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4 Comments | Jan 13, 2010

The Impossibility of the Field Goal

CB022359I was moved—more like compelled—to write this essay in response to watching Houston Texans place kicker Kris Brown miss an extraordinarily high percentage of the field goals he attempted during the 2009 season, many of them from quite close distances, chip shots in the sporting vernacular. We are not talking baseball here, where the mark of excellence is failing to get a hit only two out of every three attempts. Place kicking in football has evolved to the point where it is now considered largely automatic, particularly for kicks of less than, say, thirty yards. And again employing the baseball analogy where hitting is but one of several tasks entrusted to the players, the field goal kicker does nothing else whatsoever for the team, unless he happens to be walking up and down the sidelines handing out water during the game, which task, by the way, would have significantly enhanced Brown’s value to the Texans this year and likely improved his chances, at least somewhat, of having a contract to continue playing next year. And while the sporting press and fan base, myself included, were quick to vilify Brown for his dismal performance, with the benefit of a bit of hindsight and some cold objective engineering analysis, one realizes the real marvel is that more NFL kickers don’t perform as badly as he did this season.

There comes, more often than a loyal fan would prefer, that trenchant and all too common moment in a football game that makes fans cringe and cover their eyes, and coaches on the sidelines tear headphones from their heads. Your team has played an uninspired game or maybe just a particularly egregious second half. You’re down by two or three points. But you have, through some last-minute miracle, possession of the ball inside your opponent’s thirty-yard line, and thanks to a bit of unexpectedly fortuitous clock management there remain two seconds in the game. There’s only time for a game winning or tying field goal attempt. Good Christ—NO human should be subjected to stress like this. The only thing worse is watching, when the kick finally occurs, as it shanks right or hooks left around the outside of the goal post, leaving your team to walk, defeated and humiliated, off the field, their best efforts, their blood and sweat, undone by the failure of a single man[1] juxtaposed with the insane physics of a football and the cruel serendipity of the game itself. Many a television screen has been perforated by flying beer bottles in response to this oft-relived scenario.

Name of the game be damned, a football was never engineered or intended to be kicked[2], at least not in the strictly mechanical and aerodynamic sense. Any freshman engineer knows that if you intend to kick a ball[3], you make it spherical, so that there exists at least a passing chance of it traveling in the direction where it’s actually aimed. The real wonder is that field goals, and by extension extra points, ever pass through the uprights in the first place, what with all the forces of nature and physics conspiring against a successful outcome.

Let’s pause for a moment to review the mechanics of the process, along with some salient technical details. The football is about eleven inches long, twenty-two inches in circumference at its widest point, and weighs something like fifteen ounces. At typical indoor stadium temperatures, the fully inflated pressure is about thirteen p.s.i[4]. The ball is shaped rather like a dirigible and it is at its most aerodynamically stable when traveling point-first with a significant spin along its longitudinal axis which gyroscopic effect keeps the whole thing rather predictable. The target of the field goal kicker is, of course, the goal post at either end of the field, the horizontal cross bar of which is ten feet above the ground (at its bottom) and the vertical side posts of which are separated by a distance of eighteen and a half feet (inner sides of posts). These posts rise something like thirty feet above the horizontal bar, the better for officials to gauge the success or failure of the attempt. The objective of the kick is, of course, to propel the ball with one’s foot so that it passes both above the horizontal bar and between the two vertical ones[5]. Sounds simple enough.

The first, and most germane fact attending this discussion, obvious to anyone who has successfully taken a junior-high geometry class, is that the farther the kicker is from the goal post, the more difficult is the attempt. This is so for two reasons, one obvious, the other only slightly less so. The farther kick requires of course that greater impetus be imparted to the ball in order to cause it to clear the horizontal bar[6]. However, greater distance also requires greater accuracy, since the angle to be subtended by the kick is reduced with increasing distance from the end zone, as a simple drawing will demonstrate[7]. This means that at precisely the moment the kicker is focused on kicking the ball harder so as to cover the increased distance, an even greater degree of accuracy is called for as well. Without getting into a detailed discussion of nonlinear dynamic effects, suffice it to say that the difficulty of the kick rises at an increasingly nonlinear rate with increasing distance, e.g. a forty-yard field goal is far more than twice as difficult as a twenty-yard one[8].

