Temperature and Field Goals

As a pilot, I'm familiar with the effects of weather on things hurtling through the air. Many people intuitively sense hot, humid air as thicker and heavier, but the opposite is true. Warm air, as we all learned in 5th grade, is less dense than cold air. And the water molecules that make air humid, for some reason I've long forgotten, actually spread all the other molecules out, creating even thinner air. Aviators are wary of the Four H's--hot, humid, high (elevation), and heavy--things that can drastically alter performance and make takeoffs and landings a challenge.

Planes, and jet planes in particular, love cold dry air. The dense air helps engines work efficiently, and it helps the wings produce lift, making for shorter takeoffs and slower landing speeds. Baseballs, on the other hand, love the Four H's. Fans of our national pastime are well aware of the fact that home run rates peak in the hottest months of the season, and that balls tend to fly out of the park in Colorado.

Field goal kicks are affected by the same factors as anything else flying through the air--wind, temperature, and even altitude. In this post, we'll take a look at how temperature affects field goal success.

The graph below illustrates the success rate for field goals according to kick distance (noted as the line of scrimmage) and broken out by three temperature ranges. I choose these three ranges for clarity on the graph. The three temperature ranges are 21-30 degrees (the cold extreme), 51-60 degrees (moderate), and 81-90 degrees (warm extreme).


I think of field goals in terms of two primary factors--accuracy and distance. Accuracy is the limiting factor in shorter kicks, until the success curve starts to drop off rapidly. This is where distance becomes the limiting factor. Despite some of the sample-size noise in the graph, you can see that the cold kicks begin to be range-limited earlier than than for warmer kicks. The shorter range kicks are largely unaffected by temperature, because distance isn't an issue. But past the 25 yard line, the success rates diverge at different ranges.

Roughly, it appears about 30 degrees of temperature is equivalent to about 5 yds of distance. It's not clear-cut because wind can correlate with bitter cold temperatures, but as we'll see below, teams are good at managing wind conditions on kicks.

For example, a 52-yard attempt in moderate temperatures can be expected to be successful about 55% of the time. But in temperatures at or below 30 degrees, they can be expected to be successful about 30% of the time, which is about the success rate for 57-yd attempts.

Wind is a very difficult factor to quantify because there are two components to wind--speed and direction. Tailwinds would increase range, headwinds would hurt it, and crosswinds would hurt accuracy. The data is very messy when it comes to wind direction, and I currently don't have enough information to determine the relative direction of the wind to the kick. But I was able to cleanly pull wind speeds out of the data.




We can't draw any direct inferences for a couple reasons. First, as mentioned, we don't know the relative wind direction. And second, there is an enormous bias in the data because teams will choose to attempt kicks when the wind direction favors success. But that doesn't mean we can't learn something interesting.

Teams appear to be very good at gauging when to attempt kicks in windy conditions because the average success rate for field goals are virtually identical for each bin of wind speed. For example, the overall success rate for kicks in winds above 25 mph is 82%, same as for kicks in winds below 6 mph. All wind speed groups average between 81 and 83%, indicating teams know when the wind conditions are too unfavorable for an attempt.

In contrast, they do not appear to be as aware of the temperature effect, otherwise, we'd see the same selection bias. The difference is small, but noticeable. Overall average success rates range from 80.2%, steadily increasing to 83.2% in temperatures in the 80s and 87% in temperatures in 90s. Temperatures in the 70s see success rates as high as 85.2%, but I suspect most dome games fall into that category.

In a future post, we'll look at the effect of altitude.

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27 Responses to “Temperature and Field Goals”

  1. Adam Davis says:

    My theory: Diminished accuracy at lower temperatures is derived more from *footing* than from other factors such as wind resistance. At greater distance a kicker must hit the ball with maximum force. Maximum force requires the surest of footing. As the temperature gets to freezing or below, footing can be greatly affected (footing is even affected on synthetic surfaces). Then again, I've never been a kicker, so this might be a dumb theory...

  2. Rob F says:

    Very interesting and clear-cut data on the temperature issue. Your explanation about denser air in the cold makes perfect sense. I wonder if there are any other factors? I think it could be possible that the footballs lose air pressure as the air gets cold (similar to car tires in the winter), and that then leads to kickers' inability to transfer as much power into the ball as they can in warmer weather.

