# For an NFL quarterback, how good is good enough?

Yesterday we explored an intriguing question: “When it comes to NFL quarterbacks, what does ‘good enough to win’ actually mean?”

Looking at several hundred games over the past five seasons, we came to the conclusion that if an NFL quarterback posts a Complete Quarterback Rating (CQBR) of roughly 61.9 — slightly above average by league standards — then he has done his part to win. After that, it’s up to the defense, special teams, and perhaps the run game to hold up their end of the bargain.

We also showed that there is a remarkable correlation between a quarterback’s CQBR in an individual game and his team’s probability of securing the victory. This raised an interesting question: Given that NFL , how well does CQBR hold up against its more famous cousin?

## Tightly knit metrics

We started with the assumption that both metrics would show a similar pattern, since CQBR and NFL passer rating are pretty tightly bound, as we can see in the graph below:

It makes sense that there is so much congruence between passer rating and CQBR, since they are measuring very similar things. The biggest deviations, not surprisingly, occur at either end of the scale, where passer rating is bounded.

CQBR measures several dimensions of quarterback performance — including rushing and ball security — while passer rating only measures passing performance, yet the rating systems closely mirror each other. This shows that passing efficiency is by far the most important factor determining a quarterback’s success, which makes complete sense in a pass-oriented league like the NFL.

Although scrambling quarterbacks are sometimes pejoratively referred to as “run-first quarterbacks,” there isn’t a starting quarterback in the NFL who rushes nearly as often as he passes, and there probably hasn’t been one in several decades at least. Indeed, since 2002, the only starting quarterbacks to have posted pass/rush attempts ratios of less than 3.0 are Michael Vick in 2004 (2.7 P:R ratio in 15 starts, CQBR of 46.76) and Tim Tebow in 2011 (2.2 P:R ratio in 11 starts, CQBR of 41.80).

As important as quarterback performance is to a team’s chances of winning, then, it would be no surprise if passer rating shows a very similar trend as CQBR. But is it possible that CQBR might be just a bit more predictive of win probability, especially considering how strong of an impact turnovers can have on a team’s prospects?

## Passer rating and win probability

In order to give passer rating a fair shake, we looked at the same set of games we used for our CQBR study. Following is a histogram showing the outcomes of games based on passer rating:

Two things immediately stand out from this graph.

The first is that the relationship between passer rating and win probability is sharply defined indeed. When quarterbacks post low ratings, win probability is low, yet somewhere around a rating of 60.0 (significantly below average by today’s standards), a team’s chances of winning jump markedly.

The second is that this histogram is not quite as “neat” or “pretty” as the corresponding graph for CQBR. For example, there is that puzzling band of lower win probability in the 80.0 to 99.9 range. Given that the average passer rating over the past five years has been approximately 86, this drop in win probability is probably an artifact of the sheer number of games played in which quarterbacks produced roughly average passer ratings. There were simply more opportunities for other factors, including defensive meltdowns, special teams miscues, and bizarre flukes to impact the outcome, especially in games in which the quarterbacks are of roughly the same caliber.

In any case, it’s apparent that if a quarterback can put up an excellent game with a passer rating of over 100.0, his team is almost guaranteed to win. In reality, though, he just has to do a decent job passing (rating of somewhere around 70.0) to put his team on the path to success.

## Just enough to win

As we did with CQBR, we now plot midpoints of the passer rating bins against win probability to produce this curve:

Yet again the positive relationship between passer rating and win probability is unmistakeable. We also note that the correlation coefficient of this trend line (R² = 0.80) confirms our intuitive assessment that the relationship is not quite as tidy as it is with CQBR (R² = 0.98). Nonetheless, passer rating is still an excellent tool for judging a team’s chances of winning a game.

From the equation of the trend line, we can calculate that an NFL quarterback must produce a **passer rating of 71.6** in order to give his team a 51 percent chance of winning — surprisingly low, considering the average passer rating for the games in our sample was 86.4. This illustrates the greatest weakness of passer rating as a metric of quarterbacks: it ignores several dimensions of performance crucial to overall quarterback success.

## Final word

As a final flourish, we calculated the z-scores of the quarterbacks’ passer ratings and CQBRs for all games and plotted them against win probability. The *z-score*, as you may remember, is a statistical tool that enables us to standardize metrics that are measured on different scales (as passer rating and CQBR are) by normalizing them against the mean. Basically, it is a measure of how far above or below average a particular performance is.

Due to the nature of the z-score, the plot for both passer rating and CQBR looked identical, so we consolidate them here:

Of course, we are unable to resist the temptation of plotting the line and performing the linear regression:

Lines rarely come tidier than that! More or less, if a quarterback puts up an average performance, his team’s chances of winning the game will be slightly better than 50/50. If his performance is at least in the 86th percentile (z-score greater than 1.5), his team will win pretty much every time. If his performance is below the 13th percentile (z-score less than -1.5), the team has almost no chance of winning.

## Takeaway message

So what have we learned from all this?

Basically, it isn’t all that hard for a quarterback to put his team in a position to win. He just has to be average. If he has a below-average day, he puts his team at peril of losing. By the same token, every little bit he can do to exceed the league average is helpful to ensuring his team’s success.

In the end, though, it’s up to the rest of the team to do their jobs if they hope to notch the win.

## About the author(s)

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

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ASK AND YE SHALL RECEIVE TURD WARTS

Hey motherfuckers,

You gotta start waking up earlier and getting a morning article out so these newcomers can feel more at home.

Project for you LKP:

Determine Stafford's completion percentage when throwing over the top, at 3/4, and below 3/4. I would really like to know if it's legitimate to criticize his sidearm or if it's just so much honking on my part.

Our data on distance of pass attempts goes back to 2005. Since then, there have been 29 quarterbacks with 50 or more deep pass attempts and a seasonal DVOA below 15% on deep passes. It's a pretty harrowing list to look at if you have an optimist's view of Ponder's future.

Cubs blow a two run lead by giving up a 3-run homer with two outs in the bottom of the 8th. Typical.

I wish there was a way to force avatars on new comers for a probation period.

I know only one of his 17 picks was side arm. And he is pretty good at the side arm thing just based on perception. He threw sidearm due to interior pressure (cough Stephen Peterman sucked cough) but I could do some film study how many incompletions it caused.

I would love to see the results of a study like this. It would take a hell of a lot of film study though.

He's doing it for a reason. Based on his performance last season it's not for improved accuracy.

And T-Jack pulled off a very impressive -184 DYAR, which would be the ugliest stat I have ever seen, except JaMarcus got -189.

don't give me that look mister, or i'll stick you in the cellar with the NFCS miscreants

He should do something about the company he keeps. Jamarcus Russell Joey Harrington and Blaine Gabbert, who he barely squeaked by to avoid worst YPA in the NFL in 2012.

When someone is right in your face, you throw around them. Interior pressure is the worst kind of pressure

THe odd thing is, his deep ball doesn't seem like it should be so bad. Whenever I watch he hits a few deep shots. I think this has to do with the classification (16 or more yards downfield). Because he surely sucks shit in the mid-range. But the he throws the classic bomb alright.