

We will return to this idea when we discuss other point deficits (i.e., down 9, down 16).   When a team gets to these situations, a coach does not know how many more times he has to score, but he does know that if he is to win the game, he will need at least one two-point conversion in regulation.  The only way to eliminate the uncertainty is to try the two at the first opportunity.

There is another aspect that enters into prevailing “coachthink” in this and similar predicaments, and that is the tendency to seek a tie that sends the game into overtime, even at the cost of abandoning any chance of winning the game outright without having to play extra time.  Going for one point when trailing 14 – 12 is done in order to stay close enough so that you might be able to tie the game later and get into OT.  The decision to “stay close,” however, reduces the chance that the trailing team will win the game without having to face overtime.

Trailing 14 – 12 in the third quarter, there is a vast array of possibilities for the scoring that might occur in the remainder of the game.  The reason Team A  kicks the extra point, however, is so that when Team B  scores a (7-point) TD, Team A will lead 21 – 13, potentially allowing Team B to tie and get to OT. Down 21 – 13, however, one thing Team A cannot do with its next touchdown is take the lead and win the game.  Its only hope becomes overtime.

Going for 2 when behind 14 – 12, however, changes the equation.  If Team A succeeds in tying the game at 14, Team B then scores a 7-point touchdown, and Team A responds with a TD of its own, the score will now be 21 – 20 with Team A having the option of kicking the almost-certain conversion to get to overtime, or going for two again in order to win the game immediately.  As we have already seen, there are many reasons a coach may rationally decide to do this.  Road teams win only 43.5% of overtime games, but the NFL-wide success rate for 2-point conversions is 47%.

What this means is that a team playing in a hostile stadium should always be willing to take risks in order to preserve the possibility of winning the game in regulation.  Overtime is no bargain for a road team, which will normally get the short end of the statistical stick.

Trail by Three

This is a not-uncommon situation.  The Steelers lead by 16 – 7.  The Eagles score a touchdown, making it 16 – 13.

Kick or go for two?

Well, it depends.  With three or four minutes left, you kick, so that a subsequent score will win the game for you.  The difference between being down one and down two is meaningless if your only hope is 1) to stop the Steelers from scoring and get the ball back, and 2) kick a field goal.

If the Eagles get their TD with twelve minutes left, however, other possibilities arise.  Stopping the Steelers and kicking a FG is not the only way you might win this game.  You might be able to win even if the Steelers score again.

Suppose you kick your extra point to make the score 16 – 14 with twelve minutes left.  If the Steelers now put up a TD with a (single) extra point, they will be ahead 23 – 14 and you’re probably screwed.  Thus, when the Eagles put the ball in the end zone and trail 16 – 13, don’t they have to consider the possibility that a Pittsburgh TD will win the game?  The two-point conversion, to draw within one point at 16 – 15, still will keep them within 8 if the Steelers should put up an additional seven.

The downside, of course, is still that missing the two-point conversion on the Eagle’s first TD leaves them at 16 – 13 so that even a last-minute field goal  would only get them to OT.  However, it is less likely that this specific result will occur, since the additional time expands the tree of possibilities.

Note that the chance of an intervening Pittsburgh field goal does not change the calculation for Philly.  Whether the score is 16 – 15, 16 – 14, or 16 – 13, an additional three for the Steelers still means the Eagles can win with a TD and a conversion.

I mentioned earlier that the decision on whether to go for two probably doesn’t matter much in the first half.  Since your expectation on the conversion is .94 points regardless of your choice, the only things that matter for your choice are tactical considerations, and tactical considerations are just not that important early in the game.  But they not only matter in the second half, they can change depending on how much time is left.  The problem of what to do when you trail by three points is only one example.