    I know that footballs are intended to be at a certain air pressure (I don't know the number off the top of my head), and I'm sure the game officials get the correct air pressure before the game starts. But what I don't know is if they do that under game conditions, or if they pump the balls up in the warm air of the locker rooms and then bring the balls outside, where their air pressure drops. Does anyone know how this is done?

  3. parinella says:

    What about punting distance in cold weather? Any effect there?

  4. Sam's Hideout says:

    Minor pedantry: Ideal gas law doesn't have a mass term, as far as pressure goes, a water molecule is the same as a N_2 or O_2 molecule. However, H_2O has a molecular weight a bit over half that of N_2 or O_2 so the density of the air drops as the humidity increases, assuming constant pressure.

  5. Will F says:

    Has anyone looked into the effect of altitude? During the playoff game in Denver, Phil Simms claimed the altitude gave kickers an extra 10 yards in distance, and I thought, "You know, this is something that can be measured, not just an opinion you get to assert."

  6. Ian Simcox says:

    Will F

    Just had a quick look at low, mid and high stadia (ok, Denver is the only high one, but still).

    Looks like the elevation in Denver is worth ~5 yards on 40+ yd FG attempts. Not quite Phil Simms' made up 10 yards, but certainly nothing to ignore either.

  7. Anonymous says:

    You have to control for non-temperature stadium effects when trying to measure temperature effects. What if stadiums that have the coldest temps. in the winter also have the worst turf and worst winds -- throughout the year, even in September when it is warm? E.g., Heinz Field. You've done nothing to isolate the effect of cold air on a kicked ball. You've instead done a crude estimation of the overall effect on kicking accuracy of stadiums that happen to be in colder climates.

    Please read Mike Herman's exhuastive study of NFL kicking before going any further in your analysis. It's a ~50-page PDF he wrote for Footballguys.

  8. Anonymous says:

    Baseballs do not love the humidity (one of the 4 Hs). The humid air is less dense, which promotes longer flight, but the humid air makes the ball wetter, softer and larger, and thus more difficult to hit long distances. This is why Colorado keeps its balls relatively moist in the humidor -- to inhibit flyball distance by reducing batted ball velocity.

    http://webusers.npl.illinois.edu/~a-nathan/pob/Denver.html

    The author concludes: "I estimate that a ball hit 400 ft at 100% relative humidity will be hit 438 ft at 0% relative humidity and 419 ft at 50% relative humidity."

  9. Brian Burke says:

    One step at a time there, Mr. Herman. This isn't advancedKickingDoctoralDissertation.com.

    How about a link to your pdf please?

  10. Anonymous says:

    I have no association with Herman. I just read his stuff on footballguys.com. I believe you have to subscribe to get it (I was a subscriber when I read his report in the pre-season). As far as I remember, he has his own blog as well. The guy has looked at kicking from every angle, so that is why I would suggest contacting him or finding his research to combine it with your own.

  11. Brian Burke says:

    One more thing. Nowhere in this post do I claim to have "isolated" the pure effect of cold air on a kicked ball. I was very clear when I wrote, "In this post, we'll take a look at how temperature affects field goal success."

    Snarking that "You've done nothing to isolate the effect of cold air on a kicked ball," is childish.

    "You've instead done a crude estimation of the overall effect on kicking accuracy of stadiums that happen to be in colder climates." This is false and misleading. And if you took the time to actually read what I wrote, you'd know that.

    I presented readers with unadulterated data, illustrated in an easy to understand way. I wrote, "Roughly, it appears about 30 degrees of temperature is equivalent to about 5 yds of distance." I claim to have done nothing more.

    If you want to throw around a pejorative word like "crude", that's your right. I'll stick with "roughly."

    The snarky comments around here are getting weaker and more transparent. Or maybe I'm just better at sniffing them out. What is wrong with you people? Seriously. I came out of the Navy, not out of the academic world or the sports nerdosphere, so I find attitudes like this repulsive. Grow up.

    Here's how a mature, emotionally stable person would put that comment:

    "If you're interested in an in-depth study of various factors on kicking, here's the link... It's by so-and-so, who is..."

