Before we look at the numbers, I should note that running and passing are connected in game theory terms. The better a team’s passing attack, the more an opposing defense needs to respect it, possibly allowing bigger running gains. And same goes for a great running attack. The better it is, the more the defense needs to be on guard near the line of scrimmage, lowering its guard against the pass.
Cold temperatures, or at least the kinds of conditions that go along with cold temperatures, appear to reduce the effectiveness of passing. With that in mind, defenses might be worried slightly less about deep passes and stack the box in cold temperatures. Thus, we might expect that cold temperatures could indirectly reduce the effectiveness of running.
This is where it gets really interesting, because that’s not what happens at all.
The graph below plots the yards per carry (YPC) for all runs since 2000 according to game temperature. Home team YPC is in red, and visiting team YPC is in blue.
Visitor YPC is fairly flat, and as expected, it’s lower than home YPC. What’s so interesting is that home YPC steadily climbs (apparently) as the temperature drops. There is an unmistakable trend.
The obvious question is, over the period covered by the data, have teams that come from colder climates tended to be the better running teams? That would explain the increase in YPC for home teams in cold weather.
If that’s the case, and outdoor teams from up north have been the better running teams, then we’d see those same teams have higher than expected YPC on the road and in more moderate temperatures. But that’s not the case. The ‘cold’ weather teams get almost exactly the same YPC as the other climate types do when on the road in warmer temperatures. Cold, dome, moderate, and warm climate teams average 3.97, 3.99, 3.99, and 3.89 YPC (respectively) on the road when the weather is above 50 degrees. Below you can see that cold climate teams do not appear to be stronger running teams than the other types, at least at moderate temperatures.
Only the warm climate teams (of which there are the fewest) show any detectable deviation from the typical 4 YPC that road teams get. That's worth investigating further because it might explain the difference. Warm weather teams don't have cold home games, and if they've happened to be poor running teams, that would explain the increase in home YPC as the weather gets colder. I've replotted the graph above, but this time with the warm climate teams removed.
The same effect remains. (Note that if I remove the cold teams from the chart, there aren't enough cold games in the sample.) So cold climate teams aren’t likely to be better the running teams than the others, which leaves us wondering why home teams run better in the cold while visiting teams remain flat. The prime suspect should be our good friend the dome team. This phenomenon may help explain why dome teams win so few games in the cold.
Instead, it appears that all climate types are affected by the cold when on the road. The data are noisy, but there appears to be a universal trend that they each allow more yards by a home team when the weather is cold. The dome teams are worst overall among the four climate types, but there is a similar trend for all types of road teams, even other cold climate teams.
I'd still suspect that somehow, someway, northern outdoor teams might just be better running teams, despite not showing any better stats when on the road. It would be the simplest explanation. Playoffs would be the other obvious factor. But removing those games from the sample doesn't change the chart one bit. I'm stumped at this point. Could it be snowy conditions? I don't have precipitation coded out in the data yet, but there are so few snowy games the effect would have to be extremely large to make a difference. Plus, it wouldn't explain the overall trend of increasing YPC for home teams in temperatures above which snow is around.
Once all the other factors are eliminated, we might be left with the theory that there is some interaction effect between cold weather and home field advantage in the running game. It would be quite a strong effect, changing a home team's YPC from 4.05 in the 70's and 80's to over 4.30 when the temperature is below freezing. That would be like taking the 23rd best running team in the league and making them the 15th best this season.