In his short tenure as our Head Coach, Jim Zorn already has proven the disturbing proclivity for leaving points on the board. This kind of dramatic coaching error is simply inexcusable moving forward and I demand remedy immediately lest it cost us in the future. We all know what I'm talking about, the precise play in question where Coach Zorn foolishly left points on the board when the correct decision was different than the one chosen. It was, of course, in the Giants game at the close of the 2nd quarter after a Jason Campbell 12 yard touchdown pass to Santana Moss. With the score 16-6, Coach Zorn inexplicably, inexcusably, irrationally and illogically sent Shaun Suisham out to kick an extra point. This kind of blatant error in judgment by our head coach, by any head coach, cannot be tolerated. Coaches should almost always go for two points after touchdowns.

An analysis of the 2-point conversion was pending after the New Orleans game on Saturday. After Clinton Portis' first touchdown, down 17-15, Jim Zorn sent out the offense for a 2-point conversion that ultimately failed. Some discussion followed from the broadcasters on why this was or was not the proper time to go for two. Reader dr WNC represents the skeptic on that strategy:

I hate going for two points early. Just take the one, it's only the third qtr.

I am not picking on dr WNC. I think that pretty well covers the opinion of many fans in that particular instance while also encapsulating the thoughts of the NFL nation, including head coaches, fans, owners, players, and most commenters, generally, about the EXTRA POINT (XP) vs. the 2-Point Conversion (2PC). On Tuesday September 16th, 2008, the consensus is that after a touchdown is scored the correct move, generally speaking, is to go for the XP. Deviations from this strategy, which by elimination means exclusively the 2PC, require justification, and not the other way around.

Before I examine the issue in detail, if you're still reading (very few or none of you will finish this post) I want to encourage reader(s) to engage this problem the same manner that one of the nation's premier Constitutional Law scholars once put the evaluation of Constitutionalism to his students: Imagine you were an alien who visited earth in a spaceship and had the opportunity to review the way of life of the inhabitants, from their civil, social, and political structures all the way down to the really important stuff like the rules governing what one can and cannot do after touchdowns, and then contemplate how you might do things differently were you them. I ask reader(s) do this for two reasons: 1) Constitutionalism is at least almost as much a sacred cow in this country as the hegemony of the XP over the 2PC. A fair evaluation of the strategies in competition is impossible unless reader(s) escape their comfort zones. This analysis will require you to really question your merely traditionally held beliefs in favor of a more objective analysis unfettered by your currently held biases. I hope putting yourself in a space ship many miles above earth with the point of view of a detached alien species will better enable you to do this. 2) More on this in a moment, but the way the human psyche works -- and I'll be quoting scholarly work to support this proposition -- sends people to reach differing conclusions about the same fundamental questions depending exclusively on the manner in which a problem or controversy is presented. This is of course illogical, as the same question presented two separate ways should lead to the same result. You'll find it doesn't. Hence the importance of framing an issue in such a way to expose the illogical tendencies of the human mind such that it reaches disparate conclusions to the same controversy or, in the present case, to actually conclude towards the wrong and irrational conclusion in favor over the proper one.

Before the analysis begins I'd like to take care of some preliminary matters. When I planned this post on Sunday, it seemed like an original idea whose time had come. Unfortunately Gregg Easterbrook beat me to the punch. Today's edition of Tuesday Morning Quarterback engages this very question in the context of Mike Shanahan's decision to win over the Chargers on a 2PC rather than XP it for overtime. This would be a good time to acknowledge that Gregg Easterbrook has been a 2PC advocate for a long time and is due all the credit in the world if you ultimately reach the same conclusion that I've come to. I'm going to use some of the data cited by Easterbrook in his article and perhaps some quotes, though suffice to say I think reader(s) will benefit from a brief reading of today's TMQ.

I am indebted to Michael David Smith and Aaron Schatz of Football Outsiders. I am indebted to them generally for their work at that website because I find it very informative and entertaining, and to them specifically for aiding me in this post. Despite what felt like hours of snooping the web and NFL.com, I simply could not find statistics on 2PC attempts vs. successful conversions over the years. What little data I did find was incomplete or guess work or old. Shortly after contacting Aaron Schatz I received the answer to my inquiry, and it is his data that I use here unflinchingly; I trust Schatz. Here I plug their Pro Football Prospectus which apparnetly has the data I needed I just couldn't find it, since Gregg Easterbrook cites to PFP in his article.

