To kick or not to kick?

hey Sal where are the chances i can successfully kick a 50-yard field goal vs a 20-yarder awesome question bradley and i was able to dig around a little bit to find the information you need this chart right over here this is from decision science news.com this is the URL if you want to take a look at it take a look at it yourself and they took a look at every field goal between 2002 and 2012 and saw whether they were made or not in from the various distances and just so we can make sure we're reading this right on the horizontal axis right over here this is the yard line from which it was kicked and these were probably anomalous data points because people were not kicking field goals from the what does this look like the 85th yard line so these were probably just errors in the data but this curve that you see here is pretty interesting and actually let me let me draw on this curve let me do it in a darker color so that we can so that we can see this curve that's forms and it helps us answer the probabilities to your question so this says that a field goal that is made with a line of scrimmage is pretty much the 0 yard line is pretty much a short thing maybe there's some slight chance you miss it but it sits in the very very high ninety percent now a field goal where the line of scrimmage is on SE near the 0 yard line it's near the end zone or it's near the one yard line we know that that's an actually going to that's actually likely to be a 17-yard a field goal because you have to account for making it through the end zone or making it through well make him through the end zone and for the fact that when you when you hike the football for the kick the football goes backwards a certain number of yards so this one right over here would be a 17 yard field goal so that would be around approximately 17 yards and that one you can be very confident about making now you asked about a 20 yard field goal well a 20 yard field goal is going to be made when roughly the the ball is at the around the 33 yard line or so so 20 yard field goal so this would be the 10 yard line a 20 yard field goal would be this data point right over here it would be roughly right over there because once again if the ball gets to the 3-yard line then the field goal is going to be about a 20-yard field goal and we see that that still has a probability pretty close to one or it's a very high ninety percent probability for a 20-yard field goal so this is a 20 yard field goal now let's think about a 50-yard field goal a 50-yard field goal is going to be the case where the ball is going to be let's see 15-17 is going to be on the 33 yard line so this is 30 this right over here would be 35 so 33 is right around there so the ball is on the 33 yard line resulting in a 50-yard field goal we can see that the probability is a good bit less it looks like the probability in this situation see that would be a seventy percent this is 0 point 6.8 w point 7 it looks like it's about a sixty-six percent chance so sixty-six percent chance for 450 yard field one this is just based on obviously every kicker is different and they can different in different environments and different fields and it could be windy or not but if we were just average all of the kicks between 2002 and 2012 this is what the data is showing us a 20-yard field goal very high ninety percent a 50-yard field goal is about two-thirds as likely as that and you can see the probability drops off very quickly from there so you can see if you're if you're taking a field goal from this is if the ball is at the that looks like it around the 45 yard line you are looking at let's say you add 17 245 you're looking at a field goal that's in the low 60s so this right over here would be what a 62 yard field goal 62 yard field goal if it's taken from the 45 yard line to do that math right 45 plus 10 is 55 plus another seven is 62 as you can see over there for 62 yard field goal the probabilities a lot lower it's about a little less than a twenty percent probability so one in five of those are going to be made and if you go leave a little bit further your probability very very quickly gets close to zero and it's pretty clear that that that the that coaches are aware of this or at least they might not have seen this chart but they're intuitively aware of it because on decision science news com there was also another cool chart that shows where all the field goals were taken from the distribution and when they were made and when they were missed and so this is from one of their readers a decision science news what they found was so they looked at all the field goals and this time they actually did it by the field goal distance so this is a 17 yard field goal right over here and all of the 17 yard field goals were made as you can see but then as you get further and further as you further and further away from the goal posts as you get longer and longer for your field goals your probability goes down so for example if you were to look at a 40-yard field goal that's this group right over here like she let me do that in a more transparent color so a 40-yard field goal is this goal right over here so it looks like it looks like about looks like about 350 we're takin 350 were made and it looks like a little over 50 were missed so a total of 400 were taken 50 missed 350 made so 50 out of 350 it looks like it looks like let's see 50 out of three so I'm sorry 50 out of 400 it seems like only over in this situation it seems like one out of every eight field goals were missed or another way of thinking about seven out of eight were made so you're going to look at a you're going to be looking at a high 80s percent chance of making that but as you get further and further away from the goal you can see that people take a lot fewer of them and the ratio of the missus to the maid gets higher and higher and higher the further that you go so this is pretty interesting it's a it's an interesting thing to look at all of the data and to see that coaches are acting for the most part in a rational way