Using play by play data that I've found on the internet from many (all? most?) 2014 college football games, let's see how good college field goal kickers are:
Answer: Better than me.
There's not tons of analysis to be done here. The further away, the harder it is and the field goal percentage decreases pretty linearly until you get 54 yards out, and then it falls off a cliff. (You can compare this to NFL kickers here; the chart you want is half way down the page.)
This data set doesn't have fake field goals included. In the case of penalties, I've counted whether the kick was good or not, regardless of whether it counted. This represents 2581 field goals attempted last year, which break down by distance like this:
Short kicks are uncommon, as teams will go for it on 4th and 1 or 2 in some cases. They plateau from 25 to 45 yards out, roughly, representing the number of drives that end at those various field positions. (Note: all distances here are recording the kick distance, which I've assumed to be the line of scrimmage + 17 yards.) Beyond 45 yards though, the number of attempts drop - some teams are going for it on 4th down, others are punting (sissies). A third possibility is that the end point of drives are not evenly distributed across the field which could be effecting this chart.
One point I'll make about the data is that there are undoubtedly errors. I've found a few and eliminated those, but with 2581 attempts, I don't have the time or desire to try and double check them all. So long as the errors aren't systematic, we could hope that they will balance out in the end, but that isn't likely to be the case. As an example, assume that all field goals are, in reality, good 90% of the time. Now, lets say that the incorrect result is recorded in my data (found for free on the internet!) 10% of the time. (I'm sure the data is much, much more reliable than this, but this makes the numbers easy.) So, out of 100 kicks in my made-up universe, 10 will be recorded incorrectly. But if those 10 incorrect points are random, on average 9 of them will be good kicks that get recorded as misses, and only 1 is a miss that gets recorded as good. So, my data will show 82% field goal percentage (81 correctly recorded as 'good' plus 1 false positive) with 18% misses (9 correctly recorded misses, plus 9 false negatives). This isn't an issue unique to football stats by any means, but what this does mean, is that any random errors in the data are likely to have pushed the results lower, not higher.
(There could also be systematic errors that are decidedly not random. For instance, the data comes from a computer reading play by play data off the internet. But imagine that the code processing the data that gets pulled from one specific source (Yahoo! sports might have different formatting than ESPN) erroneously records all field goals as misses. This is clearly going to muck up results, but in a very specific way.)
Next, what are the chances of getting a field goal blocked?
Not surprisingly, this increases with distance; kicking the ball lower will make the ball go further, but it also makes it easier to block.
And, to circle back to the question I asked in the last post: When is a hail mary a better option than a field goal? The simple answer is: if you think your kicker can get it there, you're better off kicking. Hail mary plays from 30 to 45 yards out are only successful 5 to 10% of the time.
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