Other students of the go-for-two question have realized this, of course, and charts exist that are WAY more complicated than Vermeil’s, since they import another variable into the problem---time left in the game.  The best I’ve seen appears at http://www.footballcommentary.com/twoptchart.htm in a 5-29-2004 posting entitled “Two-Point Conversion Chart.”  The chart covers all score differentials from ahead-by-30 to down-by-30 on the vertical axis with different amounts of time remaining (in 3-minute increments), arrayed across the horizontal.  The advice on going for two is not a binary yes/no, but is expressed as a percentage.

For example, the footballcommentary chart makes clear that when you have just scored and are down two points with 3:00 left in the game, you must go for two.  With 30:00 left, however, while you should still go for two, the decision is much closer to a coin flip, so that if a coach has little confidence in his team converting the two, he should probably just kick.

I don’t question their results, and I certainly don’t pretend to have modeled a football game using the Markov Decision Process (as they have done), because I don’t know what the hell it is.  I do think their chart is somewhat impractical for use on the sidelines, though.  In addition, it imputes a level of mathematical certainty to these issues that cannot be justified by the data.  For example, if you are ten points down (16 – 6, let’s say), after scoring a TD with 29:48 left in the game, they say you should go for two if you have a greater than 52% chance of making it.

Another example.  Suppose you are six points down (e.g., 15 – 9) after scoring.  If there are three minutes left in the game, you should try for two only if your chance of making it is better than 54%, but if it’s the very beginning of the second half, you should go for it if your chance of success exceeds 44%.

Is this level of specificity really going to help Doug Pederson make a decision in the heat of battle with the clock ticking?

In logic, the flaw in the footballcommentary.com chart is called the fallacy of “overprecision,” and the classic illustration of it is the joke about the guard at the natural history museum who is asked about the age of the dinosaur skeleton on display.

“That dinosaur is 90,000,008 years old,” he replies.

“”Really?  How can they pin it down so precisely?” you ask.

“Well, when I started working here, they told me it was 90,000,000 years old, and that was eight years ago.”

Summarizing, when down three (e.g., 16 – 13), kick the point with three minutes left.  With more time (say, ten minutes), it’s not wrong to go for two. 

Trail by Four

Kick it, of course.  Get within a field goal.  That was my assumption, anyway, until I read http://fivethirtyeight.com/features/when-to-go-for-2-for-real/

There are no dummies at fivethirtyeight, of course, and when Nate Silver speaks, it is usually wise to at least listen.  As the article explains, “If you’re down 4 points after scoring a touchdown (with 10 minutes left), you should go for 2, because being down 2 points instead of 3 helps you more than being down 4 points instead of 3 hurts you.”  In support of this reasoning, fivethirtyeight cites ESPN’s Expected Win Percentage Model, which gives the conclusion at least a patina of science.

On reflection, however, I am unconvinced.  In particular, there is no particular reason to think “being down 2 points instead of 3 helps you more than being down 4 points instead of 3 hurts you.”  I need some data on that before I can believe it.  It must also be noted that fivethirtyeight stands alone on this point.  All the charts in common usage and all references in the go-for-two literature support the idea of kicking the point when you’re down four.

I will go this far, however.  If you are the visiting team and there is so little time left (let’s say four minutes), that your only realistic hope, after the conversion, is to hold your opponents, get the ball back, and score one more time, then there is an argument to be made for a two-point conversion.  When you’re down four and you go for two, you will either be trailing by two or four, and if you are trailing by two or four with four minutes left in the game, overtime is very unlikely.

Going for two is an avoid-OT strategy, and a coach on the road should never be criticized too harshly for an avoid-OT strategy, since the visitor is usually a significant underdog in overtime.

So kick.  Unless it’s very late in the game and you really really really want to go home after sixty minutes.  Then you might decide to go for two.


Trail by Five

Go for two.  Why not?  Again, the purpose is to get within a field goal.

Trail by Six

Go for one, though it’s hard to make much of an argument either way.  As time grows short, it makes sense to kick the point because that puts you down only five.  If your opponent then scores three, you may still have a prayer of tying the game and sending it to overtime.

