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Number Mill: Quantifying the Heatvantage the Dolphins had on Sunday

Several people have explained the Bears defense’s 4th-quarter collapse, at least in part, by fatigue from the overwhelming Miami heat. Does that excuse hold up when run through the Chicago Bears Number Mill?

Chicago Bears v Miami Dolphins
Heat exhaustion can cause a man to do some wild things.

Previously on Number Mill: Cam Meredith | Markus Wheaton / DVOA | Dontrelle Inman | Chiefs Offense | FA Receivers 1 | FA Receivers 2 | FA Edge Rushers / SAQ | Trubisky’s rookie performance / Odds Ratios |

The Bears defense got Brocked in humiliating fashion in their loss to the Dolphins Sunday. I want to think this represents a momentary lapse. I’m more-or-less happy blaming it on some kind of curse, hex, or astrological misalignment, but others have proposed a more “scientific” explanation that seems like its worth investigating. Apparently, it was hot in Miami on Sunday. As the story goes, defenses sometimes get heat fatigue, especially late in hot games. Could that be why the Bears gave up 15 points in the 4th quarter and a mountain of yards in overtime?

Bobby Massie famously claimed he lost 12 pounds sweating during the game, but I thought I would check with our boots-on-the-ground reporter, Steven Schweickert to get the real scoop. Per Schweickert “Can verify from the end zone, Bears sideline to the left: It was hot.”

You can’t argue with that.

Since this is a Number Mill installment, I suppose I’ll support this insight with some digits. According to the closest weather station to Hard Rock Stadium—Opa Locka, Florida—the temperature ranged from 88 to 90 degrees during the course of the game, and the humidity ranged from 63-67%, peaking in the 4th quarter. That’s at least uncomfortably warm.

What’s the deal with humidity anyway?

I’ve heard heat is supposed to be worse when it’s humid out, but that seems a little odd because water cools you down, right? It turns out it is worse, and some nerds have already come up with a formula to calculate how much worse. It’s worse because your body can’t shed heat by sweating nearly as efficiently in humid weather, and you end up sweating much more with less benefit.

The metric for quantifying how much worse is called the Heat Index, and it’s been used by the National Weather Service since the 70s. You can think of it as humidity-adjusted temperature. Effectively, it estimates the physiologic effect of the combination of heat and humidity on the human body in reference to the effect of pure temperature without humidity (e.g. a heat index of 100 degrees the same effect as a temperature of 100 degrees with 0% humidity.)

The Heat Index in Miami on Sunday was 101.2° F.


To test the hypothesis that heat fatigue affected defensive performance, I decided to compare the points the Dolphins scored in the first half to the points scored in the 4th quarter, only looking at early home games (evening games, in theory would have less of an effect). I excluded this years multi-delay Titans game since there were several other factors at play, and the 4th quarter was actually quite late. I excluded 3rd quarter scoring on the theory that this would be a transition period where defenses where partially fatigued, and whether I grouped it with the early stats or the late stats, there would probably be a good deal of miscategorization—this would bias towards the mean and risk making this groundbreaking analysis appear falsely unimpressive. I chose to calculate Heat Index using the average game temperature and the 4th quarter humidity since humidity varied more and the 4th quarter seemed most important.

We already know what happened with the Bears, but was this a consistent trend on hot days? I looked back at all the games for the last couple years—and continued skimming back til 2014 looking for high Heat Index examples. The table below shows every game I pulled data on, sorted by Heat Index.

Heatvantage is the ratio of the rate of Dolphins points scored during 4th quarter heat fatigue compared to the first half (4Q pts * 2 / 1st half points). Cardinals game Heat Index is NA because the formula is not application below 80 degrees F.

Initial Takeaways

The effect of heat fatigue is real (tests for statistical significance showed an insignificant chance that 4th quarter scoring would be this much higher than 1st half scoring by chance and a less than 2% chance the “scorcher” games would have a higher Heatvantage than the “balmy” games by chance).

There are fewer scorcher games than I expected—in part because many of Miami’s early-season home games have been evening games or in London.

The Bears played one of the hottest Miami home games in recent history—technically the hottest by the way I calculated heat index.

Intermediate Takeaways

In the scorcher games, the average Heatvantage was 3.0, meaning Miami scored at three times the rate in the 4th quarter of scorchers than they did in the first half. That’s certainly an amount that matters, and it makes me feel a little less catastrophic about the Bears collapse.

In the balmy games, the average Heatvantage was 1.1 (a heatvantage of 1 would mean no effect) and not statistically significant. It makes sense that this advantage only shows up when the temperature is drastically different from what the visiting time is accustomed to.

Of the scorcher games, the smallest Heatvantage was against the Titans. Nashville is relatively hot and humid compared to the other visiting teams, and the players may have been more accustomed to the oppressive weather.

This is a photograph of Miami’s Hard Rock stadium during early game hours. Guess which sideline is the one blasted with sun? This is sociopath-level stadium construction.

Even the engineers who designed the stadium were in on the heat scam.

Final Takeaways

Did the Bears defense lose effectiveness in the 4rth quarter due to the suffocating 38.4° C Heat Index? Absolutely. Why did I suddenly switch to Celcius? Because Miami conspired with the sun to use the 38.4° C Heat to C H E A T their way into a win against the Bears. Would the Bears have won if the heat weren’t a factor? I have no doubt. But although the heat was necessary to make the Bears lose, it wasn’t sufficient.

The Bears needed to shoot themselves in every paw and bite off their own tail in addition to make this loss a reality. Despite any excuses we can come up with, the Bears still whiffed big. I guess there isn’t much you can do when you’re stuck between a Brock and a Hard (Rock) Place. #AmIwrong?

At least we all learned something today.