Dome at Cold Revisited

There were 4 dome teams playing in wintery weather today, and all four lost. DET lost at PHI, MIN lost at BAL, IND lost at CIN, and ATL lost at GB.

A few years ago I looked at how dome teams tend to struggle in cold weather. I wanted to know if dome team underperformance in the cold was indeed true and if so how big was the effect. The answers were: Yes and huge. Last season I redid things using actual game temperatures and found just as big an effect.

With the weather as it is on the east coast today, I looked at this phenomenon once again. We have two more years worth of data thanks to the addition of 1999. Plus, I was able to reconstruct nearly another half season worth of data by replacing missing game temperatures from the gamebooks. I also broke out teams that played in retractable-roof stadiums by season.

Here are the results if we count retractable teams as dome teams. There's a case to be made that retractable home environments are closer to dome environments than open air stadiums. The chart below plots road team winning percentage according to game temperature.

Was Belichick Right to Take the Wind in OT?

I was surprised when Bill Belichick chose to take the second possession (and risk no possessions) in OT against Peyton Manning and a team that had scored 31 points in four quarters. Although the new OT format mitigates the advantage of the team with first possession, it's still there to the tune of about 56% to 44%.

The advantage of wind must have felt fairly strong to Belichick. His team captains thought he was crazy. At the time, it was impossible to tell from the comfort of my sofa how bad the wind was, but I was curious if we could see the effect statistically.

Fumble Rate by Temperature

The title says it all. With Sunday's night's fumble fest in the books, I thought I'd take a quick and dirty look at how cold temperature affects fumbling. It was 19 degrees in Foxboro when I checked the weather there in the 4th quarter.

I looked at all plays from 2000 through the 2012 regular season, excluding kneel downs and spikes. I counted all fumbles, not just fumbles lost. Keep in mind the sample sizes greatly diminish at the temperature extremes.

Here is the breakdown:

Running in the Cold

A few posts ago, we looked at how temperature affected the passing game. This time, we’ll look at the running game. Often, analysts will discuss how winds and cold might affect passes, but unless the conditions are exceptionally snowy or muddy, rarely does anyone consider how cold weather affects running. And why would they? I’d agree there isn’t much reason to suspect that cold temperature alone would cause runs to be any longer or shorter than in moderate weather.

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.

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.

Weather Effects on Passing

My last post looked at the effect of temperature on home field advantage. We saw that cold weather put dome and warm climate teams at a disadvantage. The post was titled How Does Temperature Affect Road Teams?, but I really didn't answer that question. I measured the size of the effect, but I didn't solve the riddle of actually how temperature makes a difference. This post will begin to look at just how weather makes a difference, starting with the passing game.

Here's how passing fares for home and visiting teams by temperature. The chart below shows  Adjusted net Yards Per Attempt (AYPA), which accounts for sacks and interceptions, according to temperature. Keep in mind there are smaller sample sizes at the extremes.

How Does Temperature Affect Road Teams? (And Dome Teams in Particular?)

A few years ago I looked at how well teams from various climates types played when visiting other climate types. The most remarkable result was that dome teams win only about 20% of the time when playing in the cold. But that study was limited in several ways. Instead of actual temperature data, I used December in a cold-weather city as a proxy for cold temperature. I also was limited to regular season games from 2002 through 2006.

With new and better data, I redid the study. This time I have actual temperatures and used all non-preseason games from 2000 through the wildcard round of the 2011 season (last Sunday). Here are the results. The graph below depicts the winning percentage of the road team by temperature at kickoff. Road teams are classified according to their home climate--dome, cold, moderate, or warm.

Cold Weather Effect on Scoring

In a recent post I theorized that the sudden importance of run defense in the playoffs might be due to cold weather. This post will continue that line of analysis and look at the effect of cold weather on scoring.

The past weekend's conference championship games were played in frigid weather. It seemed that expert after expert remarked that cold weather would keep the scoring down. Certainly it makes sense to anyone who's played sports in extremely cold weather. It definitely makes it harder to throw, catch, and even kick. But it's just as cold for defenses as for offenses. So does cold weather really keep NFL scores lower?

Here are the average home and visitor scores for various circumstances. The first column is for all regular season games in the 2002-2006 seasons (n=1280), and the second column is for those games played in cold climates (n=114), as defined here. Since many playoff games are played in cold weather, the third column is for all playoff games (n=50+5). (Super Bowl scores are not included because there is no home advantage.)