With more time left on the clock (in the third quarter for example), there will be more scoring possibilities for both sides, so going for two becomes more attractive.  A four-point spread is the difference between a TD and a field goal, and it is worth risking a missed conversion to achieve that.  For one thing, let’s assume the remainder of the scoring consists of an opponent’s field goal (going up seven), and your last-second TD to get you within one point.  As we have seen, there are many reasons why you might wish to go for two on that final score so as to win the game (or lose it), in regulation.  Going for two when down six may provide you with that opportunity.


Trail by Seven

Kick it.   The chance of getting to -5 is not worth the possibility of getting nothing and remaining down seven. 

Trail by Eight

You’ve been behind 14 – 0 since halftime and you now score a touchdown with five minutes left in the game.  Your only realistic hope is to hold your opponent scoreless the rest of the way and punch in another TD yourself.  With the score now 14 – 6, do you kick the extra point or go for two?  As Richard C. Porter, an economist at the University of Michigan, pointed out in “Extra-Point Strategy in Football” (published in The American Statistician in 1967), you need to go for two.

Coaches virtually never do this, of course.  It is believed the last time an NFL coach went for two in this situation was in the Packers-Ravens game on October 14, 2001.  The Ravens, trailing 31 – 17, scored a touchdown with 38 seconds left in the game, went for two, failed, and lost the game 31 – 23.  The decision caused little stir at the time since the Ravens were unlikely to win the game anyway, and actually failed to recover the ensuing on-side kick.

Going for two is clearly the right move, however, and by a large margin.  Kicking an extra point when down eight points significantly decreases your chance of winning the game, and we have known this for fifty years.

Assume a fourteen-point deficit with five minutes left in the game.  Further assume you will hold your opponent scoreless in the remainder of regulation, but that you will score two touchdowns.  What conversion choices should you make to maximize your chance of winning the game?

Suppose you do what every NFL coach would do---kick two extra points in order to get to overtime.  Since you have a 94% chance of making each conversion, and a 50% chance of winning in overtime (this will fluctuate, but let’s call it 50%), your chance of winning the game is .94 x .94 x .50 = 44%.

Now what happens if you go for two on your first opportunity?  Well, if you make it (47%), all you have to do is kick an extra point (94%) on your second TD, and you win the game in regulation.  Your chance of winning this way is .47 x .94 = .44, the same as your chance of winning by kicking two extra points and going to OT.

You have additional chances, however.  Even if you miss your two-point conversion try (which you will do 53% of the time), you may make a two-pointer after your second touchdown (47%) to get you into overtime, where you will then have a 50% chance of winning.  The probability of this happening is .53 x .47 x .50 = 12.5%.

There is even another possibility.  Suppose you make your first two-point conversion (47%), then miss the kick after your second touchdown (6%).  This still gets you to overtime where your chance is, as we have postulated, 50%.  The probability of this branch of the tree awarding you a victory is .47 x .06 x .50 = 1.5%.

Summarizing, your chance of winning by kicking two one-point conversions is 44%.  Your strategy is simple: get to OT and then get lucky.  Your chance of winning by going for two on your first score, however is 44% plus 12.5% plus 1.5%, for a total of 58%.

The big difference between the two strategies is that kicking the two one-point conversions gives you NO possibility of winning the game in regulation.  Going for two, however, gives you a significant chance of winning in regulation in addition to a smaller chance of prevailing in OT.  By kicking, you are a dog to win the game even if you make the two touchdowns you need.  Going for two on the first score (assuming you get the second TD as well), makes you a favorite.

This particular flawed aspect of coachthink is one we have seen before.  In the interest of staying close or staying within striking distance or maximizing the chance of getting to overtime, coaches will actually reduce their probability of winning the game.  The mistake is understandable; the idea of going for two when down eight points is counterintuitive.  Nevertheless, there has to be somebody on the sideline whose job it is to keep his eyes on the biscuit.  The goal is NOT to “get to overtime;” the goal is, or should be, to win the game.