  12. Brian Burke says:

    Here it is:
    http://subscribers.footballguys.com/2009/kickology2009.pdf

    Awesome. Now I know who to draft as my fantasy kicker. In my 2009 retro-league.

    Now that's how you do snark!

  13. Rob F says:

    Mr. Burke,

    I don't know if you were offended by the one anonymous post in particular, or by anyone else's posts as well (inlcuding mine). If you were offended by any of my posts, I sincerely apologize. I was not trying to be snarky or sarcastic or anything else, just trying to post my opinions and thoughts in hope of advancing the discussion and bringing up other possibilities.

    When I read the other posts, I did not read them as being mean-spirited; perhaps I am obtuse and missed their subtle meanings.

    This is your blog and obviously you can do whatever you want with it. I am an infrequent commenter, but I do really enjoy reading your posts and the comments of other readers. I think the work you and the other posters have done here is far above what can be found anywhere else, and it's pretty amazing that you've been able to do that, basically as a fan, as you say, not a statistician or someone who has been formally trained to crunch numbers (at least I think that's what you've been saying). You take all the risk by asking a question, figuring out a way to answer that question, and then posting the answer for us to read. We have the easy job in the peanut gallery of reviewing your work and praising or critiquing it as we see fit - right here on your blog, no less!

    I hope that we can all enjoy the discussion on these interesting topics, and through that discussion, perhaps come up with other related questions or solutions. Enjoy the community of it, etc.

    Basically, I hope we can all get along! I enjoy dissenting opinion, but of course it's nice to get affirmation that your work is good too. In this post I sincerely want to tell you thank you for all the great work you do. I know that I am a more knowledgable fan for reading it!

  14. Brian Burke says:

    Rob, no it's this dude: "You've done nothing to isolate the effect of cold air ... You've instead done a crude estimation... "

  15. Anonymous says:

    Sorry to have struck a nerve, and to have pointed out that other people have already done your work, and have reached far more rational and useful conclusions.

    According to you:

    1) I wasn't in the Navy.
    2) I am emotionally unstable.

    According to me:

    1) You wrote an aritcle titled, "Temperature and Field Goals."
    2) I boldly assumed that this article would try to assess -- "isolate," if you will -- the effect of air temperature on a field goal kick in NFL football.
    3) You wrote, "In this post, we'll take a look at how temperature affects field goal success."
    4) You proceeded not to measure temperature's actual effect on field goal success, but rather to plot an Excel chart of raw field goal success rates vs. game temperature. No control for kicker or stadium.
    5) I pointed out the obvious shortcomings of your study, which eerily resembled the shortcomings of your "domed teams don't play well in cold" study.
    6) You got emotionally agitated, and accused me of being mentally unstable and -- even worse -- of generating "snark."

    The bottom line is that your recent string of temperature "analyses" have unequivocally sucked. Is that a Navy-enough term for you? They would each get shredded to bits on sites like Fangraphs, Tango's blog, and Baseball Prospectus. The fact that football analysis is still so far behind baseball analysis is the only thing allowing you to publish this kind of article without immediate ridicule. If I am the only guy who cares enough to call out bad science and misleading conclusions when I see them, so be it.

  16. JustinH says:

    http://webusers.npl.illinois.edu/~a-nathan/pob/Denver.html

    The author concludes: "I estimate that a ball hit 400 ft at 100% relative humidity will be hit 438 ft at 0% relative humidity and 419 ft at 50% relative humidity."


    I was surprised to see the above comment, which (unless I misunderstood the intent) seems to imply that baseballs don't fly as far in more humid playing conditions due to some combination of the ball gaining weight and the change in its coefficient of restitution (bounciness). As far as I'm aware, it takes longer for the baseball to pick up enough water from the ambient air to be significantly affected by these two effects given the time scale of weather variations, but Alan Nathan usually does good work, so I looked into it a bit.

    As it turns out, the quote above refers to the humidity in which the baseball is stored (for 47 days, in this case) -- not the environmental humidity. The experiment was motivated by the humidor at Coors Field, not the variability of fly balls in different environments.

    Outside of indirect effects, like the ball rolling through wet grass in very humid conditions, actual water condensation in very high humidity, etc., baseballs should fly further when the air is more humid.