	Reg. Season	Cold	Playoff
Home	22.3	22.5	25.0
Visitor	19.8	18.6	19.9

The second table looks at scores from the same sets of games differently. The average scores of the winning and losing teams are listed. (Super Bowl scores are included as playoff games here.)

	Reg. Season	Cold	Playoff
Winner	26.8	27.0	28.9
Loser	15.3	14.1	16.5

Cold weather doesn't appear to have a large effect on scoring. It seems to slightly enhance the spread between winner and loser by depressing the score of the loser. This is likely due to the "dome at cold" effect discussed in previous posts.

Playoff scores are generally higher, both in terms of winner and loser, and for the home and visiting teams.

It doesn't appear that cold weather reduces scoring.

I can understand where the perception might come from. Because dome teams are at a disadvantage playing outdoors in cold weather, it follows that they would score less. Many competitive dome teams in recent years have been ones with fast-scoring offenses. The Vikings, Rams, and Colts of recent memories all featured very strong offenses. When these teams were competitive late in the season (and when people were paying attention to them), they would be expected to score less when playing outdoors. But this effect on dome teams would be limited to these specific circumstances and not affect teams in general.

When the Giants played in Green Bay or the Chargers played in Foxboro yesterday, we should not have expected low scores due to the cold temps. Although the frigid sub-zero temperatures yesterday were extreme, even for Green Bay standards, the point is that the weather affects both offense and defense.

Does Cold Weather Change the Game?

Recently I looked at the importance of various phases of the game in winning playoff games. I analyzed and compared regular season games featuring only playoff-caliber opponents and playoff games themselves. This analysis began with the question of whether defense really does win championships, but since has focused on broader comparisons as well.

In the last post, I found that over the past five seasons teams with the better run defense won slightly less than half of games between playoff-caliber opponents. But in the playoffs, the team with the better run defense won 67% of the time. With 114 regular season match-ups between playoff-caliber teams and 55 playoff games during the period studied, the difference may only be due to chance. However, in the comparison of regular season games and playoff games, pass offense, pass defense, and run defense did not show any differences nearly as large as run defense.

[Edit: Based on a 2-sample unpaired t-test, the difference in winning percentage of the better defense (67% vs 48%) is indeed statistically significant at the p=0.02 level. In other words, the sample sizes are large enough to say it is extremely unlikely the difference is by chance.]

Here is the table from the previous post. The winning percentage of the team with the superior stat is indicated. For example, the team with the better offensive passing efficiency won 52.6% of the regular season "good vs. good" match-ups and won 63.6% of playoff games.

Stat	Good vs Good	Playoffs
Home	59.6	64.0
O Run	45.6	45.5
D Run	48.2	67.3
O Pass	52.6	63.6
D Pass	51.8	56.3
O Int Rate	50.9	58.1
D Int Rate	55.3	58.1
O Fum Rate	55.3	40.0
D FFum Rate	54.4	54.5
Pen Rate	47.3	52.7

One possible explanation for the difference in the importance of run defense could be the weather. The playoffs are played in January when the weather is cold and often windy in most NFL cities. Teams might bias their play selection toward the run because of the perceived increase in passing difficulty.

To test if weather is the reason for the observed difference in the importance of run defense in the playoffs, I analyzed regular season games played between any-caliber opponents in cold weather. Without direct temperature and wind data for each game, I defined 'cold weather' as being played outdoors in December in a city that averages below 40 degrees wind chill. There were 118 such games between 2002 and 2006.

(I also looked at just the games between playoff-caliber teams played in the cold. However, there were only 12 such games, so the results are not very meaningful. I also expanded the definition of playoff-caliber to 9+ win teams, for which there were 26 games. I'll list both results anyway in case anyone is curious.)

Below is the table of results. Again, the percentage of games won by the team with the superior stat in each category is listed. The first column (Reg. Season) is for all regular season games and all opponent types (n=1280). The second column (In Cold) is for all games played in cold climates (n=118). The third column (9+ Wins) is for games played in cold climates between teams that ultimately finished with 9 or more wins (n=26). The last column (10+ Wins) is for games played in cold climates between teams that finished with at least 10 wins (n=12).

Stat	Reg. Season	In Cold	9+ Wins	10+ Wins
Home	57.4	66.0	71.8	91.0
O Run	55.0	55.4	45.8	50.0
D Run	50.0	48.8	58.3	50.0
O Pass	63.8	65.6	66.7	66.7
D Pass	59.8	60.4	45.8	58.3
O Int Rate	59.5	61.0	54.2	33.3
D Int Rate	59.4	59.4	33.3	33.3
O Fum Rate	60.8	65.0	54.2	33.3
D FFum Rate	58.0	61.3	54.2	50.0
Pen Rate	54.1	55.2	50.0	33.3

I'll address the results from the first and second columns. The importance of each stat appears about the same in cold weather as in all games. Other than home field advantage, fumble rates are the only stats that indicate any significant difference in cold weather.