Trail by Nine 

This is another decision-point where most NFL coaches get it wrong, and for the same reason discussed above.  Down fifteen points (22 – 7, let’s say), with five minutes left in the game, the trailing team scores a TD.  Going for two might make it 22 – 15, though missing will leave them behind by nine points.  NFL coaches routinely (and incorrectly) kick the extra point here to leave themselves eight points behind.  They do this to stay “one score behind.”

But eight points is not one score behind, is it?  It is one thing to assume you will make an extra-point kick, but who dares to assume you can make a two-point conversion?  NFL teams only make them 47% of the time.

Fifteen points is not two scores.  It is either two or three and you won’t know how many it is until you try the two-point conversion.  Therefore, you should attempt it at your first opportunity.

Dick Vermeil got this one correct, by the way, on his chart from 1970.

Trail by Ten

As time winds down, it becomes essential to go for two so as to bring the lead down to eight points.  With time for more scoring (i.e., in the third quarter), the possibilities become so numerous that the arguments for one or two are not very compelling.

Trail by Eleven

Dick Vermeil says to go for two.  Other sideline charts say kick.  It is difficult to mount a convincing argument either way.  Following your conversion attempt, you will trail by nine, ten or eleven points, meaning that you will still need a field goal, a touchdown, and a conversion to win or tie.  Since the eleven-point difference, requiring a subsequent field goal and a touchdown and a two-point conversion, is most likely to occur if you now try a two and fail, I would kick in order to bring the deficit to ten.  Then, when you later score your field goal and TD, you can decide at that point whether to go for one or two.

Trail by Twelve

This is a close call, but you should go for two.  If you make it, a field goal will get you within seven, and then when you score a touchdown with two seconds left in the game, you have the option of kicking (to reach overtime), or trying a two in order to win or lose in regulation.  Down twelve, if you kick to get within eleven, your only (narrow) path is a field goal, a TD and a two-pointer.

This is another illustration of the principle that if you are going to have to go for two at some point, you are better off doing it at your first opportunity.  

Trail by Thirteen

Go for two.  If successful, you have a shot at tying the game with a field goal, a touchdown and a two-point conversion.

Trail by Fourteen

Kick.

Trail by Fifteen

For the same reason you go for two when you are down fourteen and score a touchdown, you also should go for two when you are down twenty-one and score a touchdown.  See TRAIL BY EIGHT.

Assuming you make the three TDs you need when you are down twenty-one, kicking three extra points gives you only a 41.5 % chance of winning the game.  You’re a serious dog.  Going for two on your first touchdown, when you are down fifteen, makes you a 55.8% favorite if you get the other two TDs.     

Trail by Sixteen

This occurs more often than you think.  Trailing by 22 points (e.g., 28 – 6 or 25 -3), a team will score a touchdown.  Almost invariably (I have not found a contrary instance in the NFL), the coach will kick an extra point.

This is another instance of the “stay close” or “eight points is one score” error.  Down 22, a coach (let’s call him Jim Harbaugh), will think, “OK, I need three touchdowns and four extra points to get us into OT.  Therefore, I need two kicks and one two-point conversion.  Therefore, I will kick after my first touchdown to cut the deficit to 15 (“two scores”), and I’ll kick again after the second touchdown to bring the gap down to 8 (“one score”).  And then finally, I’ll go for two to tie the game after the third TD.”

In Superbowl XLVII, played on February III, 2013, Harbaugh’s 49ers were trailing 28 – 6 when, midway through the third quarter, Michael Crabtree caught a 31-yard pass from Colin Kaepernick to make the score 28 – 12.  Harbaugh kicked.  Still in the third quarter, Frank Gore ran it in from the six-yard line, bringing the tally to 28 – 19.  Harbaugh again kicked to make the score 28 – 20.  Then, after each team added a field goal (the score now 31 – 23), San Francisco scored their third TD with 9:57 remaining in the game to make the score 31 – 29.  Harbaugh finally decided to go for two and missed.  Oops!  I guess we weren’t really three touchdowns down after all!  Unfortunately for Harbaugh, now that he realized he needed to score some more points, he was unable to (except for a last-second gift safety from the Ravens to seal the Baltimore victory).  Final score:  Baltimore 34 San Francisco 31.