To make matters worse, there are many more variables in play that compound the magnitude of the challenge faced by our intrepid kicker. Because neither the ball nor the kicker’s foot/shoe are solid, i.e. they all compress together for a brief millisecond at the point of impact, there is additional opportunity for error to be introduced into the process at the point of initiation[9], depending on the exact spot on the ball struck by the shoe, the portion of the shoe touching the ball, any moisture on the ball, shoe or grass, and the angle at which the holder holds the ball just prior to impact. Indeed, in an effort to eliminate at least one small variable from this admittedly complex equation, the holder, like he doesn’t have enough to worry about simply catching the ball from the snapper[10], placing it on the ground at the proper angle[11], and making sure he doesn’t get his hand kicked by a cleated shoe, all in something like a tenth of a second, is also exhorted to spin the ball so that the laces face outward, i.e. toward the goal posts and away from the kicker’s shoe, the (entirely reasonable) hypothesis being that impacting the uneven laces could further discombobulate the kick. The challenges endured by the holder were tragically demonstrated during the 2007 Dallas Cowboys divisional play-off game during which quarterback Tony Romo, a player whose vastly-more-than-considerable paycheck is justified in large part by having “good hands,” summarily botched the hold on what should have been a game-winning field goal attempt, thus costing his team the win and the season. Finally it is worth noting in passing that at the exact moment these three individuals (snapper, holder, kicker) are engaged in this highly choreographed endeavor[12], there are eleven large, fast, hyperventilating humans who are vigorously engaged in trying to thwart the effort, either by leaping so as to create a barrier between the ball and its intended flight, or trying to, at a minimum, disrupt the kicker’s efforts through the psychological expedient of running toward him in a threatening and disconcerting manner and uttering all sorts of vituperative epithets.[13]

In 1998 Jason Elam of the Denver Broncos achieved the distinction of kicking a sixty-three-yard field goal, which, as astonishing as it sounds, merely tied the NFL record that had already been held for nearly thirty years by Tom Dempsey of the New Orleans Saints, whose sixty-three yarder was arguably even more memorable for the fact that he did it with only half a foot[14], and he did it, as so often seems to be the case, for the final play in a game where the kick’s outcome determined who won[15]. Indeed, a huge part of the field goal challenge is mental. For starters, dating back to high school, place kickers are the least respected members of any football team. They are the ones with the clean uniforms, the ones who never get touched, the ones who aren’t out on the field knocking heads play after play and then struggling for hours just to get out of bed on Monday morning. And yet, perhaps surprisingly, they are often the one on whom the game’s outcome depends. When the score is close and there are only seconds left in the final quarter, they are the ones over on the sidelines practicing kick after kick into the net. One wonders if they relish the position or if they are over there secretly praying for the touchdown so they won’t have to go in. And they are the ones who get frozen.

It’s not sufficient that kickers get no respect and that their entire careers are based on trying to simultaneously defy numerous laws of physics, they also have to be the one player that the opposing coach has to attempt a mind-fuck on. And even though everybody in the stadium knows it’s coming, they still do it, and, more often than not, it has the desired effect, viz. to throw the kicker off whatever psychological rhythm he has developed at that moment. If the opposing coach is really good, he will wait until the entire line is set, the kicker is in position, and just ready to motion his readiness to the snapper before calling time out, during which minute he (the opposing coach) and his team will stand around on the sideline jawing about nothing in particular and relishing the fact that they are royally pissing off the kicker who, in turn, now gets to wander around in the middle of the field wondering whether all this bullshit is really worth it and why he didn’t go to dental school like his mother wanted him to. If the opposing coach is a world-class prick, the kick is an especially crucial one, and the team has a sufficient number of time-outs remaining, he may actually repeat the process and try to freeze the guy a second time. It happens.

But let us suppose for a moment that the kick finally takes place, and let us further suppose that the impact between the kicker’s shoe and the ball is true and accurate. There now ensues the actual flight of the ball, the final destination of which ultimately determines whether the whole thing was worth it or not. The first consideration is that of the initial angle of departure of the ball, one of the few aspects of the entire endeavor that the kicker actually has the luxury of giving some thought to well prior to the kick. The choice is a function of distance required and an analysis of the defensive line’s ability to reach high enough to block the kick. This is, by the way, yet another reason why the longer kicks are significantly more difficult than shorter ones, i.e. the longer kicks typically require a lower departure angle, thus increasing the likelihood of the ball being touched by one or more defensive players, all of whom are, from the moment of the snap, leaping vigorously upward with precisely that intent[16]. Finally, one additional aspect of the kick, and one which is nominally within the kicker’s purview to select, though he in fact does not, is the force with which he kicks the ball. Intuition would suggest that the speed of the kick, i.e. the leg’s rotational velocity, would diminish with decreased kick distance. However, as it happens, place kickers are trained to always kick the ball as hard as they can, no matter the distance, and to adjust other factors to compensate as necessary. The benefit of this technique is that eliminates one important variable from our increasingly complex and multi-variate equation.