Focusing on run defense, we see that the team with the superior run stopping ability only won 48.8% of the 118 games played in cold weather. This rate is very close to the overall rate of 50.0% for all regular season games. This suggests that it is not the weather but some other factor in the playoffs that may enhance the importance of run defense.

The increased importance of home field advantage in cold weather is probably due to the 'dome at cold' effect, in which dome teams tend to have very little success playing outdoors in cold weather.

Although nothing was conclusively proven with this analysis, there are indications that playoff football is different than regular season football. Although the sample sizes weren't large enough to make solid conclusions regarding most variables, there is enough evidence to suggest that the playoffs comprise a special set of circumstances that may change the dynamics of the game. The level of competition, the weather, the prospect of elimination, or other factors may influence strategies and performances.

At the very least, we can see how fans may perceive defense as being more important in the playoffs. Whether there is truly a systematic link between run defense and playoff success, or it is only the randomness of a small sample, may not be relevant. We have witnessed teams with stronger run defenses win more playoff games. It is apparently, if not in reality, the most important part of the game come January.

'Dome at Cold'

This week features two of the three "dome team at cold weather" games of the 2007 season. Earlier, CIN defeated STL in week 14. Today CHI hosts NO and GB hosts DET.

Dome teams are at a severe disadvantage when playing in cold weather. Over the past five regular seasons, they've won only about 14% of the time in those situations. Accounting for relative team strength, they would be expected to win only 12% of the time.

GB is already a heavy favorite over DET, and the weather factor would only enhance GB's expected chance of winning. But the game prediction model features closer odds for the NO at CHI game. NO is favored with a 0.57 probability of winning.

However, when the weather is factored in CHI is going to be favored. Replacing the standard home field advantage coefficient with the "dome at cold" coefficient we get a 0.62 win probability for CHI.

With the weather factor, GB becomes a heavier favorite at 0.92.

Some people are already looking ahead to the likely AFC championship match-up between IND and NE. Although IND played NE very well, and nearly won the game earlier in the year without five starters, their next game will be very different. It will be in Foxboro, Mass. in late January. It was no fluke that the one year IND was able to get past NE to get to the Super Bowl was the year they hosted the game.

NFL Home Field Advantage by Climate 2

In a previous post, I looked at how home field advantage is affected by weather. Each NFL city was categorized by its December climate--dome, warm, moderate, and cold. By comparing the winning percentage of home teams in games in the early season (weeks 1-12) and the late season (13-17) the effect of cold weather was estimated.

In this post, the effect of cold weather on home field advantage will be measured more precisely. By using logistic regression, relative team strength is accounted for. In addition, the statistical significance of the observed weather effect indicates if the effect is real and systematic, or just a result of luck and small sample size.

The last post left off with this table. The left most column describes the visiting team's climate, and the top row describes the home team's climate. For each combination of visiting and home climate, the change in home team winning percentage from early to late in the season is listed. Positive numbers indicate that cold weather may favor the home team. For example, when dome teams play at warm cities, the home team winning percentage was 20% higher late in the season than early in the season. But when dome teams play at moderate cities, the home team winning percentage appeared to be 9% lower late in the season.

Difference	Dome	Warm	Mod	Cold
Dome	0%	+20	-9	+35
Warm	-5	+14	-7	-3
Mod	-8	-24	-6	-13
Cold	-8	+2	-15	+8

Several match-ups indicate that the cold and wind of late-season outdoor football has an effect on HFA. Consistent with other research, it appears that dome teams suffer when playing in cold climates.

Another remarkable combination is moderate weather teams playing in warm cities (-24%). But it's not clear why moderate teams would have an easier time playing in the balmy breezes of Florida or San Diego in December. Other notable match-ups are dome teams playing at warm cities (+20%), and cold teams playing at moderate cities (-15%).

To determine if the observed differences in HFA between early and late season games is really due to the change of weather, and not due to relative team strength or luck, several logistic regression models were run. The models were based on every regular season game from the 2002 through 2006 seasons (n=1280). For each game, each team was designated either Team A or Team B. The general model specification was the following:

Dependent variable:
Team A won

Independent variables:
Team A season efficiency stats
Team B season efficiency stats
AHome
[Weather dummy variable]

The team efficiency stats include offensive and defensive passing and running efficiency, turnover rates, and penalty rates. AHome is a dummy variable that is 0 when Team A is away and 1 when Team A is home. The [Weather dummy variable] is 1 when the particular climate match-up of interest is present for the game, and 0 when otherwise.

