Kicks Go Further in Denver, Right?
It’s well known that air, specifically air density, can affect the flight patterns of objects. Coors Field, home of the Colorado Rockies, is one of the best hitters’ parks in the MLB despite its large dimensions, thanks to the significantly thinner air in Denver due to its elevation. Anecdotal evidence suggests this relationship is also true in the NFL, as three of the five longest field goals in NFL history were kicked in Denver, including the current record, a 64 yard field goal from Matt Prater. However, we wanted to see if this idea is actually born out in a careful analysis. We also wanted to see if this effect is also noticeable in passing yardage, as well as if conditions have an impact on completion percentage.
To investigate these questions, we used the nflfastR package to get play by play data for the 2010–2020 NFL seasons. Each play had the stadium and weather conditions coded into the data, as well. We then used a Python script to strip down the weather conditions into temperature, as well as parse out any incomplete data. We also added the altitude of each stadium into the data, and a variable for kick accuracy. Kick accuracy is simply the percentage of made field goals in each stadium.
The analysis started with some preliminary plots examining the differences in kicking distance (for our analysis, kicking distance refers to field goals, kickoffs, and punts) and intended passing yardage by both game stadium and temperature. The box and whisker plots shown below are both for kick distance, but the pattern (medians being close to constant) is similar for passing yardage as well. The most interesting thing here is that the medians are relatively constant across the stadiums, so we are expecting to see that stadium does not affect kick or pass distance. The same holds true for temperature.
The main portion of our project was performing some analysis of variance tests on the means of our desired statistics. Each ANOVA model uses temperature, stadium, and an interaction between the two factors. Our findings show that for kick distances, only the stadium is statistically significant (F = 4884, p = approx. 0 with 41 degrees of freedom), meaning that we can expect the average kick at different stadiums to travel different distances, but this is not the case for different temperatures.
For pass distances, we see that both the stadium and the temperature were statistically significant (Stadium: F = 3.875, p = approx. 0 with41 degrees of freedom. Temperature: F = 7.67, p = 0.0056 with1 degree of freedom). These results are actually quite interesting. Because our analysis is done on air yards, it’s more accurate to say we are examining the variance amongst intended passing distance. Based on the results of the tests, we can infer that quarterbacks, at least subconsciously, will change how far they throw the ball based on the game temperature and the stadium they are playing in. Further investigation into this relationship shows (below) that quarterbacks hesitate to throw deep passes in below freezing temperatures. When we analyze completion probability, we see similar results and thus possibly the same subconscious relationship. Quarterbacks also hesitate to throw passes with a low chance of completion in colder weather.
We acknowledge that while we assumed independence and normality in the data, others may disagree with that assumption and thus would hesitate to use a standard ANOVA test for this analysis. Interested readers may want to use a nonparametric ANOVA test for their own analysis, or use a method such as bootstrapping to aid in their analysis.
Author’s note: This article was co-authored by Sejin Kim. The code used in this project can be found at his GitHub repository: https://github.com/kim3-sudo/nfl_analysis