So assuming that the ball has successfully departed the kicker’s shoe, and that, as well, it has successfully cleared the defensive line, there remains only the flight of the ball to determine the success or failure of the kicker’s effort. Two exogenous factors come into play at this point, neither of which the kicker can do anything about, but which must nonetheless be taken into account in his mental calculations prior to the kick. The first is the altitude at which the game is being played. One of the several reasons that Dempsey’s sixty-three-yard field goal is widely regarded as more impressive than Elam’s[17] is that the Broncos kicker achieved his record in the rarified air of Mile High Stadium in Denver, whereas Dempsey’s kick was, in fact, accomplished at slightly below sea level. The relatively low air pressure of a location like Denver has two salutary effects on place kicking. It makes for longer kicks simply due to the air being thinner and hence offering less resistance to the ball in flight. In addition, the thinner air interacts with the surface of the ball less and so minimizes the deleterious effects of spin to be discussed shortly. The second exogenous factor that comes into play is whether the stadium is domed or outdoors, the former being preferable to the kicker for its elimination of wind and other weather-related effects. Unfortunately for kickers, the majority of stadiums in the NFL are a) at or near sea level, and b) open to the elements.

Which is where weather comes into play. For it is ultimately the interaction between the ball, which is turning end-over-end and frequently spinning as well, and the surrounding air that determines the direction of the ball’s flight. As any golfer can easily attest, the direction in which the ball is moving at the moment of impact often bears surprisingly little resemblance to its direction of travel at the end of its journey[18]. Not being an aerodynamicist by training, it is difficult for me to opine as to the effect of specific spin and tumble elements of the ball on its ultimate direction. The following empirical observations do however seem to apply most of the time. First, the less spin imparted to the ball, the more likely is its successful bifurcation of the goal post uprights. Second, to the extent that eliminating all spin from the kick is virtually impossible, a generally clockwise spin[19] will, more often than not, cause a slice toward and possibly beyond the right upright. Conversely, a counterclockwise spin seems frequently to cause a hook toward the left upright. Spin is though an extraordinarily complex effect to model into this analysis, since the gyroscopic interactions between spin and tumble are highly correlated and unpredictable. Hence the optimal objective of eliminating all spin and reducing the ball’s motion to only an end-over-end one.

Of course, even with perfect ball motion and initial direction, the effect of winds cannot be overstated, particularly as the ballistic path of the ball routinely takes it far above field level where wind direction and velocity can vary markedly from conditions on the field at that precise instant. Mitigating this effect is, perhaps surprisingly, to some degree in the kicker’s control. A skilled kicker can attempt to gain a sense for the speed and direction of winds aloft by viewing flags, blowing debris, etc. around the stadium and attempting to alter his aim somewhat to compensate. This is however, an inexact art at best and many a perfectly kicked ball has gone left or right of the poles due to atmospheric forces unseen and/or unappreciated by the kicker.

In summary, it is worth noting that despite all of the challenges and impediments discussed in this treatise, the success rate of field goal kickers in the NFL has systematically increased year-over-year for some time. And it is not as though the equipment has improved much in that time. There are no shark-skin swim suits or carbon fiber golf clubs in play here. At the end of the day it comes down to the interactions of a ball, a leg, a shoe and some external conditions, all of which have remained more or less unchanged since before any of us were born. Suffice it to say then that the field has simply grown ever more specialized, and that, as with all manner of sports, the conditioning and coaching have improved markedly and will likely continue to do so. None of which begins to explain why a Kris Brown can, out of nowhere, have a season in which he misses more field goals than he makes (in a segment of the sport where a ninety-five-percent completion rate is not uncommon, mind you), except to say that perhaps in the end it boils down to what we convince ourselves we can do, and that the more we fail, the more we expect to fail.