A general HFA variable (AHome) was included to isolate the effect of weather from the general home field advantage due to travel, psychology, officiating, or other effects.

Several models were run for each climate match-up of interest. The table below lists the statistical significance of the 'weather variable' and the resulting home field advantage calculated from the regression results. Note that the overall HFA rate is 57.5%.

Visitor	Home	p-value	HFA (%)
Dome	Cold	0.03*	88
Dome	Warm	0.28	75
Warm	Warm	0.58	71
Warm	Cold	0.74	76
Mod	Warm	0.11	40
Mod	Cold	0.95	62
Cold	Mod	0.13	49

Accounting for relative team strength, the only truly significant result is for dome teams in cold weather (p=0.03), with an expected home team winning percentage of 88%. This result is confirmed by the actual 86% home team winning percentage when dome teams play at cold cities late in the year. The regression's estimate of 88% suggests that the cold city home teams may have been slightly weaker compared to their dome opponents over the past 5 years.

Two other types of match-ups might be considered marginally significant--moderate teams at warm cities (p=0.11), and cold teams at moderate cities (p=0.13). Both results indicate a reduced HFA later in the season for those match-up types. But since there were 16 combinations of climate match-ups, chances were that we could see one or two type-I errors, i.e. see significance when none is truly there. Because there is no a priori theoretical reason why to expect those results, we shouldn't deem them significant.

Finally, one last model specification was run to make sure no other climate match-up types were significant. The final model included all late-season match-ups types together. No additional types were significant.

It's clear that the situation of a dome team playing playing in a cold city late in the season creates a much stronger HFA than normal. But a larger data set is needed to conclusively analyze other weather match-ups. Dividing 1280 games into 16 types of match-ups and 2 weather periods creates small sub-samples.

A prediction model's accuracy may benefit from enhancing the weight of HFA in certain situations. Looking ahead, there are only three 'dome at cold' match-ups in 2007. STL travels to CIN in week 14, and NO visits CHI and DET visits GB in week 17.

NFL Home Field Advantage by Climate

In this post I'll begin an analysis of home field advantage in the NFL and its relationship to climate. Others have examined the connection between weather and HFA previously, but here I'll attempt to present the data with a clear and novel approach. This post represents the 'clear' part. In following posts, the novel part will use logistic regression to account for team strength and determine the significance of each particular type of climate match-up.

I began by dividing each home city into four categories: dome, cold, moderate, and warm based on a combination of each city's average December high temperature and wind speed. The dome cities include STL, NO, MIN, DET, IND, and ATL. The cold cities are GB, BUF, CLE, CHI, KC, DEN, NYG, NYJ, NE, PHI, PIT, and CIN. Moderate cities include BAL, WAS, CAR, SEA, OAK, SF, TEN, and DAL. The warm cities are MIA, TB, JAX, HOU, SD, and ARI.

Based on all NFL regular season games from the 2002 through 2006 seasons, the winning percentage of the home team was calculated for each type of climate match-up. I divided the season into "early" and "late." The early season is defined as weeks 1 through 12 and the late season is defined as weeks 13 through 17. For example, the winning percentage of the home team in match-ups of cold teams at moderate cities in the early season is 57%, with n=77 examples of such cases.

The home winning percentage of all types of weather match-ups are presented below in a series of pairs of tables. Each table is presented the same way, with the visiting team climate on the left and the home climate on the top. The first table in each pair is for the early season (pre-December), and the second table is for the late season (December games).

Sample size is usually an issue when populations are divided up among several classes. For that reason, the first pair of tables lists the number of cases of each type. For example, the top right cell of the first table lists the number of games featuring dome teams playing at cold cities in the early season. The same cell in the second table lists the same type of match-up in the late season.

Wk 1-12	Dome	Warm	Mod	Cold
Dome	31	29	44	62
Warm	34	20	50	62
Mod	40	49	51	78
Cold	59	66	77	128

Wk 13-17	Dome	Warm	Mod	Cold
Dome	15	17	21	21
Warm	16	11	17	30
Mod	25	20	17	40
Cold	20	28	43	59

The second pair of tables simply lists the straight-up winning percentage of the home team in each type of match-up. For example, the bottom left cell of the first table lists the home team winning percentage when cold teams play at domes in the early season. The same cell in the second table lists home winning percentage of cold teams at domes in the late season.

