Sports

NFL Analysis: Impact of Temperature on Field Goals

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As a pilot, I'm familiar with the effects of weather on things hurdling 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.