[1] Well, three men actually, but more on this to come.

[2] At least not an American NFL football. Throughout this treatment we will be analyzing only this type of football, i.e. NOT the balls used in soccer, Aussie rules, rugby, or any of the other myriad international games that have the temerity to label themselves “football”.

[3] Or for that matter, throw it, catch it, or hit it with a piece of wood.

[4] An interesting but somewhat digressive conundrum arises here, to wit, any player will tell you that the ball feels harder (both to catch and to kick) on especially cold days, yet, in fact, the air pressure in the ball actually falls as the temperature falls (ref. Charles’ Law), meaning the ball ought to be getting softer with falling temperatures. Do game officials actually add more air prior to the start of cold games?

[5] The ball is allowed to actually strike either bar, so long as it then proceeds above the cross bar and through the uprights.

[6] In fact the ball is almost always actually descending as it passes over the horizontal bar, i.e. in the second half of its more or less ballistic path.

[7] According to my analysis using graph paper and protractor, the twenty-yard field goal requires keeping the kick within a total angular range of twelve degrees, whereas the forty-yard kick requires an angular error of no more than seven degrees, nearly twice the degree, as it were, of difficulty, before taking into account the extra distance, greater opportunity for wind effects, ball spin, etc., all of which effects are exacerbated by increasing flight time, i.e. distance, and all of which will be addressed shortly.

[8] One wonders at this juncture whether a greater percentage of missed field goals are due to insufficient distance or insufficiently accurate side angle. I am not certain if this data exists, but intuition suggests that angle is by far the greater culprit. Kickers know well the maximum distance they are capable of achieving and only rarely attempt anything farther. It is also relatively rare, notwithstanding the vigorous effort expended by defensive lines, that a kick is actually blocked or deflected.

[9] After which point the matter is out of the kicker’s hands, save as a spectator.

[10] Who, lest we minimize his role in this endeavor, is attempting to accurately deliver the ball while upside down, looking through his legs at an inverted target (the holder), and all while contemplating the three-hundred-pound individual residing at that very moment approximately one half inch from his face, whose breathing he can very clearly hear, and whose intent on his person is questionable at best.

[11] In an ideal world, leaning backward at an angle of about ten degrees from the vertical, though this too is subject to variables such as kicker preference, wind and turf conditions, and hash mark placement.

[12] Which in total lasts for perhaps eight tenths of a second from snap to kick.

[13] Keeping in mind as well that of all the players on a football team roster, the place kicker is the one least routinely exposed to such physical contact, and indeed rarely is ever touched at all unlike his teammates. Hence he is equipped with the smallest amount of padding with which to mitigate the consequences of any such impacts, a fact that must surely cause him to reflect mightily each time he takes the field.

[14] Dempsey was born with no toes on his right foot, his kicking foot. And, as if this were not inconvenience enough, he was actually castigated by certain among the sporting press for having an unfair advantage due to the modified shape of his shoe, so much so that an NFL rule now exists stating that all kicking shoes must be shaped the same, even if the kicker has a deformity of some sort!

[15] Even longer field goals have been kicked in college and NFL play-off and pre-season games, the longest being that of Abilene Christian’s Ove Johansson, a 69-yarder, over two thirds the entire length of the field.

[16] Though the rules preclude defensive players from actually climbing on top of one another in an attempt to gain greater height and block the kicked ball. The fact that a rule needs to exist against this contingency doubtless means that for some period of time it was a common occurrence, cleats notwithstanding.

[17] The half-a-foot thing aside

[18] And that’s with a spherical ball!

[19] The football being viewed from above.


Brian 10:52 pm - 17th January:


You might want to check out the somewhat-related essay about punting. Glad you found this one useful.

Cheers, and thanks for reading.


Calvin 6:00 pm - 17th January:

This is a very well written and researched article. I was a kicker at a division 1 school for two years and most people just don’t understand how hard it is. You do absolutely nothing the whole game and you are expected to come into a game where you have one chance to either make a play or not. It is easy for position players and fans to criticize when every other player has a chance for redemption constantly. It is easily the most stressful position in football from a mental perspective.

Brian 9:38 pm - 10th January:

Really? How’s that exactly? I’d be interested in hearing more about your project.

Thanks for reading,


jake foop 5:28 pm - 10th January:

yay u help me with science fair project!

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