Personally, I fire Harbaugh after this performance (though every other NFL coach would have done the same thing).  I fire him for refusing to get help in an area that he must have known he was unfamiliar with.  I mean, even Jim Harbaugh knows that he was not hired as coach of the 49ers to do math problems, so why not hire somebody who can?  His crime is especially unforgiveable considering he coached San Francisco, a city where there are approximately 14,000 Asian kids with 800s on their math SATs, any one of whom would have been thrilled to stand next to Harbaugh on the sidelines and tell him the right thing to do.

Let’s examine Harbaugh’s strategy.

First, assume the deficit is 22 points and assume the trailing team will score three touchdowns.  What conversion choices should be made in order to maximize the chance of victory?

Harbaugh’s plan is TD plus kick, then TD plus kick, then TD plus two-point conversion.  This gets him to overtime where his chance of winning is 50%.  Thus, Harbaugh’s probability of winning the game is .94 x .94 x .47 x .50 =
.208.

Suppose, however, that Harbaugh goes to two at his first opportunity.  If he succeeds, and then kicks after the second and third touchdowns, he is again in OT with a 50% chance of winning.  This probability is the same as above: .208.  (If you are only trying a two-point conversion one time, it obviously doesn’t matter which touchdown you attach it to.)

But what if he misses that first opportunity?  This gives him an additional chance to win the game that is not available if he waits until the final touchdown to try the two-pointer.  He can still tie the game by missing the first two but making a two after both the second and third touchdowns.  This additional possibility is .53 (missing a two-pointer) x .47 (making the second) x .47 (making the third) x .50 (winning in OT), for a total of 5.8%.  Harbaugh’s plan gives him a 20.8% chance of winning.  By trying the two-pointer after the first TD, the chances increase to 26.6%.

But even this is not the optimal strategy.

Go back and look at the TRAIL BY EIGHT section.  There is a thorough explanation of the counterintuitive finding that a team trailing by fourteen points must go for two when it scores its first touchdown.  Now apply that reasoning to the problem we are dealing with in this section.  Specifically, if you are trailing by twenty-two and you score a touchdown and make a two-point conversion, you will then be trailing by fourteen.  A subsequent touchdown puts you down eight, and this means you must go for two again!  In other words, when you trail by twenty-two points, you should go for two on both of your first two touchdowns.  (If you miss one of them, you’ll have to go for two on your third TD as well.)

Going for two on at least the first two touchdowns presents the following probabilities of winning which, since they are mutually exclusive, must be summed to arrive at the total chance of success:

1) TD plus two points AND TD plus two points AND TD plus kick.  This probability is .47 x .47 x .94 = 20.8%.  (Note: the twenty-three points wins in regulation, so there is no factoring in overtime chances.)

2) TD plus two points AND TD plus two points AND TD with missed kick AND winning in OT.  This probability is .47 x .47 x .06 x .50 = 0.6%

2) TD plus two points AND TD with missed conversion AND TD plus two points AND winning in OT.  This probability is .47 x .53 x .47 x .50 = 5.9%

3) TD with missed conversion AND TD plus two points AND TD plus two points AND winning in OT.  This probability is .53 x .47 x .47 x .50 = 5.9%.

Since 20.8% + 0.6% + 5.9% + 5.9% = 33.2%, this is the probability of winning the game if you go for two on the first two touchdowns.  You are 1 ½ times more likely to win the game by following this path than by using the standard strategy of kicking after the first two touchdowns and going for two only after the third one.

Lead by One

The obvious answer is to go for two, in order to stretch the lead to three points.  All of the Vermeilian sideline charts say so.

