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Jesus, do you people not realize that a 29 yard field goal is
easier for an NFL kicker than a 24 yarder when you're kicking it from the hash? The angle's the only thing that can make it remotely missable and the angle's easier from further out.
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Since the hashes are at the width of the uprights, I don't think this is the case.
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This interested me so I looked up the dimensions.
Field goal pole is 9.75' from center.
Hash is 20' from center.
Hash to pole distances are thus 10.25' and 29.75'.
Kicks are 72' and 87' respectively.
Thus, angle for the 24 yarder is 14.348 degrees.
The angle for the 29 yarder is 12.159 degrees.
Second one is more difficult.
But to factor how much more difficult, you need to find the standard deviation of a kicker's (or more specifically, Vinitari's) error from the center (in degrees) and turn that into a probability distribution.
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Are you sure you are looking at dimentions for an NFL field. It's different than college.
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Not at all. Feel free to correct me if you find different measurements. It's basic geometry stuff... arctans and all that.
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Well, according to my eyes, and
this web site, the NFL hash marks are the width of the goal posts. I trust that I don't have to go through the trigonometry to show that as long as the ball is between the goal posts, the angle will decrease the further back you go.
The dimentions you gave are for a college field, so for college, your analysis would be correct.