To win more games, get a better quarterback

By
Updated: March 29, 2013

Complete Quarterback Ratings (CQBR) shows what we’ve suspected all along: no one influences a team’s chances of winning more than the quarterback.

A few days ago we looked at the relationship between Complete Quarterback Rating (CQBR) and a team’s divisional standing. We found that over the past 20 years, teams who put up higher CQBRs tend to place higher in the division. While the findings were certainly interesting, they were still more or less intuitive.

We decided we wanted to do something a little more mathematically rigorous: determine the actual relationship between CQBR and season win/loss percentage.

This problem was complicated by the fact that average CQBR has risen steadily in the past two decades. No doubt you remember this chart, which shows the trend graphically:

Figure 1. Average and highest team Complete Quarterback Rating (CQBR) have risen significantly in the NFC Central (now NFC North) between 1992 and 20012. Year (season) explains about 5% of the variation in season win percentage.

Methods

Our first task was to determine whether we would need to adjust for this seasonal rise in CQBR when looking at the relationship to win/loss record.

A statistical test known as linear regression revealed that indeed there is a significant relationship between year (season) and average CQBR. To be more precise, average CQBR has risen about 0.6 points every year for the past 20 years. At the same time, however, the year only explains about five percent of the variation in average CQBR. Although this might seem like a minuscule amount of correlation, the fact that the trend is still apparent despite all that variation corroborates just how significant the trend is. For the sake of the nerdy among us who are wondering what the equation is, here it is:

Equation 1. Team CQBR has climbed approximately 0.6 points every season for the past 20 years.

Equation 1. Team CQBR has climbed approximately 0.6 points every season for the past 20 years.

We then ran a partial correlation test to determine if the relationship between CQBR and win percentage is still significant when controlling for year, and the answer was yes (P < 0.01, R = 0.60 for you nerds out there). That meant that we could run the analysis by looking only at the correlation between CQBR and season record, which was our goal in the first place.

The final regression analysis revealed that there is a highly significant relationship between CQBR and win percentage and that, in fact, a team’s season CQBR is responsible for 33 percent of variation in their win percentage. Again, for you stats nerds:

Equation 2. For every point CQBR rises, a team can expect win percentage to increase by roughly 0.7 percent.

Equation 2. For every point CQBR rises, a team can expect win percentage to increase by roughly 0.7 percent.

Figure 2. There is a significant positive relationship between team Complete Quarterback Rating (CQBR) and season win percentage (win/loss record). CQBR explains approximately 33% of the variation in team win percentage.

Most important player

Although 33 percent might not seem like much at first glance, it’s actually pretty impressive when you think about it. A quarterback represents only 9.1 percent of the offensive players on the field at any one time (and only 4.54 percent of the starters a team fields), yet he is responsible for one-third of the variation in his team’s winning percentage. In other words, the quarterback’s statistical performance has a vastly disproportionately impact on the team’s final record.

While this finding is certainly remarkable, it probably doesn’t come as a great surprise to football fans. After all, it passes the “eye test”: other than the center, the quarterback is the one player on the field who touches the ball on every play and has the chance to influence the outcome of every down. Of course, more goes into a quarterback’s CQBR than his own performance; it’s also dependent on how well his offensive line holds up and how skillful or talented his receivers are. Nevertheless, there is a reason why the quarterback is the highest-paid player on the team: no other player has such a profound impact on the team’s success or failure.

In short, all things being equal, the better quarterback a team has, the more games that team is going to win.

Next step

Because football is such a complex sport, no one statistical metric is likely to explain a majority of variation in win percentage over the course of a season. However, within individual games we are likely to see much stronger correlations.

The next step in this project will be to look at individual games and see how often the team with the higher CQBR wins. Even more interesting will be to see how strong the relationship between CQBR differential (difference between a team’s CQBR and its opponent’s CQBR) and win probability is. Since the correlation between NFL passer rating differential and win probability is higher than it is between passer rating and win probability, it would stand to reason that we will find a similar relationship with CQBR too.