But be prepared to be second-guessed if you miss the two-point conversion and then lose the game.  This was the story in the aftermath of the Washington-Atlanta game on October 15, 2015.  There, with eight minutes left in regulation, the Redskins scored a TD to go ahead 13 – 12.  Washington coach Jay Gruden ordered a two-point try, which failed, and the Redskins ultimately lost the game 25 – 19, in overtime.

That night, in a lengthy article in USA Today, Chris Chase delivered his analysis.  In what may be the apotheosis of the “look-what-can-go-wrong” school of go-for-two theory, Chase blamed the Washington loss on Gruden’s decision to try a two-point conversion.  His conclusion: “Always take the points (or point, in this case).  Always.”  Chase does acknowledge certain “late-late” game situations where there is no alternative but a two-point conversion, but otherwise, there is apparently never a valid reason to go for two.  See: http://ftw.usatoday.com/2015/10/two-point-conversion-chart-up-one-point-nfl-teams-washington-redskins-went-for-two-atlanta-falcons-jay-gruden

My advice to football coaches:  do your best to win games, no matter what the Chris Chases of the world will say the next day.

Lead by Two

Everybody kicks this, but the correct answer is not so obvious.  Certainly the single point, stretching the lead to a field goal, is valuable, and will almost always make sense for the home team.  On the road, however, going for two virtually eliminates the chance of going to OT and, as noted, OT is not where visiting teams want to be.  Unless the visiting coach has strong reasons to think he will be a favorite to win in extra time, he should go for two.

Lead by Three

Kick.

Lead by Four

Kick.  Vermeil says go for two and other charts say kick.  Dick’s wrong about this one.  The only relevant scenario to be concerned about is: 1) other team scores TD for 7 or 8 points, and 2) you manage a FG to win or tie the game.  Getting the five-point lead matters.

Lead by Five

Go for two.  Make your lead seven points. 

Lead by Six

The obvious, and correct, decision is to kick.  However, it’s a closer call than you might think.  This is another situation where a visiting coach might reasonably decide to go for two if he has a good two-point conversion play in his pocket, if he has some injured players and doesn’t want any more of them, or if he just doesn’t care for his chances in OT.

Lead by Seven

The charts all say kick in this situation, and that’s what every NFL coach will do.  In fact, there is no difference in your chance of winning the game whether you go for one or two.

The calculations are long and complicated because of the many possibilities that must be considered and given probabilities, and I will not reproduce all the numbers here.  The question is this: assuming your opponent will score a touchdown in the remaining limited time of regulation (let’s call it three minutes), are you more likely to win the game by kicking or going for two when up by seven?

If you go for two and make it, you are up by nine and you’ve won the game.  That’s the easy one.  If you miss, however, your opponents may 1) tie you with a one-point conversion, sending the game to overtime, 2) beat you with a two-point conversion, 3) lose to you by missing a two-point conversion, or 4) lose to you by missing a kick.

Then there are all the possibilities if you go for one.

Adding it all up, if you score a touchdown that puts you up seven points in the closing minutes, you are approximately a 75% favorite to win this game whether you go for one or two, even assuming your opponent subsequently scores a touchdown.

Lead by Eight

Kick, of course.  Nine points ahead is exactly where you want to be.

Lead by Nine

At this point, once you are ahead by more than one score, it begins to matter less and less whether you go for one or two.  Going for two when up nine, and making it, puts you in a situation where an opposing touchdown AND a field goal cannot beat you in regulation.  On the other hand, getting the more-certain single point to stretch the lead to ten, seems at least as worthwhile.  All the charts say kick this, and I won’t argue.

Lead by Ten

The considerations here are quite similar to those in the previous entry.  Kick it.  Sure, going up by twelve (requiring the opponent to score two touchdowns), has some value, but I’ll take the single point.

Lead by Eleven

Obviously, you kick this.  Leading by eleven is a TD and a field goal (maybe); getting the twelfth point forces the other guys to score two touchdowns.