Ok, first, some history. The NFL scooped the 2PC in 1994 probably in large part as a result of the USFL. Praise the USFL. Success rate in the early days of the 2PC are difficult to find, but have been pegged well below 50% by sources I'm calling reliable here and here. This success rate was consequential to the 2PC for reasons stated below:

When their success rate is well shy of 50 percent, 2-point conversions produce fewer points on average than extra points, which are almost always successful. A number of commentators, including Phil Simms of CBS and a Rutgers statistics professor named Harold Sackrowitz, picked up on this fact and argued during these years that teams were too quick for try for 2.

The problem, they said, was that coaches had become dependent on a chart — created around 1970 by U.C.L.A. Coach Tommy Prothro and his offensive coordinator, Dick Vermeil — that dictated when to go for 2. Trailing by 5 points after a touchdown, for instance, a team should go for 2 to cut the lead to a field goal, according to the chart.

The chart is an interesting phenomenon considering that it was developed 24 years before the NFL adopted the 2PC in a game that was fundamentally different in Re: that rule. In College you start on the 3 yard line instead of the 2 yard line (PRO!) and a returned 2PC in CFB actually costs you points whereas the defense cannot score on a 2PC in the NFL. ALL HAIL THE MAGICAL CHART OF WONDEROUS MAGIC available here. Incredibly this little thing actually has an enormous amount of influence on coaches today. And there it is: behind by 2, go for 2, which is precisely what Jim Zorn did against New Orleans. He fudged up against the Giants, as the chart instructs you to go for 2 when down by 10. I'm going to suggest that the chart is largely meaningless, that he should've gone for two in both instances and in many instances where the chart says go for one.

So what am I going to tell you? Basically that: the 2PC is now the superior post-touchdown strategy and is and should be the norm whenever a touchdown is scored. Deviations from this strategy, ie. XP, need to be justified. This is the exact opposite of the football universe as it exists today.

Although the argument is far more multi-premised and nuanced than presented below, a short-hand of it would look something like:

Premise 1: More points is better in the NFL.

Premise 2: The odds of successfully converting a 2PC are higher than 50% and success leads to two points.

Premise 3: The odds of successfully converting an XP are between 96% and 100% and success leads to one point.

Conclusion: Teams should (generally) go for a 2PC after scoring touchdowns.

A tighter argument would include the premises where you put the numbers together, but I thought that would be best done afterwards followed by a brief personal experiment to explain how that works. Premise 2 and Premise 3 are actually interpretations of empirical data that certainly can be questioned, although some truths here: XP conversion rate cannot be above 100%. Assuming for the sake of argument that I am correct, that 2PC success rate is above 50%, say, 52%, and XP conversion rate is no higher than 98% (although the reasoning works at 100%) consider:

Each XP attempt is worth 1 x .98 = .98 points.

Each 2PC attempt is worth 1 x .52 = 1.04 points.

Supposing those numbers are correct, it's quite obvious that the 2PC strategy leads to more points than an XP strategy. Put differently, suppose you were given the choice of playing two games. In the first game, you flip a coin that turns up heads 98% of the time, and everytime it hits heads you win 98 cents a dollar. In the 2nd game you get a coin that lands heads 52% of the time and gives you a dollar and four cents two dollars everytime that happens. Given a choice of which game to play which would you take?

Rational people choose one game, irrational people choose the other game. You would select the game that maximizes the money made, and more money is made per throw on the 2nd game. Anyone who argues for the former simply isn't a logical person and should be inspected for dimentia. This isn't to say that people who go for XPs are illogical (I think they are, but that's besides the point) but an argument will have to proceed that explains why the game of football is fundamentally different than the game presented above.

And I frame it in such a way to force a conclusion towards the optimal scoring strategy for a reason, because I happen to think framing it in the football context is precisely what leads people astray in their reasoning. In the NFL the current hegemonic strategy is to kick the XP. The success rate on XPs is so high that the point after touchdowns is largely assumed as already earned after one scores. As fans we tend to think of touchdowns as worth 7 points (which they are not worth) and, just to claim guilty party status, that's precisely how I think up my tie-breaking MNF scores in Pick'Em Leagues. I don't think in terms of 8 point or 6 point touchdowns but in nicely ordered 7 point touchdowns and 3 point field goals. The overwhelming majority of touchdowns scored are improved upon with an extra point. It is helpful to think of that extra point as being "house money" given to the coaches that they are reluctant to relinquish (for a number of reasons, the most damning of which more will be said shortly).