More statistical deliciousness will be coming your way next week.

About the author

Rourke Douglas Decker covers the Green Bay Packers beat for the Water Cooler Sports Network. He resides with his family in La Crosse, Wisconsin. He can be reached for questions or comments at . Connect with .

1518 comments
niemerg1
niemerg1

ouch

niemerg1
niemerg1

o dear lord...

JVince 11
JVince 11 moderator like.author.displayName 1 Like

 Looks like a chicken wing.... 

Buhlitz
Buhlitz

 fuck I was about to post that

J. Walter Weatherman
J. Walter Weatherman

I need ideas!

Anyone?

I wonder how many women are gonna fall for this: 

Buhlitz
Buhlitz like.author.displayName like.author.displayName 2 Like

chris brown, we need you!

Buhlitz
Buhlitz like.author.displayName 1 Like

You can tell she was trying to provoke him into attacking her so she could file some kind of lawsuit. What a fucking bitch.

Mad respect to him for keeping his cool though, if I were in his position i'd have benched her dumb ass back into her father's nutsack

Joedirte
Joedirte

 Yea but you don't have to hit women but no one ever said a good rear naked choke wouldn't work

J. Walter Weatherman
J. Walter Weatherman

  He didn't hit her, she was all over him, and he tackled her to the ground.  Bitch got what she deserved!

Joedirte
Joedirte like.author.displayName 1 Like

 Chris Brown we need you......TO GO AWAY

Preparation_A
Preparation_A like.author.displayName like.author.displayName 2 Like

  

What did he do to bring down that kind of hellatious shit storm?

Buhlitz
Buhlitz

  at the end she goes HAM on him

Preparation_A
Preparation_A

   

I am actually a robot. Built by Skynet. They decided they were done making death machines and made like-bots instead.

Buhlitz
Buhlitz

  HOW THE FUCK DO YOU LIKE THIS SHIT SO FAST

Buhlitz
Buhlitz like.author.displayName 1 Like

  hard as a motherfucker

Buhlitz
Buhlitz

Hey prep- how does it feel to have 28k likes given?

Joedirte
Joedirte like.author.displayName 1 Like

 Well he has to balance out Rourke and he 7 likes given

ReggiesNoJackpondavre
ReggiesNoJackpondavre moderator

  

One of which i have received lol

Joedirte
Joedirte

   Well that like a and a dollar will get you a cup of coffee

ReggiesNoJackpondavre
ReggiesNoJackpondavre moderator

   

It was on my article about my Great Grandfather and he said something about a part he edited in that he was proud about and i said something like "i saw that. well done."


Then the like was bestowed upon my collection.

Joedirte
Joedirte

    What was the comment

Preparation_A
Preparation_A

But I am also closing in on 15k gotten, so eventually they'll balance out.

Um...
Um... moderator like.author.displayName 1 Like

 I just came back to call prep a slut. Bye now.

Um...
Um... moderator

I'm done. Goodnight, twatlets.

Preparation_A
Preparation_A like.author.displayName like.author.displayName 2 Like

  

Later penile cyst.

Buhlitz
Buhlitz like.author.displayName like.author.displayName 2 Like

  rofl. I'm going to have to use that one irl

EvilDonkey
EvilDonkey moderator like.author.displayName 1 Like

   It killed Capone, that's kinda funny.

Preparation_A
Preparation_A like.author.displayName like.author.displayName 2 Like

    

There's nothing funny about syphilis.

Joedirte
Joedirte

Tim Tebow named 1st string QB of the Jets......APRIL FOOLS!!!!!

Preparation_A
Preparation_A

  

No one believed that.

Joedirte
Joedirte

   Well I believe Children are our futureeeeee teach em..........SEXUAL CHOCLATE

Joedirte
Joedirte like.author.displayName 1 Like

   coming to America reference

ReggiesNoJackpondavre
ReggiesNoJackpondavre moderator like.author.displayName 1 Like

Having just got over a knee injury that was caused by eerily the same type of jump and landing...that was freaky.