Assignment 6:

Exploring the changes in difficulty of kicking a field goal in the NCAA after rule changes, as well as exploring the idea of 'centering' a ball before the kick.



Teo Paoletti

A series of rule changes occured to NCAA football in the early 90's that many thought affected a kickers ability to hit a field goal. Going back to 1959 the standard field goal post width was 23 ft 4 inches (still used in high schools today). However, in 1991 officials decided to lessen the width to 18 ft 6 inches. However, the officials did not change the width of the hashmarks which at the time were 53 ft 4 inches apart. During this time, many felt that field goal kickers, kicking at the hashmarks, were at a disadvantage then kickers before them as their kicking angles were more severe. In 1993 the NCAA shortened the distance between hashmarks to 40 feet, alleviating some claims that field goal kicking had been much more difficult from the hashmarks. Below we analyze these claims looking specifically at a 10 yard attempt, 30 yard attempt, and 50 yard attempt. Also available are applets that allow the reader to play with the angles themselves.

10 - yard Attempts

A 10 - yard attempt is the minimum distance of a field goal attempt. It is essentially on the goalline.

1990 Rules

1992 Rules

Current Rules

Looking at the different angles at the hashmarks, clearly the kickers pre-1991 had a a much better angle (25 degrees) then after they lessened the width of the goal post (9 degrees). Also, shortening the hashmarks did not make life that much easier for the college kicker, increasing the angle only by 2 degrees. 'Chip shots' have definitely become much more difficult for college kickers after the rule changing the size of the goal post, and changing the hashmarks has done little to make them easier! If we consider the value of the difference from the original to the new method, divided by the new method as the percentage increase in difficulty, we see that in 1992 it was about 64% harder to hit a field goal and currently it is about 56% harder to hit a field goal.

30-yard Attempts

1990 Rules

1992 Rules

Current Rules

Again, we see that pattern that it was much easier to hit a field goal before 1991 then after. Similarly, moving in the hashmarks did little to make the field goal easier. Looking at the percent increase of difficulty, in 1992 it was about 64% harder while currently it is about 62% harder.


50-yard Attempts.

1990 Rules

1992 Rules

Current Rules

While it initially appears that the level of difficulty has levelled off a bit at the 50-yard mark, we should first check our percentage of difficulty before we assume this (as all of the numbers are smaller). In 1992 it was about 64% more difficult to hit a 50 yard field goal, and currently it is 63% harder to hit a field goal.

Our analysis shows that hitting a field goal from the hashmarks did get significantly more difficult after the 1991 rule change decreasing the size of the goal post 5 ft. Also, decreasing the of the distance between the hashmarks made close field goals easier, but has a shrinking affect the further we move from the goalline, so much so that by the time we reach a 50 yard field goal there is no difference in difficulty in relation to hashmark width.

Here are the applets used to produce these pictures (in html form) so that you can play yourself!

1990 Field

1992 Field

Current Field

One thing you can see while playing with the applets is that, no matter what, on a regulation football field, it makes no sense to take a penalty to "get a better angle." Starting at the goalline, the angle decreases the further away from the goalline you are. So not only are you making the kick more difficult by adding to the distance, you are also shrinking your angle.

However, any avid football fan has seen the 2nd to last play of a game where an offensive player takes a snap, moves the center of the field then falls down, in order to center the kick. (Occasionally they move to a different hashmark due to wind, kickers hook or draw etc, but for mathematical purposes let's assume there is no wind and the kicker kicks straight!) Let's look at the advantage of kicking from the center of the field vs the hashmark at a range of 10 yards, 30 yards, and 50 yards on the current football field.

10 yards

Centered we have an angle of 16 degrees vs an angle of 11.2 degrees from the hashmark. Using our same formula of (new-old)/old, we see that the centered field goal is actually 44% easier then the fieldgoal from the hashmark, supporting the use of a play to center the football.

30 yards

At 30 yards centered we have an angle of 5.4 degrees vs 5.2 degrees at the hashmark, which is only a 3% improvement. Significantly less then we saw above!

50 yard

At 50 yards we have a centered angle of 3.23 degrees vs 3.18 degrees from the hashmarks, an improvement of 2%.

Using the results above, it appears that the logic of having a quarterback or running back 'center' the ball for the kicker only makes sense at shorter distances. The further the distance from the goalline the less this helps. As it does not help, I would suggest not doing it for fear of a botched snap or fumble that could result in a turnover.

Here is an applet that lets you play with the location of the ball, both the angle from center and from the hashmark and the percentage of how much easier the centered kick is.

When playing with the applet, move the point M.

You may notice that any kick beyond 21 yards is only 10 percent easier, because of this, that would be my limit for when it is worth it to center the kick. However, you need to make this decision for yourself!


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