The problem with "house money" betting is that people tend to treat problems that are not unique in unique ways when they are using it (house money). The floor belongs to Peter L. Bernstein, author of Against the Gods: The Remarkable Story of Risk which is a history of risk that I have not yet finished because, so far as books go, it is merely good. He says:

[Two researchers I'll reference shortly] found that the valuation of a risky opportunity appears to depend far more on the reference point from which the possible gain or loss will occur than on the final value of the assets that would result. It is not how rich you are that motivates your decision, but whether that decision will make you richer or poorer. As a consequence, [one of the researchers] warns, "our preferences... can be manipulated by changes in the reference points."

The two researchers are Daniel Kahneman and Amos Tversky. Their work is quoted more extensively in Against the Gods than I will quote here, though if you're interested in pursuing the scholarly works themselves, look no further then:

Kahneman, Daniel, and Amos Tversky, 1979. "Prospect Theory: An Analysis of Decision under Risk." Econometrica, Vol. 47, No.2, pp. 263-291.

Kahneman, Daniel, and Amos Tversky, 1984. "Choices, Values, and Frames." American Psychologist, Vol. 39, No. 4 (April), pp. 342-347.

More floor ceding to Bernstein, discussing their work:

Where significant sums are involved, most people will reject a fair gamble in favor of a certain gain---$100,000 certain is preferable to a 50-50 possibility of $200,000 or nothing. We are risk-averse, in other words.

But what about losses? Kahneman and Tversky's first paper on Prospect Theory, which appeared in 1979, describes an experiment showing that our choices between negative outcomes are mirror images of our choices between positive outcomes. In one of their experiments they first asked the subjects to choose between an 80% chance of winning $4,000 and a 20% chance of winning nothing versus a 100% chance of receiving $3,000. Even though the risky choice has a higher mathematical expectation --$3,200--80% of the subjects chose the $3,000 certain. These people were risk-averse...

And illogical, says me. Continuing:

Then Kahneman and Tversky offered a choice between taking the risk of an 80% chance of losing $4,000 and a 20% chance of breaking even versus a 100% chance of losing $3,000. Now 92% of the respondents chose the gamble, even though its mathematical expectation of a loss of $3,200 was once again larger than the certain loss of $3,000. When the choice involves losses, we are risk-seekers, not risk-averse.

Similar results are found over a wide variety of experiments involving either weak strategies beating out strong strategies or identical strategies resulting in disparate conclusions based on the manner in which the issue is framed (as loss vs. gain, for instance). As Bernstein puts it:

This behavior, although understandable, is inconsistent with the assumptions of rational behavior. The answer to a question should be the same regardless of the setting in which it is posed.

One more experiment just for fun, presented by Bernstein from Richard Thaler:

...Thaler has described an experiment that uses starting wealth to illustrate Tversky's warning [cited above]. Thaler proposed to a class of students that they had just won $30 and were now offered the following choice: a coin flip where the individual wins $9 on heads and loses $9 on tails versus no coin flip. Seventy percent of the subjects selected the coin flip. Thaler offered his next class the following options: starting wealth of zero and then a coin flip where the individual wins $39 on heads and wins $21 on tails versus $30 for certain. Only 43 percent selected the coin flip.

And finally, here comes "house money":

Thaler describes this result as the "house money" effect. Although the choice of payoffs offered to both classes is identical---regardless of the amount of the starting wealth, the individual will end up with either $39 or $21 versus $30 for sure---people who start out with money in their pockets will choose the gamble, while people who start out with empty pockets will reject the gamble.

Coaches have empty pockets after a touchdown, they start with zero points. They are then presented with the proposition of taking 1 point for certain (or assumed certain) or gambling for 0 or 2 points. Perhaps coaches would act differently if, instead, after a touchdown they were simply given 7 points and then extended the option of gambling on a 2PC where failure actually lost them 1 point and success gained them a point.

In any event, while it is natural for coaches to choose the way they do based on the evidence above, they are hardly saved. As Bernstein pointed out, this "is inconsistent with the assumptions of rational behavior." Thaler's students don't make millions a year and will hardly be blamed for lacking rational behavior. Coaches, on the other hand, should be held to that standard.

More damning than the realization that framing influences the manner in which people, coaches make decisions is the fact that this isn't an either-or proposition. This is not a case of coaches being handed a 50-50 chance to get 2 points or a 100% chance to get 1 point. Rather the likelihood of a successful XP is actually below absolute certainty and, at least per the data I'm calling relevant, the likelihood of a 2PC is higher than 50%. This wasn't always true, as stated above. Here's the data from Easterbrook:

The invaluable Pro Football Prospectus reports that since 2003, deuce attempts have succeeded about 55 percent of the time, which sounds better than trotting on to overtime.