Wk 1-12	Dome	Warm	Mod	Cold
Dome	61%	45	61	51
Warm	68	50	66	66
Mod	60	59	59	76
Cold	53	52	57	50

Wk 13-17	Dome	Warm	Mod	Cold
Dome	61%	65	52	86
Warm	63	64	59	63
Mod	52	35	53	63
Cold	45	54	42	58

What immediately stands out is the very high winning percentage of cold teams hosting dome teams late in the season. The most remarkable result, however, may be the 35% home winning percentage of warm teams hosting moderate teams. Note that there are only about 20 cases of each type of match-up in the past 5 years, so these results could be due to luck or due to general team strengths of the according type of teams. Perhaps a couple moderate teams have been relatively dominant over warm weather division rivals between '02 and '06.

The final table lists the difference in home winning percentage between late season and early season match-ups. Simply put, it is late season winning percentage minus early season winning percentage. A high positive number indicates cold weather may give an advantage to the home team. A negative number or near-zero number suggests otherwise. We'd expect to see a zero for dome teams at dome teams, because outdoor weather is obviously not a factor. This method begins to account for relative team strengths over the period studied.

Difference	Dome	Warm	Mod	Cold
Dome	0%	20	-9	35
Warm	-5	14	-7	-3
Mod	-8	-24	-6	-13
Cold	-8	2	-15	8

Take dome teams for example. By reading across, we see that dome teams seem to have no greater HFA in late season than the early season against other dome teams--as we'd expect. We also see that they are at a 20% disadvantage playing at warm cities but, for some reason, have a 9% better advantage playing at moderate cities late rather than early. Lastly, we see that dome teams appear to be at a severe disadvantage playing in cold cities late in the season, apparently giving up 35% advantage to the cold.

As mentioned above, some of the observed differences in HFA due to weather may be due to luck and relative team strengths among the weather-classes. The final table is a simple way of accounting for team strength, but it does not address the possibility that the differences are primarily due to luck. The final part of this article will use logistic regression to more powerfully account for team strength and test for statistical significance.

Weather and Home Field Advantage

Someone recently pointed out a study that indicated home field advantage (HFA) is not the same for every stadium. While that's certainly true, it's very hard to quantify. By definition, the same team is always the home team when measuring a particular location's HFA, so in any given year there would be a lot of team strength captured in a variable accounting for the field's HFA.

The efficiency model I've used includes a factor for HFA, but it is the same regardless of climate. This is the beginning of an effort to quantify the effect of climate on HFA and to see how much of HFA is due to climate differences and how much is due to other factors such as crowd noise, referee psychology, or travel.

The table below lists each home team along with their average December weather. Click on the table headers to sort

Team	Avg Dec T	Avg Dec Wind	Wind Chill
GB	29	10.5	19.7
BUF	36	13.3	27.3
CLE	37	12.1	29.0
CHI	37	11.0	29.5
NE	42	12.2	35.3
KC	42	11.2	35.7
PIT	42	10.4	36.0
NYG	44	10.8	38.3
NYJ	44	10.8	38.3
CIN	44	10.2	38.5
PHI	44	10.1	38.6
DEN	44	8.4	39.3
SEA	46	9.5	41.3
WAS	46	7.8	42.0
BAL	49	9.3	45.0
TEN	49	8.9	45.2
CAR	54	7.4	51.9
SF	56	7.1	54.4
DAL	57	10.8	54.5
OAK	58	7.1	56.8
HOU	65	8.0	65.0
ARI	65	5.1	65.8
JAX	66	7.8	66.3
SD	66	5.6	66.8
TB	72	8.4	73.5
MIA	75	9.2	77.1
ATL	70	0.0	79.2
DET	70	0.0	79.2
IND	70	0.0	79.2
MIN	70	0.0	79.2
NO	70	0.0	79.2
STL	70	0.0	79.2

It's not a surprise that Green Bay is coldest by far, followed by places such as Buffalo, Cleveland, and Chicago. Green Bay would even qualify as a cold climate through November with an average 36 deg wind chill. But I was surprised by how much colder (and windier) a place like Kansas City is than Baltimore or Washington. I'm still considering how to classify each city. Domes are easy, but where is the line drawn between cold and moderate? Should there be cold, moderate, and "warm" classes? For now I'd put the line between cold and moderate at 40 deg wind chill, between DEN and SEA. I'd also define warm weather teams starting at 60 deg between OAK and HOU.

Continue reading this article here.