by Tim Lehman and Becky Dragan
After the NCAA decreased of the width between the goal posts, some have argued that extra points would be easier from farther back. Such people maintain it would be wise to take a delay of game penalty to get a "better angle" at the extra point. Common sense implies at some point the angle would begin to decrease but the question remains where does it decrease.
For this write-up, we will consider when the ball is on a hash mark. At the hash mark, the angle of a "good" extra point will be at its least. Thus, if it makes no effect with the ball at the hash mark, it will never make an effect.
Click here for a GSP sketch almost to scale (off by half of a yard or less.) In the sketch, angle (ABC) shows the angle a kick can be and still be good with the new goal posts rule. Angle (DEF) demonstrates the angle for the older, wider goal posts.
Let's look at an exact calculation of the best angle to kick a field goal. In the following chart, x is the distance in yards from the back line where the goal post is. So, the goal line on a football field would correspond to 10 yards in the chart. Y is the distance in yards from the right side of the goal post to the right hash mark. W is the distance in yards from the left side of the goal post to the right hash mark. We then calculate angle theta and then angle phi in degrees. Angle theta is the angle from the right goal post to the kicker to the hash mark on the back line. Angle phi is the angle from the left goal post to the kicker to then along the yard line the kicker is on. Finally, we calculate the angle of the field goal.
| x | y | w | arctan(y/x) | arctan(x/w) | best angle |
| 2 | 5 | 9.16666666 | 68.1985905136482 | 12.3080158261064 | 9.49339366024544 |
| 4 | 5 | 9.16666666 | 51.3401917459099 | 23.5747062171872 | 15.0851020369028 |
| 6 | 5 | 9.16666666 | 39.8055710922652 | 33.2065703341837 | 16.9878585735511 |
| 8 | 5 | 9.16666666 | 32.0053832080835 | 41.1120904598102 | 16.8825263321063 |
| 10 | 5 | 9.16666666 | 26.565051177078 | 47.4895529427554 | 15.9453958801666 |
| 12 | 5 | 9.16666666 | 22.6198649480404 | 52.6241925245532 | 14.7559425274064 |
| 14 | 5 | 9.16666666 | 19.6538240580533 | 56.7847485253595 | 13.5614274165872 |
| 16 | 5 | 9.16666666 | 17.3540246362613 | 60.1908858112672 | 12.4550895524715 |
| 18 | 5 | 9.16666666 | 15.5241109967543 | 63.0121094351021 | 11.4637795681437 |
| 20 | 5 | 9.16666666 | 14.0362434679265 | 65.3764352296194 | 10.5873213024541 |
| 22 | 5 | 9.16666666 | 12.8042660652868 | 67.3801350667535 | 9.81559886795971 |
| 24 | 5 | 9.16666666 | 11.7682889320206 | 69.0959209305567 | 9.13579013742269 |
| 26 | 5 | 9.16666666 | 10.8855270546587 | 70.5791790606002 | 8.53529388474111 |
| 30 | 5 | 9.16666666 | 9.46232220802562 | 73.009176719659 | 7.52850107231539 |
| 35 | 5 | 9.16666666 | 8.13010235415598 | 75.3236068727629 | 6.54629077308111 |
| 40 | 5 | 9.16666666 | 7.1250163489018 | 77.092591337807 | 5.78239231329124 |
| 45 | 5 | 9.16666666 | 6.34019174590991 | 78.4861688236631 | 5.17363943042703 |
| 50 | 5 | 9.16666666 | 5.71059313749964 | 79.6111421919214 | 4.67826467057895 |
| 55 | 5 | 9.16666666 | 5.19442890773481 | 80.5376777987316 | 4.26789329353358 |
| 60 | 5 | 9.16666666 | 4.76364169072618 | 81.3136454249843 | 3.92271288428948 |
From the chart, one can see that the widest possible angle is at 6 yards from the goal post. However, the extra point (or any field goal for that matter) is not kicked from within the endzone. So the best place to kick the field goal would be at the goal line (or 5-7) yards back because the field goal is usually kicked from 5-7 yards from the line of scrimmage. It would never make sense to take a delay of game penalty to improve the angle.
We conclude by saying that sports commentators would benefit from having a little high school mathematics.
Click here for the NCAA football rules homepage. If rules change, this information will no longer be current.