  17. Tom says:

    Being a bit picky Brian, but I think you meant 'hurtling' rather than 'hurdling' in the first paragraph.

  18. Jonathan says:

    "Sorry to have struck a nerve,"

    This kind of fake contrition will get you nowhere, Mr. Herman. It's the quintessence of snark. Critique if you must, but don't expect anybody to take you seriously when you drop lines like "unequivocally suck" throughout your entire post.

  19. Anonymous says:

    Regarding Anonymous dude who was being a bit of a dick, just ignore him.

    Very interesting article and it would seem to explain why temperature controlled domed stadiums and warm weather stadiums would see better field goal success rates (all things being equal). Good stuff.

  20. Anonymous says:

    Brian - don't worry about kids like that. Having your own personal trolls is how you know you've made it.

  21. Pat R. says:

    I just found this site and am enjoying reading your analyses. I teach college-level statistics and like having these kinds of examples to show my classes. I've started trying to come up with some of my own as well. A site like this is inspiring as well as fun to read/debate.

    I also think it is nice to be able to have these discussions without being "academically perfect". That can take all of the fun out of it!

    Keep up the good work!

  22. Anonymous says:

    As someone who just recommended your work over in the forums of Footballguys.com -- and was completely unaware of this comment section and then decided to read it -- I'd advocate reading Herman's study, too. I think it might be behind a subscription pay wall, or perhaps you can contact Herman at his Kickology blog. I read it a while back and forget his conclusions, frankly.

    *I just went back and read it again (skimmed). There's no statistical study about field goal efficiency in certain weather conditions. It's anecdotal. There are charts on stadiums and their avg. temperatures and precipitation. There is kicking success/efficiency measured by stadium, where the success is broken down by month. He does discuss turf with respect to kicking efficiency. But nowhere in his study is there anything that controls for individual kicking efficiency within these discussions. He doesn't even discuss weather conditions on the particular day of the event; they're gleaned from monthly averages. He talks about stadium weather, breaks down temp. and precip. by month per stadium, and then interviews kickers about how they feel about weather in the next section, presented in anecdotal snippets. I guess you could fuse your research and control for those things, and it would make it more reliable, but I'm not sure what it would do to correlations and sample size, really.

    Just figured I'd give an FYI. Assuming you were using game-day temperatures, your work wasn't even close to done by someone else. If the commenter had taken ten minutes to go back and read what Herman wrote, he'd know that. My user name over there is rockaction, so this isn't completely anon.

    @Pat R. Any free resources you find helpful for those of us interested in taking a sort of intro prob/stat course on our own? I'd appreciate anything interesting, in a sort of course-esque format. (I took a college prob/stat course, and did terribly -- I was too young to show up and care, I guess.)

  23. Jonathan says:

    Haha you read my mind.

  24. Anonymous says:

    still nothing on Punting +/- 32 degrees F?

    Want to know if my punter Anger will be booming them no matter where we are.

  25. Anonymous says:

    I'm a statistical meteorologist and a field goal kicker (retired) so this is right up my ally! so here are a few notes...

    ... first, thanks for the really cool site
    ... golfers subtract about 10% for elevation in Denver. Not sure about footballs.
    ... as a kicker, I most feared "footing" as a previous poster suggested. NFL fields are way better than what I had to kick on...deep grass and mud. But poor footing is much more likely in the cold.
    ... cold affects ball carry and footing but also the physical condition of the kicker. I hated standing there stiff and cold. Much preferred being comfortable. Once again, NFL easier than in my day with no heater or blanket and often no practice net.

    ... golf tests have show perhaps 5% drop in carry due to cold but less than 1% due to humidity.

    ... on a different note...kickers are so much better now than in the 1960's it's incredible. Soccer style, weight training, junior kicking camps, field conditions, etc. The response has been about a dozen rule changes to stop kickers from taking over the game.

  26. Anonymous says:

    Great blog and post. I wonder if another way to determine the effects of wind on fg's would be to to examine how often they occur at your wind buckets. Is it possible that at higher wind speeds teams just attempt fewer kicks? If so, are they punting more often - showing the importance of D in the wind?

  27. Mark P. says:
    This comment has been removed by the author.

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