Lead by Twelve

And here you might as well go for two.  If the bad guys do score their two touchdowns, leading by thirteen rather than twelve is probably not going to help you, but if you add two, for a lead of fourteen, you might limp into OT and get lucky.



THE STUFF TO REMEMBER

This “Practical Guide” is not quite as practical as a simple gridlike chart a coach can consult on the sidelines.  Trailing by sixteen when he scores a touchdown, we can’t really expect a coach to pull out this treatise and read 800 words on the subject.  On the other hand, the charts invented by Dick Vermeil provide only crude approximations of the truth, and many of the specific entries are wrong.

A similar chart could be created out of the work presented here, and it would be better than the existing charts, and maybe that is one thing a coach might do to reduce the errors that are routinely made in the go-for-two decision.  More important, however, is that the insights contained here be understood and incorporated into his thinking.  Somebody else can do the math.

And that’s the first point.  These decisions have nothing to do with your “gut.”  These are math problems.  Some of them have clear answers and others are much more situation-dependent and nuanced, but none of them cares about your feelings.  And this presents you with a choice---either master the problems yourself or hire a geek to tell you what to do.  Jim Harbaugh might have won himself a Superbowl had he done so.  So find some math whiz from a local college and let him hang out on the sidelines, his only job being to run over and advise you whenever you score a TD.  Free hotdogs and a couple of Uber rides is all he will cost.

The next point: change your approach to the question of whether to go for two.  For almost all of everyone’s football career, it generally made sense to kick the point because, in the long run, you would score more points that way than if you went for two after every touchdown.  Now, with the scrimmage line for kicks pushed back to the 15-yard-line and the extra point no longer automatic, there is no longer a reason not to go for two.  It’s not a desperation move anymore.  So when in doubt, go for two.  You pay no price for doing so.

The traditional view, that going for two is a desperation tactic, is one reason coaches have put off the two-point conversion until they have no other choice.  This is why, when trailing by fifteen, a team that scores a touchdown will kick the extra point and defer the two-point attempt until its next touchdown.  This never made a lot of sense, but now it is indefensible.  When you are fifteen behind (with limited time remaining), there must be a two-pointer in your comeback run, and that means you are as likely to require three scores as you are to require two.  So unless there is some reason you don’t want to know how many times you have to score, you must go for two at your first opportunity.

The same issue arises in many score/time-remaining situations, but the rule is the same: if there is a two-point try somewhere in your future, do it NOW.  When you are trailing late in the game, the number of times you need to score is a very important question.  Get it answered as soon as you can.

Much of this Guide is concerned with the distinction, much ignored, between 1) winning the game, and 2) getting to overtime.  NFL coaches routinely lose sight of what should be their goal (winning the game), and instead pursue a different goal---getting to overtime.  The two goals are not identical.  In fact, they are often in conflict.

If you trail by eight points with one minute left in the game, the only way to win is to score a touchdown, make a two-point conversion, get to overtime and triumph there.  In that situation, the goals of getting to OT and winning the game are inseparable.  More often, however, the two goals will point in different directions.  To change the above example slightly, if you trail by seven points (rather than eight), with one minute remaining, there are many situations where kicking a point after your touchdown and heading for overtime is a mistake because it will reduce your probability of winning.  In that case, the rational coach will go for two in order to maximize his chances of winning the game even though it eliminates the possibility of overtime.  (These decisions also turn on the fact that home teams are usually a distinct favorite in overtime.)

The best explanation of this phenomenon is in the Trail by Eight section above, which examines a scenario where you are behind by fourteen points and you score a touchdown.  You must go for two in this spot because it significantly increases your chance of winning, even though it almost destroys any shot of getting to overtime.  As Thomas Aquinas taught us, all clear thinking begins by making distinctions.  For an NFL coach, one distinction that needs to be foremost in his thinking is that trying to get to overtime and trying to win the game are two different things.

Copyright2017MichaelKubacki  

Note: Additions, suggestions, corrections and arguments are welcome.


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