He went to the PFP, I went to its author, Aaron Schatz, who told me:

> 2003    47%    62
> 2004    50%    74
> 2005    54%    50
> 2006    60%    35
> 2007    53%    57
>
> Overall: 52% success over last five years.

That is, ostensibly, year success rate% attempts.

Speculate on the reasons for this, but here's one explanation:

..the success rate has not risen because coaches are pickier about which defenses they test. Teams were just as likely to go for 2 against a good defense this season as a bad one, according to Football Outsiders, an analytical Web site.

Instead, more creative play-calling, including more passes, seems to be the main reason that teams are again succeeding more than half the time. "Offenses have become more sophisticated and more unique with what they do in that situation," Vermeil, who coached the Rams and the Chiefs over the last decade, said. "More time is devoted to it."

I suppose my data set is subject to debate. My justification for this limited set of the past five years vs. the less friendly overall data since 1994 is that I simply don't think the year 1997 has much interesting to tell us about the likelihood that any given offense will succeed on a 2PC against any given defense in the 2008 season. Since coaches only make decisions in the present, the more recent the data, the better. Hundreds of 2PC attempts is a substantial enough data set for me to conclude:

Right now the average success rate of a 2PC exceeds 50%

From that alone I'm happy concluding that 2PC is the optimal post-touchdown strategy to that of the XP because it nets more points. The way to win football games is to score more points than your opponent. After every touchdown you are given an opportunity to increase your score by either .98 points on average or 1.04 points on average. The smart coach will choose the former except under extenuating circumstances.

What might those circumstances be? I'm an admittedly hyberbolic person and would happily tell you that there are no circumstances whatsoever in which an XP is superior to a 2PC. That would not do credit to the argument, though, as there are obviously situations where that isn't the case. 4th quarter, 0 seconds on clock, XP wins the game, you should take the XP. That's a no-brainer. 4th quarter, 1:00 remaining on the clock, you are up 3, you should take the XP.

Those are about the only two situations I can think of that would necessarily demand an XP. And the reason is simple: Major Premise 1 from above, that scoring more points is better in the NFL, ceases to operate in those circumstances. And this is because under the two scenarios above, the point differential between an XP and 2PC is result neutral whereas the point differential between an XP and a failed 2PC is not. The former is simple; you will win whether you have two more points or one more point than your opponent. If the score is tied and there is no time remaining, you should win the game with the more likely XP.

Regarding the latter, with a minute remaining in the 4th quarter and you having just scored to take the lead by three, it could reasonably be concluded that one meaningful possession remains and it belongs to the bad guy. You will either take the lead by 4 with an XP, take the lead by 5 with a 2PC, or remain stat at 3 with a failed 2PC. On the following drive your opponent will score zero or three or six or seven or eight points. That represents the entire world of possible scores your opponent has on his (presumptively) final drive. And where he will score zero or three or six or seven or eight points, your four or else five point lead is result-neutral. Which is to say, in all those instances where five is enough points to win the game (opponent scores zero or three, which he wouldn't do, since coaches don't kick field goals just to lose by less) so is four. In all those instances where four is not enough to win the game (he scores six, seven, or eight points) well, shoot, neither is five. But where your four points wins a game against a field goal and essentially forces him to score, your three points after a failed 2PC is not result-neutral; it leads to overtime should he kick it through the uprights.

People are free to introduce their own scenarios in the comments section. I can imagine a strategy that says: down by 3 late in the 4th quarter you should take the XP because then you can win with a FG on your next drive. That's not my strategy. My problem with that is the farther away from endgame that one gets (ie., on my next drive presumes enough time to get another drive) the less capable one is of predicting with any credible accuracy the manner in which the game will sort itself out. Time matters but only in a very limited sense; if you're choosing to kick an XP over a 2PC at any point prior to the 4th quarter you are acting in error. You have presumed to know the amount of and manner in which the remaining possessions will play out.

Anyways, have at these iterations all you want, the point is just that: the XP is the one that has some 'splainin' to do and not the other way around. The optimal strategy, generally speaking, is the one that produces the most points, except under those circumstances where increased points are irrelevant or result-neutral. Touchdowns in the 1st through 3rd quarter should always be followed by a 2PC attempt.

Yikes, time to back off once more. If the league averages over the past five years are either 52% (and growing!) or 55%, that means some teams in the league are getting 2PC less often than 50%. As much as I take it as personal mantra that one should almost always go for 2PC, there are some teams where that isn't true. Really bad offenses, for example. Or teams that are playing against really good defenses. But in those situations where a coach has determined that his odds of a successful 2PC are higher than 50% -- even 50.0000001% -- he's simply irrational for avoiding it in the vast majority of circumstances that present. And this should tell us that a lot of coaches on a lot of teams (good offensive ones) in a lot of situations (against very bad defenses) have simply screwed the pooch by sending out the XP unit. And if 32 coaches have collectively concluded that the general odds of success on a 2PC are less than 50%, well, they aren't apparently interested in the available data.

The truly disturbing aspect of all this is that everyone knows what the deal is, we are all aware of the reason why coaches routinely choose the XP over the 2PC and it has absolutely nothing whatsoever to do with the relative merits of those strategies as relates to winning. As Gregg Easterbrook points out:

Shanahan's decision was "bold" mainly in the sense that if the gamble failed, sports pundits would now be bashing, bashing, bashing him. Whereas if he ordered a kick and the Broncos lost in overtime, the players would be blamed. Coaches act like cowards mainly to avoid criticism -- how wonderful to see Shanahan not caring about that.

David Leonhardt of the New York Times:

Today, the biggest reason an N.F.L. coach might shy away from doing what Petersen did, Vermeil said, is "fear of failing." If a coach ended his team’s season by failing on a conversion, he would face a torrent of abuse, even if he had given his team its best shot at winning.

And this is tacitly acknowledged in broadcast booths when they feel the need to justify a 2PC or explicitly come out and wonder or speculate how much criticism the coach would get if they fail. If I'm the owner of a football team and I employ a person to perform the exclusive task of winning football games, I want them concerned with exactly and only the goal of winning football games and not about whether or not they will face media criticism following a loss.

And we all know this is why coaches routinely make cowardly, illogical decisions, and no one seems the least bit surprised or amazed or baffled or finds this bats!

Many smart people are complicit, including most of these coaches. I had this same discussion with an Ivy Leaguer friend of mine just last night, and he's much, much smarter than I am. His reaction was: C'mon Skin Patrol, do you really think you're the first person to think of this? Do you really think NFL coaches and owners aren't aware of the statistics? Obviously you're wrong, because everyone else does it the exact opposite of what you are advocating.

And you know what, that's kind of compelling. Who and how am I to question the collective wisdom of everyone in the NFL business? Well, I'm someone who understands that the expectation of rational behavior in human beings is largely a myth, that the mere framing of a decision influences the outcome, and that whatever the fuck the NFL thinks is the right thing to do, it can't be because Dick Vermeil made a chart 38 years ago with Xs on it. If I can't convince reader(s) that the 2PC is the right starting strategy deviated from only under justification, at least let me convince you that Phil Simms was right about one thing: whether you should kick an XP or go for a 2PC has everything to do with the actual likelihood of success, and not some chart. If a 2PC is always successful, there would be no reason whatsoever to kick XPs. If an XP is never successful, there's no reason to try it. And at some point, if and when 2PC rates increase above 55, 60, 65% success, the world-is-flat-cuz-we-all-agree mantra will cease to be reasonable in spite of the collective wisdom verbalized weekly by what many agree are the least critical thinking people on the planet, NFL Broadcasters (minus John Madden, he just rules). If I'm wrong -- I'm not -- it ain't because I don't have the right chart and it ain't because I'm so different.

In closing, imagine you're one of these two guys.

via www.rob-clarkson.com

You visit earth to watch your first football game having just read the NFL rule book and made yourself aware of the past five years of statistics on the 2PC vs. that of the XP. It is the first quarter. Last year's New England Patriots, one of the greatest offensive teams in the history of the league, against the Detroit Lions (I don't know if they played last year, but bare with me), the worst defense in the league by some measures last year. And then something very strange happens: Out comes the Patriots' kicker to attempt the XP. But that's not even the craziest thing about what is happening on the field, which is the Patriots' coach, who is alleged to be some kind of cheating but brilliant genius, just sacrificed some amount more than 1 point for some amount less than 1 point in a trade-off that has no rational justification.

No, what's absolutely mind-boggling about it is that as you watch no one in the stands, no one in the broadcast booth, no one on the entire planet seems the least bit surprised by this decision. Millions upon millions of allegedly logical people all acquiesce in this flagrantly irrational decision in unison, without so much as a murmur that something amiss has just happened in the brain-unit of the Patriots' head coach. Satisfied that things can only go down from here, you change the channel to soccer before fleeing the atmosphere in your space ship. This planet is filled with crazy people, and they are not to be trifled with.